<!DOCTYPE html><html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>[2402.11078] Model Editing by Pure Fine-Tuning</title><meta property="og:description" content="Fine-tuning is dismissed as not effective for model editing
due to its poor performance compared to more specialized methods.
However, fine-tuning is simple, agnostic to the architectural details of the model being edi…">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="twitter:card" content="summary">
<meta name="twitter:title" content="Model Editing by Pure Fine-Tuning">
<meta name="twitter:image:src" content="https://ar5iv.labs.arxiv.org/assets/ar5iv_card.png">
<meta name="twitter:image:alt" content="ar5iv logo">
<meta property="og:title" content="Model Editing by Pure Fine-Tuning">
<meta property="og:site_name" content="ar5iv">
<meta property="og:image" content="https://ar5iv.labs.arxiv.org/assets/ar5iv_card.png">
<meta property="og:type" content="article">
<meta property="og:url" content="https://ar5iv.labs.arxiv.org/html/2402.11078">

<!--Generated on Tue Mar  5 16:50:50 2024 by LaTeXML (version 0.8.8) http://dlmf.nist.gov/LaTeXML/.-->
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">

<script>
  function detectColorScheme(){
    var theme="light";
    var current_theme = localStorage.getItem("ar5iv_theme");
    if(current_theme){
      if(current_theme == "dark"){
        theme = "dark";
      } }
    else if(!window.matchMedia) { return false; }
    else if(window.matchMedia("(prefers-color-scheme: dark)").matches) {
      theme = "dark"; }
    if (theme=="dark") {
      document.documentElement.setAttribute("data-theme", "dark");
    } else {
      document.documentElement.setAttribute("data-theme", "light"); } }

  detectColorScheme();

  function toggleColorScheme(){
    var current_theme = localStorage.getItem("ar5iv_theme");
    if (current_theme) {
      if (current_theme == "light") {
        localStorage.setItem("ar5iv_theme", "dark"); }
      else {
        localStorage.setItem("ar5iv_theme", "light"); } }
    else {
        localStorage.setItem("ar5iv_theme", "dark"); }
    detectColorScheme(); }
</script>
<link media="all" rel="stylesheet" href="/assets/ar5iv-fonts.0.7.9.min.css"><link media="all" rel="stylesheet" href="/assets/ar5iv.0.7.9.min.css"><link media="all" rel="stylesheet" href="/assets/ar5iv-site.0.2.2.css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<article class="ltx_document">
<h1 class="ltx_title ltx_title_document">Model Editing by Pure Fine-Tuning</h1>
<div class="ltx_authors">
<span class="ltx_creator ltx_role_author">
<span class="ltx_personname">Govind Gangadhar
</span></span>
<span class="ltx_author_before">  </span><span class="ltx_creator ltx_role_author">
<span class="ltx_personname">Karl Stratos 
<br class="ltx_break">Department of Computer Science 
<br class="ltx_break">Rutgers University 
<br class="ltx_break"><span id="id1.1.id1" class="ltx_text ltx_font_typewriter">{govind.gangadhar, karl.stratos}@rutgers.edu</span>
</span></span>
</div>

<div class="ltx_abstract">
<h6 class="ltx_title ltx_title_abstract">Abstract</h6>
<p id="id2.id1" class="ltx_p">Fine-tuning is dismissed as not effective for model editing
due to its poor performance compared to more specialized methods.
However, fine-tuning is simple, agnostic to the architectural details of the model being edited,
and able to leverage ongoing advances in standard training methods (e.g., PEFT),
making it an appealing choice for a model editor.
In this work, we show that pure fine-tuning can be a viable approach to model editing.
We propose a slight modification of naive fine-tuning with two key ingredients.
First, we optimize the conditional likelihood rather than the full likelihood.
Second, we augment the data with random paraphrases and facts to encourage generalization and locality.
Our experiments on ZsRE and <span id="id2.id1.1" class="ltx_text ltx_font_smallcaps">CounterFact</span> show that this simple modification
allows fine-tuning to often match or outperform specialized editors in the edit score.</p>
</div>
<div id="p1" class="ltx_para ltx_noindent">
<div id="p1.1" class="ltx_block ltx_align_bottom">
<p id="p1.1.1" class="ltx_p"><span id="p1.1.1.1" class="ltx_text ltx_font_bold">Model Editing by Pure Fine-Tuning</span></p>
<br class="ltx_break ltx_centering">
<p id="p1.1.2" class="ltx_p ltx_align_center" style="width:433.6pt;"><span id="p1.1.2.1" class="ltx_text ltx_inline-block" style="width:0.0pt;">
<span id="p1.1.2.1.1" class="ltx_tabular ltx_guessed_headers ltx_align_top">
<span class="ltx_thead">
<span id="p1.1.2.1.1.1.1" class="ltx_tr">
<span id="p1.1.2.1.1.1.1.1" class="ltx_td ltx_align_center ltx_th ltx_th_column"><span id="p1.1.2.1.1.1.1.1.1" class="ltx_text ltx_font_bold">Govind Gangadhar  </span>and<span id="p1.1.2.1.1.1.1.1.2" class="ltx_text ltx_font_bold"> Karl Stratos</span></span></span>
</span>
<span class="ltx_tbody">
<span id="p1.1.2.1.1.2.1" class="ltx_tr">
<span id="p1.1.2.1.1.2.1.1" class="ltx_td ltx_align_center">Department of Computer Science</span></span>
<span id="p1.1.2.1.1.3.2" class="ltx_tr">
<span id="p1.1.2.1.1.3.2.1" class="ltx_td ltx_align_center">Rutgers University</span></span>
<span id="p1.1.2.1.1.4.3" class="ltx_tr">
<span id="p1.1.2.1.1.4.3.1" class="ltx_td ltx_align_center"><span id="p1.1.2.1.1.4.3.1.1" class="ltx_text ltx_font_typewriter">{govind.gangadhar, karl.stratos}@rutgers.edu</span></span></span>
</span>
</span></span></p>
<br class="ltx_break ltx_centering">
</div>
</div>
<section id="S1" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">1 </span>Introduction</h2>

<div id="S1.p1" class="ltx_para">
<p id="S1.p1.1" class="ltx_p">Model editing is a promising approach to combating incorrect or otherwise unwanted knowledge in LLMs.
It assumes a set of edits that assert desired information
and aims to alter the model so that it not only succeeds in memorizing
the edits (efficacy), but also applying the asserted information
to new prompts (generalization), <em id="S1.p1.1.1" class="ltx_emph ltx_font_italic">without</em> affecting
inference that should remain unchanged (locality).
There is clearly a trade-off between these metrics.
At one extreme, the model can achieve high efficacy by
memorizing the edits, but it will fail in generalization and locality.
At another extreme, the model can achieve high locality by
staying unmodified, but it will fail in efficacy and generalization.</p>
</div>
<div id="S1.p2" class="ltx_para">
<p id="S1.p2.1" class="ltx_p">A straightforward approach of fine-tuning the model on the requested edits
is well known to perform poorly, especially in locality.
This motivated researchers to dismiss fine-tuning as an ineffective solution
to model editing and develop very specialized methods
such as MEND <cite class="ltx_cite ltx_citemacro_citep">(Mitchell et al., <a href="#bib.bib8" title="" class="ltx_ref">2022</a>)</cite>, ROME <cite class="ltx_cite ltx_citemacro_citep">(Meng et al., <a href="#bib.bib6" title="" class="ltx_ref">2022</a>)</cite>,
and MEMIT <cite class="ltx_cite ltx_citemacro_citep">(Meng et al., <a href="#bib.bib7" title="" class="ltx_ref">2023</a>)</cite>.
A central theme of these methods is “minimally invasive modification”,
typically involving a careful selection of weights and rank-one updates.
While technically interesting, they require a suite of assumptions
which may not be satisfied in other contexts (e.g., with a different model architecture).
In contrast, fine-tuning is simple, completely agnostic to the details of the model,
and can take advantage of advances in standard training such as
parameter-efficient fine-tuning (PEFT) techniques.</p>
</div>
<figure id="S1.T1" class="ltx_table">
<table id="S1.T1.1" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S1.T1.1.1.1" class="ltx_tr">
<th id="S1.T1.1.1.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_t" style="padding:1pt 3.0pt;">Editor</th>
<th id="S1.T1.1.1.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">
<table id="S1.T1.1.1.1.2.1" class="ltx_tabular ltx_align_middle">
<tr id="S1.T1.1.1.1.2.1.1" class="ltx_tr">
<td id="S1.T1.1.1.1.2.1.1.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">Standard</td>
</tr>
<tr id="S1.T1.1.1.1.2.1.2" class="ltx_tr">
<td id="S1.T1.1.1.1.2.1.2.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">model?</td>
</tr>
</table>
</th>
<th id="S1.T1.1.1.1.3" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">
<table id="S1.T1.1.1.1.3.1" class="ltx_tabular ltx_align_middle">
<tr id="S1.T1.1.1.1.3.1.1" class="ltx_tr">
<td id="S1.T1.1.1.1.3.1.1.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">Batched</td>
</tr>
<tr id="S1.T1.1.1.1.3.1.2" class="ltx_tr">
<td id="S1.T1.1.1.1.3.1.2.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">edits?</td>
</tr>
</table>
</th>
<th id="S1.T1.1.1.1.4" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">
<table id="S1.T1.1.1.1.4.1" class="ltx_tabular ltx_align_middle">
<tr id="S1.T1.1.1.1.4.1.1" class="ltx_tr">
<td id="S1.T1.1.1.1.4.1.1.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">No</td>
</tr>
<tr id="S1.T1.1.1.1.4.1.2" class="ltx_tr">
<td id="S1.T1.1.1.1.4.1.2.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">training?</td>
</tr>
</table>
</th>
<th id="S1.T1.1.1.1.5" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">
<table id="S1.T1.1.1.1.5.1" class="ltx_tabular ltx_align_middle">
<tr id="S1.T1.1.1.1.5.1.1" class="ltx_tr">
<td id="S1.T1.1.1.1.5.1.1.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">Effective</td>
</tr>
<tr id="S1.T1.1.1.1.5.1.2" class="ltx_tr">
<td id="S1.T1.1.1.1.5.1.2.1" class="ltx_td ltx_nopad_r ltx_align_center" style="padding:1pt 3.0pt;">edits?</td>
</tr>
</table>
</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S1.T1.1.2.1" class="ltx_tr">
<th id="S1.T1.1.2.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t" style="padding:1pt 3.0pt;">Naive fine-tuning</th>
<td id="S1.T1.1.2.1.2" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.2.1.2.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.2.1.3" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.2.1.3.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.2.1.4" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.2.1.4.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.2.1.5" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.2.1.5.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
</tr>
<tr id="S1.T1.1.3.2" class="ltx_tr">
<th id="S1.T1.1.3.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding:1pt 3.0pt;">MEND</th>
<td id="S1.T1.1.3.2.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.3.2.2.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.3.2.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.3.2.3.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.3.2.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.3.2.4.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.3.2.5" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.3.2.5.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
</tr>
<tr id="S1.T1.1.4.3" class="ltx_tr">
<th id="S1.T1.1.4.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding:1pt 3.0pt;">ROME</th>
<td id="S1.T1.1.4.3.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.4.3.2.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.4.3.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.4.3.3.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.4.3.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.4.3.4.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.4.3.5" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.4.3.5.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
</tr>
<tr id="S1.T1.1.5.4" class="ltx_tr">
<th id="S1.T1.1.5.4.1" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding:1pt 3.0pt;">MEMIT</th>
<td id="S1.T1.1.5.4.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.5.4.2.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.5.4.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.5.4.3.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.5.4.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.5.4.4.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.5.4.5" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S1.T1.1.5.4.5.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
</tr>
<tr id="S1.T1.1.6.5" class="ltx_tr">
<th id="S1.T1.1.6.5.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">Our fine-tuning</th>
<td id="S1.T1.1.6.5.2" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.6.5.2.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.6.5.3" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.6.5.3.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
<td id="S1.T1.1.6.5.4" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.6.5.4.1" class="ltx_text" style="color:#FF0000;">✗</span></td>
<td id="S1.T1.1.6.5.5" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;"><span id="S1.T1.1.6.5.5.1" class="ltx_text" style="color:#03BF3D;">✓</span></td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">Table 1: </span>Conceptual comparisons of model editors.</figcaption>
</figure>
<div id="S1.p3" class="ltx_para">
<p id="S1.p3.1" class="ltx_p">In this work, we show that fine-tuning can be a viable approach to model editing,
focusing primarily on improving the edit score.
We shift the focus from models and algorithms to
training objectives and data augmentation.
See Table <a href="#S1.T1" title="Table 1 ‣ 1 Introduction ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">1</span></a> for conceptual comparisons between our approach and other editors.
Our method is a slight variation on naive fine-tuning with two small but important differences.
First, in line with the theme of minimal modification, we optimize the <em id="S1.p3.1.1" class="ltx_emph ltx_font_italic">conditional</em>
likelihood (i.e., mask all tokens except the edited target).
Second, we augment the data with self-induced paraphrases of the prompt
and arbitrary unrelated facts to encourage generalization and locality.
This simple change is sufficient for pure fine-tuning to match or outperform
specialized editors in mass-editing
and also perform respectably in single-editing.</p>
</div>
</section>
<section id="S2" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">2 </span>Task</h2>

<div id="S2.p1" class="ltx_para">
<p id="S2.p1.12" class="ltx_p">We consider the task of mass-editing.
Let <math id="S2.p1.1.m1.1" class="ltx_Math" alttext="\mathcal{V}" display="inline"><semantics id="S2.p1.1.m1.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p1.1.m1.1.1" xref="S2.p1.1.m1.1.1.cmml">𝒱</mi><annotation-xml encoding="MathML-Content" id="S2.p1.1.m1.1b"><ci id="S2.p1.1.m1.1.1.cmml" xref="S2.p1.1.m1.1.1">𝒱</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.1.m1.1c">\mathcal{V}</annotation></semantics></math> denote the vocabulary.
A <span id="S2.p1.12.1" class="ltx_text ltx_font_bold">fact</span> is a sentence <math id="S2.p1.2.m2.1" class="ltx_Math" alttext="x\in\mathcal{V}^{T}" display="inline"><semantics id="S2.p1.2.m2.1a"><mrow id="S2.p1.2.m2.1.1" xref="S2.p1.2.m2.1.1.cmml"><mi id="S2.p1.2.m2.1.1.2" xref="S2.p1.2.m2.1.1.2.cmml">x</mi><mo id="S2.p1.2.m2.1.1.1" xref="S2.p1.2.m2.1.1.1.cmml">∈</mo><msup id="S2.p1.2.m2.1.1.3" xref="S2.p1.2.m2.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.p1.2.m2.1.1.3.2" xref="S2.p1.2.m2.1.1.3.2.cmml">𝒱</mi><mi id="S2.p1.2.m2.1.1.3.3" xref="S2.p1.2.m2.1.1.3.3.cmml">T</mi></msup></mrow><annotation-xml encoding="MathML-Content" id="S2.p1.2.m2.1b"><apply id="S2.p1.2.m2.1.1.cmml" xref="S2.p1.2.m2.1.1"><in id="S2.p1.2.m2.1.1.1.cmml" xref="S2.p1.2.m2.1.1.1"></in><ci id="S2.p1.2.m2.1.1.2.cmml" xref="S2.p1.2.m2.1.1.2">𝑥</ci><apply id="S2.p1.2.m2.1.1.3.cmml" xref="S2.p1.2.m2.1.1.3"><csymbol cd="ambiguous" id="S2.p1.2.m2.1.1.3.1.cmml" xref="S2.p1.2.m2.1.1.3">superscript</csymbol><ci id="S2.p1.2.m2.1.1.3.2.cmml" xref="S2.p1.2.m2.1.1.3.2">𝒱</ci><ci id="S2.p1.2.m2.1.1.3.3.cmml" xref="S2.p1.2.m2.1.1.3.3">𝑇</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.2.m2.1c">x\in\mathcal{V}^{T}</annotation></semantics></math> that expresses
a subject-relation-object triple <math id="S2.p1.3.m3.3" class="ltx_Math" alttext="(s,r,o)" display="inline"><semantics id="S2.p1.3.m3.3a"><mrow id="S2.p1.3.m3.3.4.2" xref="S2.p1.3.m3.3.4.1.cmml"><mo stretchy="false" id="S2.p1.3.m3.3.4.2.1" xref="S2.p1.3.m3.3.4.1.cmml">(</mo><mi id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml">s</mi><mo id="S2.p1.3.m3.3.4.2.2" xref="S2.p1.3.m3.3.4.1.cmml">,</mo><mi id="S2.p1.3.m3.2.2" xref="S2.p1.3.m3.2.2.cmml">r</mi><mo id="S2.p1.3.m3.3.4.2.3" xref="S2.p1.3.m3.3.4.1.cmml">,</mo><mi id="S2.p1.3.m3.3.3" xref="S2.p1.3.m3.3.3.cmml">o</mi><mo stretchy="false" id="S2.p1.3.m3.3.4.2.4" xref="S2.p1.3.m3.3.4.1.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.p1.3.m3.3b"><vector id="S2.p1.3.m3.3.4.1.cmml" xref="S2.p1.3.m3.3.4.2"><ci id="S2.p1.3.m3.1.1.cmml" xref="S2.p1.3.m3.1.1">𝑠</ci><ci id="S2.p1.3.m3.2.2.cmml" xref="S2.p1.3.m3.2.2">𝑟</ci><ci id="S2.p1.3.m3.3.3.cmml" xref="S2.p1.3.m3.3.3">𝑜</ci></vector></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.3.m3.3c">(s,r,o)</annotation></semantics></math> in natural language.
We follow the convention in the model editing literature and assume that
the object <math id="S2.p1.4.m4.1" class="ltx_Math" alttext="o\in\mathcal{V}^{m}" display="inline"><semantics id="S2.p1.4.m4.1a"><mrow id="S2.p1.4.m4.1.1" xref="S2.p1.4.m4.1.1.cmml"><mi id="S2.p1.4.m4.1.1.2" xref="S2.p1.4.m4.1.1.2.cmml">o</mi><mo id="S2.p1.4.m4.1.1.1" xref="S2.p1.4.m4.1.1.1.cmml">∈</mo><msup id="S2.p1.4.m4.1.1.3" xref="S2.p1.4.m4.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.p1.4.m4.1.1.3.2" xref="S2.p1.4.m4.1.1.3.2.cmml">𝒱</mi><mi id="S2.p1.4.m4.1.1.3.3" xref="S2.p1.4.m4.1.1.3.3.cmml">m</mi></msup></mrow><annotation-xml encoding="MathML-Content" id="S2.p1.4.m4.1b"><apply id="S2.p1.4.m4.1.1.cmml" xref="S2.p1.4.m4.1.1"><in id="S2.p1.4.m4.1.1.1.cmml" xref="S2.p1.4.m4.1.1.1"></in><ci id="S2.p1.4.m4.1.1.2.cmml" xref="S2.p1.4.m4.1.1.2">𝑜</ci><apply id="S2.p1.4.m4.1.1.3.cmml" xref="S2.p1.4.m4.1.1.3"><csymbol cd="ambiguous" id="S2.p1.4.m4.1.1.3.1.cmml" xref="S2.p1.4.m4.1.1.3">superscript</csymbol><ci id="S2.p1.4.m4.1.1.3.2.cmml" xref="S2.p1.4.m4.1.1.3.2">𝒱</ci><ci id="S2.p1.4.m4.1.1.3.3.cmml" xref="S2.p1.4.m4.1.1.3.3">𝑚</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.4.m4.1c">o\in\mathcal{V}^{m}</annotation></semantics></math> is the last <math id="S2.p1.5.m5.1" class="ltx_Math" alttext="m" display="inline"><semantics id="S2.p1.5.m5.1a"><mi id="S2.p1.5.m5.1.1" xref="S2.p1.5.m5.1.1.cmml">m</mi><annotation-xml encoding="MathML-Content" id="S2.p1.5.m5.1b"><ci id="S2.p1.5.m5.1.1.cmml" xref="S2.p1.5.m5.1.1">𝑚</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.5.m5.1c">m</annotation></semantics></math> tokens of <math id="S2.p1.6.m6.1" class="ltx_Math" alttext="x" display="inline"><semantics id="S2.p1.6.m6.1a"><mi id="S2.p1.6.m6.1.1" xref="S2.p1.6.m6.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S2.p1.6.m6.1b"><ci id="S2.p1.6.m6.1.1.cmml" xref="S2.p1.6.m6.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.6.m6.1c">x</annotation></semantics></math>.
The prefix <math id="S2.p1.7.m7.1" class="ltx_Math" alttext="\pi=(x_{1}\ldots x_{m-1})" display="inline"><semantics id="S2.p1.7.m7.1a"><mrow id="S2.p1.7.m7.1.1" xref="S2.p1.7.m7.1.1.cmml"><mi id="S2.p1.7.m7.1.1.3" xref="S2.p1.7.m7.1.1.3.cmml">π</mi><mo id="S2.p1.7.m7.1.1.2" xref="S2.p1.7.m7.1.1.2.cmml">=</mo><mrow id="S2.p1.7.m7.1.1.1.1" xref="S2.p1.7.m7.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p1.7.m7.1.1.1.1.2" xref="S2.p1.7.m7.1.1.1.1.1.cmml">(</mo><mrow id="S2.p1.7.m7.1.1.1.1.1" xref="S2.p1.7.m7.1.1.1.1.1.cmml"><msub id="S2.p1.7.m7.1.1.1.1.1.2" xref="S2.p1.7.m7.1.1.1.1.1.2.cmml"><mi id="S2.p1.7.m7.1.1.1.1.1.2.2" xref="S2.p1.7.m7.1.1.1.1.1.2.2.cmml">x</mi><mn id="S2.p1.7.m7.1.1.1.1.1.2.3" xref="S2.p1.7.m7.1.1.1.1.1.2.3.cmml">1</mn></msub><mo lspace="0em" rspace="0em" id="S2.p1.7.m7.1.1.1.1.1.1" xref="S2.p1.7.m7.1.1.1.1.1.1.cmml">​</mo><mi mathvariant="normal" id="S2.p1.7.m7.1.1.1.1.1.3" xref="S2.p1.7.m7.1.1.1.1.1.3.cmml">…</mi><mo lspace="0em" rspace="0em" id="S2.p1.7.m7.1.1.1.1.1.1a" xref="S2.p1.7.m7.1.1.1.1.1.1.cmml">​</mo><msub id="S2.p1.7.m7.1.1.1.1.1.4" xref="S2.p1.7.m7.1.1.1.1.1.4.cmml"><mi id="S2.p1.7.m7.1.1.1.1.1.4.2" xref="S2.p1.7.m7.1.1.1.1.1.4.2.cmml">x</mi><mrow id="S2.p1.7.m7.1.1.1.1.1.4.3" xref="S2.p1.7.m7.1.1.1.1.1.4.3.cmml"><mi id="S2.p1.7.m7.1.1.1.1.1.4.3.2" xref="S2.p1.7.m7.1.1.1.1.1.4.3.2.cmml">m</mi><mo id="S2.p1.7.m7.1.1.1.1.1.4.3.1" xref="S2.p1.7.m7.1.1.1.1.1.4.3.1.cmml">−</mo><mn id="S2.p1.7.m7.1.1.1.1.1.4.3.3" xref="S2.p1.7.m7.1.1.1.1.1.4.3.3.cmml">1</mn></mrow></msub></mrow><mo stretchy="false" id="S2.p1.7.m7.1.1.1.1.3" xref="S2.p1.7.m7.1.1.1.1.1.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p1.7.m7.1b"><apply id="S2.p1.7.m7.1.1.cmml" xref="S2.p1.7.m7.1.1"><eq id="S2.p1.7.m7.1.1.2.cmml" xref="S2.p1.7.m7.1.1.2"></eq><ci id="S2.p1.7.m7.1.1.3.cmml" xref="S2.p1.7.m7.1.1.3">𝜋</ci><apply id="S2.p1.7.m7.1.1.1.1.1.cmml" xref="S2.p1.7.m7.1.1.1.1"><times id="S2.p1.7.m7.1.1.1.1.1.1.cmml" xref="S2.p1.7.m7.1.1.1.1.1.1"></times><apply id="S2.p1.7.m7.1.1.1.1.1.2.cmml" xref="S2.p1.7.m7.1.1.1.1.1.2"><csymbol cd="ambiguous" id="S2.p1.7.m7.1.1.1.1.1.2.1.cmml" xref="S2.p1.7.m7.1.1.1.1.1.2">subscript</csymbol><ci id="S2.p1.7.m7.1.1.1.1.1.2.2.cmml" xref="S2.p1.7.m7.1.1.1.1.1.2.2">𝑥</ci><cn type="integer" id="S2.p1.7.m7.1.1.1.1.1.2.3.cmml" xref="S2.p1.7.m7.1.1.1.1.1.2.3">1</cn></apply><ci id="S2.p1.7.m7.1.1.1.1.1.3.cmml" xref="S2.p1.7.m7.1.1.1.1.1.3">…</ci><apply id="S2.p1.7.m7.1.1.1.1.1.4.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4"><csymbol cd="ambiguous" id="S2.p1.7.m7.1.1.1.1.1.4.1.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4">subscript</csymbol><ci id="S2.p1.7.m7.1.1.1.1.1.4.2.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4.2">𝑥</ci><apply id="S2.p1.7.m7.1.1.1.1.1.4.3.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4.3"><minus id="S2.p1.7.m7.1.1.1.1.1.4.3.1.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4.3.1"></minus><ci id="S2.p1.7.m7.1.1.1.1.1.4.3.2.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4.3.2">𝑚</ci><cn type="integer" id="S2.p1.7.m7.1.1.1.1.1.4.3.3.cmml" xref="S2.p1.7.m7.1.1.1.1.1.4.3.3">1</cn></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.7.m7.1c">\pi=(x_{1}\ldots x_{m-1})</annotation></semantics></math> expresses <math id="S2.p1.8.m8.2" class="ltx_Math" alttext="(s,r)" display="inline"><semantics id="S2.p1.8.m8.2a"><mrow id="S2.p1.8.m8.2.3.2" xref="S2.p1.8.m8.2.3.1.cmml"><mo stretchy="false" id="S2.p1.8.m8.2.3.2.1" xref="S2.p1.8.m8.2.3.1.cmml">(</mo><mi id="S2.p1.8.m8.1.1" xref="S2.p1.8.m8.1.1.cmml">s</mi><mo id="S2.p1.8.m8.2.3.2.2" xref="S2.p1.8.m8.2.3.1.cmml">,</mo><mi id="S2.p1.8.m8.2.2" xref="S2.p1.8.m8.2.2.cmml">r</mi><mo stretchy="false" id="S2.p1.8.m8.2.3.2.3" xref="S2.p1.8.m8.2.3.1.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.p1.8.m8.2b"><interval closure="open" id="S2.p1.8.m8.2.3.1.cmml" xref="S2.p1.8.m8.2.3.2"><ci id="S2.p1.8.m8.1.1.cmml" xref="S2.p1.8.m8.1.1">𝑠</ci><ci id="S2.p1.8.m8.2.2.cmml" xref="S2.p1.8.m8.2.2">𝑟</ci></interval></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.8.m8.2c">(s,r)</annotation></semantics></math> and is denoted as the <span id="S2.p1.12.2" class="ltx_text ltx_font_bold">prompt</span>.
Let <math id="S2.p1.9.m9.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S2.p1.9.m9.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p1.9.m9.1.1" xref="S2.p1.9.m9.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S2.p1.9.m9.1b"><ci id="S2.p1.9.m9.1.1.cmml" xref="S2.p1.9.m9.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.9.m9.1c">\mathcal{E}</annotation></semantics></math> denote a set of facts to enforce (i.e., requested edits).
Our goal is to edit a pretrained language model so that
it upholds the relations expressed in <math id="S2.p1.10.m10.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S2.p1.10.m10.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p1.10.m10.1.1" xref="S2.p1.10.m10.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S2.p1.10.m10.1b"><ci id="S2.p1.10.m10.1.1.cmml" xref="S2.p1.10.m10.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.10.m10.1c">\mathcal{E}</annotation></semantics></math>
without changing its behavior on other facts.
In ZsRE, <math id="S2.p1.11.m11.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S2.p1.11.m11.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p1.11.m11.1.1" xref="S2.p1.11.m11.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S2.p1.11.m11.1b"><ci id="S2.p1.11.m11.1.1.cmml" xref="S2.p1.11.m11.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.11.m11.1c">\mathcal{E}</annotation></semantics></math> consists of 10,000 factual statements
(e.g., “The artwork Gideon’s Way was by who? John Creasey”).
In <span id="S2.p1.12.3" class="ltx_text ltx_font_smallcaps">CounterFact</span>, <math id="S2.p1.12.m12.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S2.p1.12.m12.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p1.12.m12.1.1" xref="S2.p1.12.m12.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S2.p1.12.m12.1b"><ci id="S2.p1.12.m12.1.1.cmml" xref="S2.p1.12.m12.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p1.12.m12.1c">\mathcal{E}</annotation></semantics></math> consists of 10,000 counterfactual statements (e.g., “TextEdit, a product of Nintendo”).</p>
</div>
<div id="S2.p2" class="ltx_para">
<p id="S2.p2.17" class="ltx_p">An editor is evaluated by three competing metrics: efficacy, generalization, and locality.
Let <math id="S2.p2.1.m1.1" class="ltx_Math" alttext="p_{\theta}" display="inline"><semantics id="S2.p2.1.m1.1a"><msub id="S2.p2.1.m1.1.1" xref="S2.p2.1.m1.1.1.cmml"><mi id="S2.p2.1.m1.1.1.2" xref="S2.p2.1.m1.1.1.2.cmml">p</mi><mi id="S2.p2.1.m1.1.1.3" xref="S2.p2.1.m1.1.1.3.cmml">θ</mi></msub><annotation-xml encoding="MathML-Content" id="S2.p2.1.m1.1b"><apply id="S2.p2.1.m1.1.1.cmml" xref="S2.p2.1.m1.1.1"><csymbol cd="ambiguous" id="S2.p2.1.m1.1.1.1.cmml" xref="S2.p2.1.m1.1.1">subscript</csymbol><ci id="S2.p2.1.m1.1.1.2.cmml" xref="S2.p2.1.m1.1.1.2">𝑝</ci><ci id="S2.p2.1.m1.1.1.3.cmml" xref="S2.p2.1.m1.1.1.3">𝜃</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.1.m1.1c">p_{\theta}</annotation></semantics></math> denote a language model edited on <math id="S2.p2.2.m2.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S2.p2.2.m2.1a"><mi class="ltx_font_mathcaligraphic" id="S2.p2.2.m2.1.1" xref="S2.p2.2.m2.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S2.p2.2.m2.1b"><ci id="S2.p2.2.m2.1.1.cmml" xref="S2.p2.2.m2.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.2.m2.1c">\mathcal{E}</annotation></semantics></math>.
In ZsRE, efficacy is the accuracy of <math id="S2.p2.3.m3.1" class="ltx_Math" alttext="o=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi)" display="inline"><semantics id="S2.p2.3.m3.1a"><mrow id="S2.p2.3.m3.1.1" xref="S2.p2.3.m3.1.1.cmml"><mi id="S2.p2.3.m3.1.1.3" xref="S2.p2.3.m3.1.1.3.cmml">o</mi><mo id="S2.p2.3.m3.1.1.2" xref="S2.p2.3.m3.1.1.2.cmml">=</mo><mrow id="S2.p2.3.m3.1.1.1" xref="S2.p2.3.m3.1.1.1.cmml"><mrow id="S2.p2.3.m3.1.1.1.3" xref="S2.p2.3.m3.1.1.1.3.cmml"><msub id="S2.p2.3.m3.1.1.1.3.1" xref="S2.p2.3.m3.1.1.1.3.1.cmml"><mrow id="S2.p2.3.m3.1.1.1.3.1.2" xref="S2.p2.3.m3.1.1.1.3.1.2.cmml"><mi id="S2.p2.3.m3.1.1.1.3.1.2.2" xref="S2.p2.3.m3.1.1.1.3.1.2.2.cmml">arg</mi><mo lspace="0.170em" rspace="0em" id="S2.p2.3.m3.1.1.1.3.1.2.1" xref="S2.p2.3.m3.1.1.1.3.1.2.1.cmml">​</mo><mi id="S2.p2.3.m3.1.1.1.3.1.2.3" xref="S2.p2.3.m3.1.1.1.3.1.2.3.cmml">max</mi></mrow><mi id="S2.p2.3.m3.1.1.1.3.1.3" xref="S2.p2.3.m3.1.1.1.3.1.3.cmml">y</mi></msub><mo id="S2.p2.3.m3.1.1.1.3a" xref="S2.p2.3.m3.1.1.1.3.cmml">⁡</mo><msub id="S2.p2.3.m3.1.1.1.3.2" xref="S2.p2.3.m3.1.1.1.3.2.cmml"><mi id="S2.p2.3.m3.1.1.1.3.2.2" xref="S2.p2.3.m3.1.1.1.3.2.2.cmml">p</mi><mi id="S2.p2.3.m3.1.1.1.3.2.3" xref="S2.p2.3.m3.1.1.1.3.2.3.cmml">θ</mi></msub></mrow><mo lspace="0em" rspace="0em" id="S2.p2.3.m3.1.1.1.2" xref="S2.p2.3.m3.1.1.1.2.cmml">​</mo><mrow id="S2.p2.3.m3.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.3.m3.1.1.1.1.1.2" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.3.m3.1.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml"><mi id="S2.p2.3.m3.1.1.1.1.1.1.2" xref="S2.p2.3.m3.1.1.1.1.1.1.2.cmml">y</mi><mo fence="false" id="S2.p2.3.m3.1.1.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.1.cmml">|</mo><mi id="S2.p2.3.m3.1.1.1.1.1.1.3" xref="S2.p2.3.m3.1.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.p2.3.m3.1.1.1.1.1.3" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.3.m3.1b"><apply id="S2.p2.3.m3.1.1.cmml" xref="S2.p2.3.m3.1.1"><eq id="S2.p2.3.m3.1.1.2.cmml" xref="S2.p2.3.m3.1.1.2"></eq><ci id="S2.p2.3.m3.1.1.3.cmml" xref="S2.p2.3.m3.1.1.3">𝑜</ci><apply id="S2.p2.3.m3.1.1.1.cmml" xref="S2.p2.3.m3.1.1.1"><times id="S2.p2.3.m3.1.1.1.2.cmml" xref="S2.p2.3.m3.1.1.1.2"></times><apply id="S2.p2.3.m3.1.1.1.3.cmml" xref="S2.p2.3.m3.1.1.1.3"><apply id="S2.p2.3.m3.1.1.1.3.1.cmml" xref="S2.p2.3.m3.1.1.1.3.1"><csymbol cd="ambiguous" id="S2.p2.3.m3.1.1.1.3.1.1.cmml" xref="S2.p2.3.m3.1.1.1.3.1">subscript</csymbol><apply id="S2.p2.3.m3.1.1.1.3.1.2.cmml" xref="S2.p2.3.m3.1.1.1.3.1.2"><times id="S2.p2.3.m3.1.1.1.3.1.2.1.cmml" xref="S2.p2.3.m3.1.1.1.3.1.2.1"></times><ci id="S2.p2.3.m3.1.1.1.3.1.2.2.cmml" xref="S2.p2.3.m3.1.1.1.3.1.2.2">arg</ci><ci id="S2.p2.3.m3.1.1.1.3.1.2.3.cmml" xref="S2.p2.3.m3.1.1.1.3.1.2.3">max</ci></apply><ci id="S2.p2.3.m3.1.1.1.3.1.3.cmml" xref="S2.p2.3.m3.1.1.1.3.1.3">𝑦</ci></apply><apply id="S2.p2.3.m3.1.1.1.3.2.cmml" xref="S2.p2.3.m3.1.1.1.3.2"><csymbol cd="ambiguous" id="S2.p2.3.m3.1.1.1.3.2.1.cmml" xref="S2.p2.3.m3.1.1.1.3.2">subscript</csymbol><ci id="S2.p2.3.m3.1.1.1.3.2.2.cmml" xref="S2.p2.3.m3.1.1.1.3.2.2">𝑝</ci><ci id="S2.p2.3.m3.1.1.1.3.2.3.cmml" xref="S2.p2.3.m3.1.1.1.3.2.3">𝜃</ci></apply></apply><apply id="S2.p2.3.m3.1.1.1.1.1.1.cmml" xref="S2.p2.3.m3.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.3.m3.1.1.1.1.1.1.1.cmml" xref="S2.p2.3.m3.1.1.1.1.1.1.1">conditional</csymbol><ci id="S2.p2.3.m3.1.1.1.1.1.1.2.cmml" xref="S2.p2.3.m3.1.1.1.1.1.1.2">𝑦</ci><ci id="S2.p2.3.m3.1.1.1.1.1.1.3.cmml" xref="S2.p2.3.m3.1.1.1.1.1.1.3">𝜋</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.3.m3.1c">o=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi)</annotation></semantics></math> for <math id="S2.p2.4.m4.2" class="ltx_Math" alttext="(\pi,o)\in\mathcal{E}" display="inline"><semantics id="S2.p2.4.m4.2a"><mrow id="S2.p2.4.m4.2.3" xref="S2.p2.4.m4.2.3.cmml"><mrow id="S2.p2.4.m4.2.3.2.2" xref="S2.p2.4.m4.2.3.2.1.cmml"><mo stretchy="false" id="S2.p2.4.m4.2.3.2.2.1" xref="S2.p2.4.m4.2.3.2.1.cmml">(</mo><mi id="S2.p2.4.m4.1.1" xref="S2.p2.4.m4.1.1.cmml">π</mi><mo id="S2.p2.4.m4.2.3.2.2.2" xref="S2.p2.4.m4.2.3.2.1.cmml">,</mo><mi id="S2.p2.4.m4.2.2" xref="S2.p2.4.m4.2.2.cmml">o</mi><mo stretchy="false" id="S2.p2.4.m4.2.3.2.2.3" xref="S2.p2.4.m4.2.3.2.1.cmml">)</mo></mrow><mo id="S2.p2.4.m4.2.3.1" xref="S2.p2.4.m4.2.3.1.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S2.p2.4.m4.2.3.3" xref="S2.p2.4.m4.2.3.3.cmml">ℰ</mi></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.4.m4.2b"><apply id="S2.p2.4.m4.2.3.cmml" xref="S2.p2.4.m4.2.3"><in id="S2.p2.4.m4.2.3.1.cmml" xref="S2.p2.4.m4.2.3.1"></in><interval closure="open" id="S2.p2.4.m4.2.3.2.1.cmml" xref="S2.p2.4.m4.2.3.2.2"><ci id="S2.p2.4.m4.1.1.cmml" xref="S2.p2.4.m4.1.1">𝜋</ci><ci id="S2.p2.4.m4.2.2.cmml" xref="S2.p2.4.m4.2.2">𝑜</ci></interval><ci id="S2.p2.4.m4.2.3.3.cmml" xref="S2.p2.4.m4.2.3.3">ℰ</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.4.m4.2c">(\pi,o)\in\mathcal{E}</annotation></semantics></math>;
generalization is the accuracy of <math id="S2.p2.5.m5.1" class="ltx_Math" alttext="o=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi_{\text{par}})" display="inline"><semantics id="S2.p2.5.m5.1a"><mrow id="S2.p2.5.m5.1.1" xref="S2.p2.5.m5.1.1.cmml"><mi id="S2.p2.5.m5.1.1.3" xref="S2.p2.5.m5.1.1.3.cmml">o</mi><mo id="S2.p2.5.m5.1.1.2" xref="S2.p2.5.m5.1.1.2.cmml">=</mo><mrow id="S2.p2.5.m5.1.1.1" xref="S2.p2.5.m5.1.1.1.cmml"><mrow id="S2.p2.5.m5.1.1.1.3" xref="S2.p2.5.m5.1.1.1.3.cmml"><msub id="S2.p2.5.m5.1.1.1.3.1" xref="S2.p2.5.m5.1.1.1.3.1.cmml"><mrow id="S2.p2.5.m5.1.1.1.3.1.2" xref="S2.p2.5.m5.1.1.1.3.1.2.cmml"><mi id="S2.p2.5.m5.1.1.1.3.1.2.2" xref="S2.p2.5.m5.1.1.1.3.1.2.2.cmml">arg</mi><mo lspace="0.170em" rspace="0em" id="S2.p2.5.m5.1.1.1.3.1.2.1" xref="S2.p2.5.m5.1.1.1.3.1.2.1.cmml">​</mo><mi id="S2.p2.5.m5.1.1.1.3.1.2.3" xref="S2.p2.5.m5.1.1.1.3.1.2.3.cmml">max</mi></mrow><mi id="S2.p2.5.m5.1.1.1.3.1.3" xref="S2.p2.5.m5.1.1.1.3.1.3.cmml">y</mi></msub><mo id="S2.p2.5.m5.1.1.1.3a" xref="S2.p2.5.m5.1.1.1.3.cmml">⁡</mo><msub id="S2.p2.5.m5.1.1.1.3.2" xref="S2.p2.5.m5.1.1.1.3.2.cmml"><mi id="S2.p2.5.m5.1.1.1.3.2.2" xref="S2.p2.5.m5.1.1.1.3.2.2.cmml">p</mi><mi id="S2.p2.5.m5.1.1.1.3.2.3" xref="S2.p2.5.m5.1.1.1.3.2.3.cmml">θ</mi></msub></mrow><mo lspace="0em" rspace="0em" id="S2.p2.5.m5.1.1.1.2" xref="S2.p2.5.m5.1.1.1.2.cmml">​</mo><mrow id="S2.p2.5.m5.1.1.1.1.1" xref="S2.p2.5.m5.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.5.m5.1.1.1.1.1.2" xref="S2.p2.5.m5.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.5.m5.1.1.1.1.1.1" xref="S2.p2.5.m5.1.1.1.1.1.1.cmml"><mi id="S2.p2.5.m5.1.1.1.1.1.1.2" xref="S2.p2.5.m5.1.1.1.1.1.1.2.cmml">y</mi><mo fence="false" id="S2.p2.5.m5.1.1.1.1.1.1.1" xref="S2.p2.5.m5.1.1.1.1.1.1.1.cmml">|</mo><msub id="S2.p2.5.m5.1.1.1.1.1.1.3" xref="S2.p2.5.m5.1.1.1.1.1.1.3.cmml"><mi id="S2.p2.5.m5.1.1.1.1.1.1.3.2" xref="S2.p2.5.m5.1.1.1.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.5.m5.1.1.1.1.1.1.3.3" xref="S2.p2.5.m5.1.1.1.1.1.1.3.3a.cmml">par</mtext></msub></mrow><mo stretchy="false" id="S2.p2.5.m5.1.1.1.1.1.3" xref="S2.p2.5.m5.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.5.m5.1b"><apply id="S2.p2.5.m5.1.1.cmml" xref="S2.p2.5.m5.1.1"><eq id="S2.p2.5.m5.1.1.2.cmml" xref="S2.p2.5.m5.1.1.2"></eq><ci id="S2.p2.5.m5.1.1.3.cmml" xref="S2.p2.5.m5.1.1.3">𝑜</ci><apply id="S2.p2.5.m5.1.1.1.cmml" xref="S2.p2.5.m5.1.1.1"><times id="S2.p2.5.m5.1.1.1.2.cmml" xref="S2.p2.5.m5.1.1.1.2"></times><apply id="S2.p2.5.m5.1.1.1.3.cmml" xref="S2.p2.5.m5.1.1.1.3"><apply id="S2.p2.5.m5.1.1.1.3.1.cmml" xref="S2.p2.5.m5.1.1.1.3.1"><csymbol cd="ambiguous" id="S2.p2.5.m5.1.1.1.3.1.1.cmml" xref="S2.p2.5.m5.1.1.1.3.1">subscript</csymbol><apply id="S2.p2.5.m5.1.1.1.3.1.2.cmml" xref="S2.p2.5.m5.1.1.1.3.1.2"><times id="S2.p2.5.m5.1.1.1.3.1.2.1.cmml" xref="S2.p2.5.m5.1.1.1.3.1.2.1"></times><ci id="S2.p2.5.m5.1.1.1.3.1.2.2.cmml" xref="S2.p2.5.m5.1.1.1.3.1.2.2">arg</ci><ci id="S2.p2.5.m5.1.1.1.3.1.2.3.cmml" xref="S2.p2.5.m5.1.1.1.3.1.2.3">max</ci></apply><ci id="S2.p2.5.m5.1.1.1.3.1.3.cmml" xref="S2.p2.5.m5.1.1.1.3.1.3">𝑦</ci></apply><apply id="S2.p2.5.m5.1.1.1.3.2.cmml" xref="S2.p2.5.m5.1.1.1.3.2"><csymbol cd="ambiguous" id="S2.p2.5.m5.1.1.1.3.2.1.cmml" xref="S2.p2.5.m5.1.1.1.3.2">subscript</csymbol><ci id="S2.p2.5.m5.1.1.1.3.2.2.cmml" xref="S2.p2.5.m5.1.1.1.3.2.2">𝑝</ci><ci id="S2.p2.5.m5.1.1.1.3.2.3.cmml" xref="S2.p2.5.m5.1.1.1.3.2.3">𝜃</ci></apply></apply><apply id="S2.p2.5.m5.1.1.1.1.1.1.cmml" xref="S2.p2.5.m5.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.5.m5.1.1.1.1.1.1.1.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.1">conditional</csymbol><ci id="S2.p2.5.m5.1.1.1.1.1.1.2.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.2">𝑦</ci><apply id="S2.p2.5.m5.1.1.1.1.1.1.3.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.5.m5.1.1.1.1.1.1.3.1.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.3">subscript</csymbol><ci id="S2.p2.5.m5.1.1.1.1.1.1.3.2.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.3.2">𝜋</ci><ci id="S2.p2.5.m5.1.1.1.1.1.1.3.3a.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.5.m5.1.1.1.1.1.1.3.3.cmml" xref="S2.p2.5.m5.1.1.1.1.1.1.3.3">par</mtext></ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.5.m5.1c">o=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi_{\text{par}})</annotation></semantics></math>
where <math id="S2.p2.6.m6.1" class="ltx_Math" alttext="\pi_{\text{par}}" display="inline"><semantics id="S2.p2.6.m6.1a"><msub id="S2.p2.6.m6.1.1" xref="S2.p2.6.m6.1.1.cmml"><mi id="S2.p2.6.m6.1.1.2" xref="S2.p2.6.m6.1.1.2.cmml">π</mi><mtext id="S2.p2.6.m6.1.1.3" xref="S2.p2.6.m6.1.1.3a.cmml">par</mtext></msub><annotation-xml encoding="MathML-Content" id="S2.p2.6.m6.1b"><apply id="S2.p2.6.m6.1.1.cmml" xref="S2.p2.6.m6.1.1"><csymbol cd="ambiguous" id="S2.p2.6.m6.1.1.1.cmml" xref="S2.p2.6.m6.1.1">subscript</csymbol><ci id="S2.p2.6.m6.1.1.2.cmml" xref="S2.p2.6.m6.1.1.2">𝜋</ci><ci id="S2.p2.6.m6.1.1.3a.cmml" xref="S2.p2.6.m6.1.1.3"><mtext mathsize="70%" id="S2.p2.6.m6.1.1.3.cmml" xref="S2.p2.6.m6.1.1.3">par</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.6.m6.1c">\pi_{\text{par}}</annotation></semantics></math> is some paraphrase of <math id="S2.p2.7.m7.1" class="ltx_Math" alttext="\pi" display="inline"><semantics id="S2.p2.7.m7.1a"><mi id="S2.p2.7.m7.1.1" xref="S2.p2.7.m7.1.1.cmml">π</mi><annotation-xml encoding="MathML-Content" id="S2.p2.7.m7.1b"><ci id="S2.p2.7.m7.1.1.cmml" xref="S2.p2.7.m7.1.1">𝜋</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.7.m7.1c">\pi</annotation></semantics></math>;
locality is the accuracy of <math id="S2.p2.8.m8.1" class="ltx_Math" alttext="o_{\text{unrel}}=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi_{\text{unrel}})" display="inline"><semantics id="S2.p2.8.m8.1a"><mrow id="S2.p2.8.m8.1.1" xref="S2.p2.8.m8.1.1.cmml"><msub id="S2.p2.8.m8.1.1.3" xref="S2.p2.8.m8.1.1.3.cmml"><mi id="S2.p2.8.m8.1.1.3.2" xref="S2.p2.8.m8.1.1.3.2.cmml">o</mi><mtext id="S2.p2.8.m8.1.1.3.3" xref="S2.p2.8.m8.1.1.3.3a.cmml">unrel</mtext></msub><mo id="S2.p2.8.m8.1.1.2" xref="S2.p2.8.m8.1.1.2.cmml">=</mo><mrow id="S2.p2.8.m8.1.1.1" xref="S2.p2.8.m8.1.1.1.cmml"><mrow id="S2.p2.8.m8.1.1.1.3" xref="S2.p2.8.m8.1.1.1.3.cmml"><msub id="S2.p2.8.m8.1.1.1.3.1" xref="S2.p2.8.m8.1.1.1.3.1.cmml"><mrow id="S2.p2.8.m8.1.1.1.3.1.2" xref="S2.p2.8.m8.1.1.1.3.1.2.cmml"><mi id="S2.p2.8.m8.1.1.1.3.1.2.2" xref="S2.p2.8.m8.1.1.1.3.1.2.2.cmml">arg</mi><mo lspace="0.170em" rspace="0em" id="S2.p2.8.m8.1.1.1.3.1.2.1" xref="S2.p2.8.m8.1.1.1.3.1.2.1.cmml">​</mo><mi id="S2.p2.8.m8.1.1.1.3.1.2.3" xref="S2.p2.8.m8.1.1.1.3.1.2.3.cmml">max</mi></mrow><mi id="S2.p2.8.m8.1.1.1.3.1.3" xref="S2.p2.8.m8.1.1.1.3.1.3.cmml">y</mi></msub><mo id="S2.p2.8.m8.1.1.1.3a" xref="S2.p2.8.m8.1.1.1.3.cmml">⁡</mo><msub id="S2.p2.8.m8.1.1.1.3.2" xref="S2.p2.8.m8.1.1.1.3.2.cmml"><mi id="S2.p2.8.m8.1.1.1.3.2.2" xref="S2.p2.8.m8.1.1.1.3.2.2.cmml">p</mi><mi id="S2.p2.8.m8.1.1.1.3.2.3" xref="S2.p2.8.m8.1.1.1.3.2.3.cmml">θ</mi></msub></mrow><mo lspace="0em" rspace="0em" id="S2.p2.8.m8.1.1.1.2" xref="S2.p2.8.m8.1.1.1.2.cmml">​</mo><mrow id="S2.p2.8.m8.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.8.m8.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml"><mi id="S2.p2.8.m8.1.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.2.cmml">y</mi><mo fence="false" id="S2.p2.8.m8.1.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.1.cmml">|</mo><msub id="S2.p2.8.m8.1.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.3.cmml"><mi id="S2.p2.8.m8.1.1.1.1.1.1.3.2" xref="S2.p2.8.m8.1.1.1.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.8.m8.1.1.1.1.1.1.3.3" xref="S2.p2.8.m8.1.1.1.1.1.1.3.3a.cmml">unrel</mtext></msub></mrow><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.8.m8.1b"><apply id="S2.p2.8.m8.1.1.cmml" xref="S2.p2.8.m8.1.1"><eq id="S2.p2.8.m8.1.1.2.cmml" xref="S2.p2.8.m8.1.1.2"></eq><apply id="S2.p2.8.m8.1.1.3.cmml" xref="S2.p2.8.m8.1.1.3"><csymbol cd="ambiguous" id="S2.p2.8.m8.1.1.3.1.cmml" xref="S2.p2.8.m8.1.1.3">subscript</csymbol><ci id="S2.p2.8.m8.1.1.3.2.cmml" xref="S2.p2.8.m8.1.1.3.2">𝑜</ci><ci id="S2.p2.8.m8.1.1.3.3a.cmml" xref="S2.p2.8.m8.1.1.3.3"><mtext mathsize="70%" id="S2.p2.8.m8.1.1.3.3.cmml" xref="S2.p2.8.m8.1.1.3.3">unrel</mtext></ci></apply><apply id="S2.p2.8.m8.1.1.1.cmml" xref="S2.p2.8.m8.1.1.1"><times id="S2.p2.8.m8.1.1.1.2.cmml" xref="S2.p2.8.m8.1.1.1.2"></times><apply id="S2.p2.8.m8.1.1.1.3.cmml" xref="S2.p2.8.m8.1.1.1.3"><apply id="S2.p2.8.m8.1.1.1.3.1.cmml" xref="S2.p2.8.m8.1.1.1.3.1"><csymbol cd="ambiguous" id="S2.p2.8.m8.1.1.1.3.1.1.cmml" xref="S2.p2.8.m8.1.1.1.3.1">subscript</csymbol><apply id="S2.p2.8.m8.1.1.1.3.1.2.cmml" xref="S2.p2.8.m8.1.1.1.3.1.2"><times id="S2.p2.8.m8.1.1.1.3.1.2.1.cmml" xref="S2.p2.8.m8.1.1.1.3.1.2.1"></times><ci id="S2.p2.8.m8.1.1.1.3.1.2.2.cmml" xref="S2.p2.8.m8.1.1.1.3.1.2.2">arg</ci><ci id="S2.p2.8.m8.1.1.1.3.1.2.3.cmml" xref="S2.p2.8.m8.1.1.1.3.1.2.3">max</ci></apply><ci id="S2.p2.8.m8.1.1.1.3.1.3.cmml" xref="S2.p2.8.m8.1.1.1.3.1.3">𝑦</ci></apply><apply id="S2.p2.8.m8.1.1.1.3.2.cmml" xref="S2.p2.8.m8.1.1.1.3.2"><csymbol cd="ambiguous" id="S2.p2.8.m8.1.1.1.3.2.1.cmml" xref="S2.p2.8.m8.1.1.1.3.2">subscript</csymbol><ci id="S2.p2.8.m8.1.1.1.3.2.2.cmml" xref="S2.p2.8.m8.1.1.1.3.2.2">𝑝</ci><ci id="S2.p2.8.m8.1.1.1.3.2.3.cmml" xref="S2.p2.8.m8.1.1.1.3.2.3">𝜃</ci></apply></apply><apply id="S2.p2.8.m8.1.1.1.1.1.1.cmml" xref="S2.p2.8.m8.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.8.m8.1.1.1.1.1.1.1.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.1">conditional</csymbol><ci id="S2.p2.8.m8.1.1.1.1.1.1.2.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.2">𝑦</ci><apply id="S2.p2.8.m8.1.1.1.1.1.1.3.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.8.m8.1.1.1.1.1.1.3.1.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.3">subscript</csymbol><ci id="S2.p2.8.m8.1.1.1.1.1.1.3.2.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.3.2">𝜋</ci><ci id="S2.p2.8.m8.1.1.1.1.1.1.3.3a.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.8.m8.1.1.1.1.1.1.3.3.cmml" xref="S2.p2.8.m8.1.1.1.1.1.1.3.3">unrel</mtext></ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.8.m8.1c">o_{\text{unrel}}=\operatorname*{arg\,max}_{y}p_{\theta}(y|\pi_{\text{unrel}})</annotation></semantics></math>
where <math id="S2.p2.9.m9.2" class="ltx_Math" alttext="(\pi_{\text{unrel}},o_{\text{unrel}})" display="inline"><semantics id="S2.p2.9.m9.2a"><mrow id="S2.p2.9.m9.2.2.2" xref="S2.p2.9.m9.2.2.3.cmml"><mo stretchy="false" id="S2.p2.9.m9.2.2.2.3" xref="S2.p2.9.m9.2.2.3.cmml">(</mo><msub id="S2.p2.9.m9.1.1.1.1" xref="S2.p2.9.m9.1.1.1.1.cmml"><mi id="S2.p2.9.m9.1.1.1.1.2" xref="S2.p2.9.m9.1.1.1.1.2.cmml">π</mi><mtext id="S2.p2.9.m9.1.1.1.1.3" xref="S2.p2.9.m9.1.1.1.1.3a.cmml">unrel</mtext></msub><mo id="S2.p2.9.m9.2.2.2.4" xref="S2.p2.9.m9.2.2.3.cmml">,</mo><msub id="S2.p2.9.m9.2.2.2.2" xref="S2.p2.9.m9.2.2.2.2.cmml"><mi id="S2.p2.9.m9.2.2.2.2.2" xref="S2.p2.9.m9.2.2.2.2.2.cmml">o</mi><mtext id="S2.p2.9.m9.2.2.2.2.3" xref="S2.p2.9.m9.2.2.2.2.3a.cmml">unrel</mtext></msub><mo stretchy="false" id="S2.p2.9.m9.2.2.2.5" xref="S2.p2.9.m9.2.2.3.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.9.m9.2b"><interval closure="open" id="S2.p2.9.m9.2.2.3.cmml" xref="S2.p2.9.m9.2.2.2"><apply id="S2.p2.9.m9.1.1.1.1.cmml" xref="S2.p2.9.m9.1.1.1.1"><csymbol cd="ambiguous" id="S2.p2.9.m9.1.1.1.1.1.cmml" xref="S2.p2.9.m9.1.1.1.1">subscript</csymbol><ci id="S2.p2.9.m9.1.1.1.1.2.cmml" xref="S2.p2.9.m9.1.1.1.1.2">𝜋</ci><ci id="S2.p2.9.m9.1.1.1.1.3a.cmml" xref="S2.p2.9.m9.1.1.1.1.3"><mtext mathsize="70%" id="S2.p2.9.m9.1.1.1.1.3.cmml" xref="S2.p2.9.m9.1.1.1.1.3">unrel</mtext></ci></apply><apply id="S2.p2.9.m9.2.2.2.2.cmml" xref="S2.p2.9.m9.2.2.2.2"><csymbol cd="ambiguous" id="S2.p2.9.m9.2.2.2.2.1.cmml" xref="S2.p2.9.m9.2.2.2.2">subscript</csymbol><ci id="S2.p2.9.m9.2.2.2.2.2.cmml" xref="S2.p2.9.m9.2.2.2.2.2">𝑜</ci><ci id="S2.p2.9.m9.2.2.2.2.3a.cmml" xref="S2.p2.9.m9.2.2.2.2.3"><mtext mathsize="70%" id="S2.p2.9.m9.2.2.2.2.3.cmml" xref="S2.p2.9.m9.2.2.2.2.3">unrel</mtext></ci></apply></interval></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.9.m9.2c">(\pi_{\text{unrel}},o_{\text{unrel}})</annotation></semantics></math> is an unrelated fact.
In <span id="S2.p2.17.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>, efficacy and generalization measure the accuracy of <math id="S2.p2.10.m10.2" class="ltx_Math" alttext="p_{\theta}(o|\pi)&gt;p_{\theta}(o_{\text{true}}|\pi)" display="inline"><semantics id="S2.p2.10.m10.2a"><mrow id="S2.p2.10.m10.2.2" xref="S2.p2.10.m10.2.2.cmml"><mrow id="S2.p2.10.m10.1.1.1" xref="S2.p2.10.m10.1.1.1.cmml"><msub id="S2.p2.10.m10.1.1.1.3" xref="S2.p2.10.m10.1.1.1.3.cmml"><mi id="S2.p2.10.m10.1.1.1.3.2" xref="S2.p2.10.m10.1.1.1.3.2.cmml">p</mi><mi id="S2.p2.10.m10.1.1.1.3.3" xref="S2.p2.10.m10.1.1.1.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.10.m10.1.1.1.2" xref="S2.p2.10.m10.1.1.1.2.cmml">​</mo><mrow id="S2.p2.10.m10.1.1.1.1.1" xref="S2.p2.10.m10.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.10.m10.1.1.1.1.1.2" xref="S2.p2.10.m10.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.10.m10.1.1.1.1.1.1" xref="S2.p2.10.m10.1.1.1.1.1.1.cmml"><mi id="S2.p2.10.m10.1.1.1.1.1.1.2" xref="S2.p2.10.m10.1.1.1.1.1.1.2.cmml">o</mi><mo fence="false" id="S2.p2.10.m10.1.1.1.1.1.1.1" xref="S2.p2.10.m10.1.1.1.1.1.1.1.cmml">|</mo><mi id="S2.p2.10.m10.1.1.1.1.1.1.3" xref="S2.p2.10.m10.1.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.p2.10.m10.1.1.1.1.1.3" xref="S2.p2.10.m10.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.p2.10.m10.2.2.3" xref="S2.p2.10.m10.2.2.3.cmml">&gt;</mo><mrow id="S2.p2.10.m10.2.2.2" xref="S2.p2.10.m10.2.2.2.cmml"><msub id="S2.p2.10.m10.2.2.2.3" xref="S2.p2.10.m10.2.2.2.3.cmml"><mi id="S2.p2.10.m10.2.2.2.3.2" xref="S2.p2.10.m10.2.2.2.3.2.cmml">p</mi><mi id="S2.p2.10.m10.2.2.2.3.3" xref="S2.p2.10.m10.2.2.2.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.10.m10.2.2.2.2" xref="S2.p2.10.m10.2.2.2.2.cmml">​</mo><mrow id="S2.p2.10.m10.2.2.2.1.1" xref="S2.p2.10.m10.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.p2.10.m10.2.2.2.1.1.2" xref="S2.p2.10.m10.2.2.2.1.1.1.cmml">(</mo><mrow id="S2.p2.10.m10.2.2.2.1.1.1" xref="S2.p2.10.m10.2.2.2.1.1.1.cmml"><msub id="S2.p2.10.m10.2.2.2.1.1.1.2" xref="S2.p2.10.m10.2.2.2.1.1.1.2.cmml"><mi id="S2.p2.10.m10.2.2.2.1.1.1.2.2" xref="S2.p2.10.m10.2.2.2.1.1.1.2.2.cmml">o</mi><mtext id="S2.p2.10.m10.2.2.2.1.1.1.2.3" xref="S2.p2.10.m10.2.2.2.1.1.1.2.3a.cmml">true</mtext></msub><mo fence="false" id="S2.p2.10.m10.2.2.2.1.1.1.1" xref="S2.p2.10.m10.2.2.2.1.1.1.1.cmml">|</mo><mi id="S2.p2.10.m10.2.2.2.1.1.1.3" xref="S2.p2.10.m10.2.2.2.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S2.p2.10.m10.2.2.2.1.1.3" xref="S2.p2.10.m10.2.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.10.m10.2b"><apply id="S2.p2.10.m10.2.2.cmml" xref="S2.p2.10.m10.2.2"><gt id="S2.p2.10.m10.2.2.3.cmml" xref="S2.p2.10.m10.2.2.3"></gt><apply id="S2.p2.10.m10.1.1.1.cmml" xref="S2.p2.10.m10.1.1.1"><times id="S2.p2.10.m10.1.1.1.2.cmml" xref="S2.p2.10.m10.1.1.1.2"></times><apply id="S2.p2.10.m10.1.1.1.3.cmml" xref="S2.p2.10.m10.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.10.m10.1.1.1.3.1.cmml" xref="S2.p2.10.m10.1.1.1.3">subscript</csymbol><ci id="S2.p2.10.m10.1.1.1.3.2.cmml" xref="S2.p2.10.m10.1.1.1.3.2">𝑝</ci><ci id="S2.p2.10.m10.1.1.1.3.3.cmml" xref="S2.p2.10.m10.1.1.1.3.3">𝜃</ci></apply><apply id="S2.p2.10.m10.1.1.1.1.1.1.cmml" xref="S2.p2.10.m10.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.10.m10.1.1.1.1.1.1.1.cmml" xref="S2.p2.10.m10.1.1.1.1.1.1.1">conditional</csymbol><ci id="S2.p2.10.m10.1.1.1.1.1.1.2.cmml" xref="S2.p2.10.m10.1.1.1.1.1.1.2">𝑜</ci><ci id="S2.p2.10.m10.1.1.1.1.1.1.3.cmml" xref="S2.p2.10.m10.1.1.1.1.1.1.3">𝜋</ci></apply></apply><apply id="S2.p2.10.m10.2.2.2.cmml" xref="S2.p2.10.m10.2.2.2"><times id="S2.p2.10.m10.2.2.2.2.cmml" xref="S2.p2.10.m10.2.2.2.2"></times><apply id="S2.p2.10.m10.2.2.2.3.cmml" xref="S2.p2.10.m10.2.2.2.3"><csymbol cd="ambiguous" id="S2.p2.10.m10.2.2.2.3.1.cmml" xref="S2.p2.10.m10.2.2.2.3">subscript</csymbol><ci id="S2.p2.10.m10.2.2.2.3.2.cmml" xref="S2.p2.10.m10.2.2.2.3.2">𝑝</ci><ci id="S2.p2.10.m10.2.2.2.3.3.cmml" xref="S2.p2.10.m10.2.2.2.3.3">𝜃</ci></apply><apply id="S2.p2.10.m10.2.2.2.1.1.1.cmml" xref="S2.p2.10.m10.2.2.2.1.1"><csymbol cd="latexml" id="S2.p2.10.m10.2.2.2.1.1.1.1.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.1">conditional</csymbol><apply id="S2.p2.10.m10.2.2.2.1.1.1.2.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.2"><csymbol cd="ambiguous" id="S2.p2.10.m10.2.2.2.1.1.1.2.1.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.2">subscript</csymbol><ci id="S2.p2.10.m10.2.2.2.1.1.1.2.2.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.2.2">𝑜</ci><ci id="S2.p2.10.m10.2.2.2.1.1.1.2.3a.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.2.3"><mtext mathsize="70%" id="S2.p2.10.m10.2.2.2.1.1.1.2.3.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.2.3">true</mtext></ci></apply><ci id="S2.p2.10.m10.2.2.2.1.1.1.3.cmml" xref="S2.p2.10.m10.2.2.2.1.1.1.3">𝜋</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.10.m10.2c">p_{\theta}(o|\pi)&gt;p_{\theta}(o_{\text{true}}|\pi)</annotation></semantics></math>
and <math id="S2.p2.11.m11.2" class="ltx_Math" alttext="p_{\theta}(o|\pi_{\text{par}})&gt;p_{\theta}(o_{\text{true}}|\pi_{\text{par}})" display="inline"><semantics id="S2.p2.11.m11.2a"><mrow id="S2.p2.11.m11.2.2" xref="S2.p2.11.m11.2.2.cmml"><mrow id="S2.p2.11.m11.1.1.1" xref="S2.p2.11.m11.1.1.1.cmml"><msub id="S2.p2.11.m11.1.1.1.3" xref="S2.p2.11.m11.1.1.1.3.cmml"><mi id="S2.p2.11.m11.1.1.1.3.2" xref="S2.p2.11.m11.1.1.1.3.2.cmml">p</mi><mi id="S2.p2.11.m11.1.1.1.3.3" xref="S2.p2.11.m11.1.1.1.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.11.m11.1.1.1.2" xref="S2.p2.11.m11.1.1.1.2.cmml">​</mo><mrow id="S2.p2.11.m11.1.1.1.1.1" xref="S2.p2.11.m11.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.11.m11.1.1.1.1.1.2" xref="S2.p2.11.m11.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.11.m11.1.1.1.1.1.1" xref="S2.p2.11.m11.1.1.1.1.1.1.cmml"><mi id="S2.p2.11.m11.1.1.1.1.1.1.2" xref="S2.p2.11.m11.1.1.1.1.1.1.2.cmml">o</mi><mo fence="false" id="S2.p2.11.m11.1.1.1.1.1.1.1" xref="S2.p2.11.m11.1.1.1.1.1.1.1.cmml">|</mo><msub id="S2.p2.11.m11.1.1.1.1.1.1.3" xref="S2.p2.11.m11.1.1.1.1.1.1.3.cmml"><mi id="S2.p2.11.m11.1.1.1.1.1.1.3.2" xref="S2.p2.11.m11.1.1.1.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.11.m11.1.1.1.1.1.1.3.3" xref="S2.p2.11.m11.1.1.1.1.1.1.3.3a.cmml">par</mtext></msub></mrow><mo stretchy="false" id="S2.p2.11.m11.1.1.1.1.1.3" xref="S2.p2.11.m11.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.p2.11.m11.2.2.3" xref="S2.p2.11.m11.2.2.3.cmml">&gt;</mo><mrow id="S2.p2.11.m11.2.2.2" xref="S2.p2.11.m11.2.2.2.cmml"><msub id="S2.p2.11.m11.2.2.2.3" xref="S2.p2.11.m11.2.2.2.3.cmml"><mi id="S2.p2.11.m11.2.2.2.3.2" xref="S2.p2.11.m11.2.2.2.3.2.cmml">p</mi><mi id="S2.p2.11.m11.2.2.2.3.3" xref="S2.p2.11.m11.2.2.2.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.11.m11.2.2.2.2" xref="S2.p2.11.m11.2.2.2.2.cmml">​</mo><mrow id="S2.p2.11.m11.2.2.2.1.1" xref="S2.p2.11.m11.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.p2.11.m11.2.2.2.1.1.2" xref="S2.p2.11.m11.2.2.2.1.1.1.cmml">(</mo><mrow id="S2.p2.11.m11.2.2.2.1.1.1" xref="S2.p2.11.m11.2.2.2.1.1.1.cmml"><msub id="S2.p2.11.m11.2.2.2.1.1.1.2" xref="S2.p2.11.m11.2.2.2.1.1.1.2.cmml"><mi id="S2.p2.11.m11.2.2.2.1.1.1.2.2" xref="S2.p2.11.m11.2.2.2.1.1.1.2.2.cmml">o</mi><mtext id="S2.p2.11.m11.2.2.2.1.1.1.2.3" xref="S2.p2.11.m11.2.2.2.1.1.1.2.3a.cmml">true</mtext></msub><mo fence="false" id="S2.p2.11.m11.2.2.2.1.1.1.1" xref="S2.p2.11.m11.2.2.2.1.1.1.1.cmml">|</mo><msub id="S2.p2.11.m11.2.2.2.1.1.1.3" xref="S2.p2.11.m11.2.2.2.1.1.1.3.cmml"><mi id="S2.p2.11.m11.2.2.2.1.1.1.3.2" xref="S2.p2.11.m11.2.2.2.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.11.m11.2.2.2.1.1.1.3.3" xref="S2.p2.11.m11.2.2.2.1.1.1.3.3a.cmml">par</mtext></msub></mrow><mo stretchy="false" id="S2.p2.11.m11.2.2.2.1.1.3" xref="S2.p2.11.m11.2.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.11.m11.2b"><apply id="S2.p2.11.m11.2.2.cmml" xref="S2.p2.11.m11.2.2"><gt id="S2.p2.11.m11.2.2.3.cmml" xref="S2.p2.11.m11.2.2.3"></gt><apply id="S2.p2.11.m11.1.1.1.cmml" xref="S2.p2.11.m11.1.1.1"><times id="S2.p2.11.m11.1.1.1.2.cmml" xref="S2.p2.11.m11.1.1.1.2"></times><apply id="S2.p2.11.m11.1.1.1.3.cmml" xref="S2.p2.11.m11.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.11.m11.1.1.1.3.1.cmml" xref="S2.p2.11.m11.1.1.1.3">subscript</csymbol><ci id="S2.p2.11.m11.1.1.1.3.2.cmml" xref="S2.p2.11.m11.1.1.1.3.2">𝑝</ci><ci id="S2.p2.11.m11.1.1.1.3.3.cmml" xref="S2.p2.11.m11.1.1.1.3.3">𝜃</ci></apply><apply id="S2.p2.11.m11.1.1.1.1.1.1.cmml" xref="S2.p2.11.m11.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.11.m11.1.1.1.1.1.1.1.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.1">conditional</csymbol><ci id="S2.p2.11.m11.1.1.1.1.1.1.2.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.2">𝑜</ci><apply id="S2.p2.11.m11.1.1.1.1.1.1.3.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.11.m11.1.1.1.1.1.1.3.1.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.3">subscript</csymbol><ci id="S2.p2.11.m11.1.1.1.1.1.1.3.2.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.3.2">𝜋</ci><ci id="S2.p2.11.m11.1.1.1.1.1.1.3.3a.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.11.m11.1.1.1.1.1.1.3.3.cmml" xref="S2.p2.11.m11.1.1.1.1.1.1.3.3">par</mtext></ci></apply></apply></apply><apply id="S2.p2.11.m11.2.2.2.cmml" xref="S2.p2.11.m11.2.2.2"><times id="S2.p2.11.m11.2.2.2.2.cmml" xref="S2.p2.11.m11.2.2.2.2"></times><apply id="S2.p2.11.m11.2.2.2.3.cmml" xref="S2.p2.11.m11.2.2.2.3"><csymbol cd="ambiguous" id="S2.p2.11.m11.2.2.2.3.1.cmml" xref="S2.p2.11.m11.2.2.2.3">subscript</csymbol><ci id="S2.p2.11.m11.2.2.2.3.2.cmml" xref="S2.p2.11.m11.2.2.2.3.2">𝑝</ci><ci id="S2.p2.11.m11.2.2.2.3.3.cmml" xref="S2.p2.11.m11.2.2.2.3.3">𝜃</ci></apply><apply id="S2.p2.11.m11.2.2.2.1.1.1.cmml" xref="S2.p2.11.m11.2.2.2.1.1"><csymbol cd="latexml" id="S2.p2.11.m11.2.2.2.1.1.1.1.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.1">conditional</csymbol><apply id="S2.p2.11.m11.2.2.2.1.1.1.2.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.2"><csymbol cd="ambiguous" id="S2.p2.11.m11.2.2.2.1.1.1.2.1.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.2">subscript</csymbol><ci id="S2.p2.11.m11.2.2.2.1.1.1.2.2.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.2.2">𝑜</ci><ci id="S2.p2.11.m11.2.2.2.1.1.1.2.3a.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.2.3"><mtext mathsize="70%" id="S2.p2.11.m11.2.2.2.1.1.1.2.3.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.2.3">true</mtext></ci></apply><apply id="S2.p2.11.m11.2.2.2.1.1.1.3.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.11.m11.2.2.2.1.1.1.3.1.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.3">subscript</csymbol><ci id="S2.p2.11.m11.2.2.2.1.1.1.3.2.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.3.2">𝜋</ci><ci id="S2.p2.11.m11.2.2.2.1.1.1.3.3a.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.11.m11.2.2.2.1.1.1.3.3.cmml" xref="S2.p2.11.m11.2.2.2.1.1.1.3.3">par</mtext></ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.11.m11.2c">p_{\theta}(o|\pi_{\text{par}})&gt;p_{\theta}(o_{\text{true}}|\pi_{\text{par}})</annotation></semantics></math>
where <math id="S2.p2.12.m12.1" class="ltx_Math" alttext="o_{\text{true}}" display="inline"><semantics id="S2.p2.12.m12.1a"><msub id="S2.p2.12.m12.1.1" xref="S2.p2.12.m12.1.1.cmml"><mi id="S2.p2.12.m12.1.1.2" xref="S2.p2.12.m12.1.1.2.cmml">o</mi><mtext id="S2.p2.12.m12.1.1.3" xref="S2.p2.12.m12.1.1.3a.cmml">true</mtext></msub><annotation-xml encoding="MathML-Content" id="S2.p2.12.m12.1b"><apply id="S2.p2.12.m12.1.1.cmml" xref="S2.p2.12.m12.1.1"><csymbol cd="ambiguous" id="S2.p2.12.m12.1.1.1.cmml" xref="S2.p2.12.m12.1.1">subscript</csymbol><ci id="S2.p2.12.m12.1.1.2.cmml" xref="S2.p2.12.m12.1.1.2">𝑜</ci><ci id="S2.p2.12.m12.1.1.3a.cmml" xref="S2.p2.12.m12.1.1.3"><mtext mathsize="70%" id="S2.p2.12.m12.1.1.3.cmml" xref="S2.p2.12.m12.1.1.3">true</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.12.m12.1c">o_{\text{true}}</annotation></semantics></math> is a true object for <math id="S2.p2.13.m13.2" class="ltx_Math" alttext="(\pi,o)\in\mathcal{E}" display="inline"><semantics id="S2.p2.13.m13.2a"><mrow id="S2.p2.13.m13.2.3" xref="S2.p2.13.m13.2.3.cmml"><mrow id="S2.p2.13.m13.2.3.2.2" xref="S2.p2.13.m13.2.3.2.1.cmml"><mo stretchy="false" id="S2.p2.13.m13.2.3.2.2.1" xref="S2.p2.13.m13.2.3.2.1.cmml">(</mo><mi id="S2.p2.13.m13.1.1" xref="S2.p2.13.m13.1.1.cmml">π</mi><mo id="S2.p2.13.m13.2.3.2.2.2" xref="S2.p2.13.m13.2.3.2.1.cmml">,</mo><mi id="S2.p2.13.m13.2.2" xref="S2.p2.13.m13.2.2.cmml">o</mi><mo stretchy="false" id="S2.p2.13.m13.2.3.2.2.3" xref="S2.p2.13.m13.2.3.2.1.cmml">)</mo></mrow><mo id="S2.p2.13.m13.2.3.1" xref="S2.p2.13.m13.2.3.1.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S2.p2.13.m13.2.3.3" xref="S2.p2.13.m13.2.3.3.cmml">ℰ</mi></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.13.m13.2b"><apply id="S2.p2.13.m13.2.3.cmml" xref="S2.p2.13.m13.2.3"><in id="S2.p2.13.m13.2.3.1.cmml" xref="S2.p2.13.m13.2.3.1"></in><interval closure="open" id="S2.p2.13.m13.2.3.2.1.cmml" xref="S2.p2.13.m13.2.3.2.2"><ci id="S2.p2.13.m13.1.1.cmml" xref="S2.p2.13.m13.1.1">𝜋</ci><ci id="S2.p2.13.m13.2.2.cmml" xref="S2.p2.13.m13.2.2">𝑜</ci></interval><ci id="S2.p2.13.m13.2.3.3.cmml" xref="S2.p2.13.m13.2.3.3">ℰ</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.13.m13.2c">(\pi,o)\in\mathcal{E}</annotation></semantics></math>
(e.g., “Apple” in “TextEdit, a product of Nintendo”).
Locality measures the accuracy of <math id="S2.p2.14.m14.2" class="ltx_Math" alttext="p_{\theta}(o_{\text{true}}|\pi_{\text{nb}})&gt;p_{\theta}(o|\pi_{\text{nb}})" display="inline"><semantics id="S2.p2.14.m14.2a"><mrow id="S2.p2.14.m14.2.2" xref="S2.p2.14.m14.2.2.cmml"><mrow id="S2.p2.14.m14.1.1.1" xref="S2.p2.14.m14.1.1.1.cmml"><msub id="S2.p2.14.m14.1.1.1.3" xref="S2.p2.14.m14.1.1.1.3.cmml"><mi id="S2.p2.14.m14.1.1.1.3.2" xref="S2.p2.14.m14.1.1.1.3.2.cmml">p</mi><mi id="S2.p2.14.m14.1.1.1.3.3" xref="S2.p2.14.m14.1.1.1.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.14.m14.1.1.1.2" xref="S2.p2.14.m14.1.1.1.2.cmml">​</mo><mrow id="S2.p2.14.m14.1.1.1.1.1" xref="S2.p2.14.m14.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.14.m14.1.1.1.1.1.2" xref="S2.p2.14.m14.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.14.m14.1.1.1.1.1.1" xref="S2.p2.14.m14.1.1.1.1.1.1.cmml"><msub id="S2.p2.14.m14.1.1.1.1.1.1.2" xref="S2.p2.14.m14.1.1.1.1.1.1.2.cmml"><mi id="S2.p2.14.m14.1.1.1.1.1.1.2.2" xref="S2.p2.14.m14.1.1.1.1.1.1.2.2.cmml">o</mi><mtext id="S2.p2.14.m14.1.1.1.1.1.1.2.3" xref="S2.p2.14.m14.1.1.1.1.1.1.2.3a.cmml">true</mtext></msub><mo fence="false" id="S2.p2.14.m14.1.1.1.1.1.1.1" xref="S2.p2.14.m14.1.1.1.1.1.1.1.cmml">|</mo><msub id="S2.p2.14.m14.1.1.1.1.1.1.3" xref="S2.p2.14.m14.1.1.1.1.1.1.3.cmml"><mi id="S2.p2.14.m14.1.1.1.1.1.1.3.2" xref="S2.p2.14.m14.1.1.1.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.14.m14.1.1.1.1.1.1.3.3" xref="S2.p2.14.m14.1.1.1.1.1.1.3.3a.cmml">nb</mtext></msub></mrow><mo stretchy="false" id="S2.p2.14.m14.1.1.1.1.1.3" xref="S2.p2.14.m14.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.p2.14.m14.2.2.3" xref="S2.p2.14.m14.2.2.3.cmml">&gt;</mo><mrow id="S2.p2.14.m14.2.2.2" xref="S2.p2.14.m14.2.2.2.cmml"><msub id="S2.p2.14.m14.2.2.2.3" xref="S2.p2.14.m14.2.2.2.3.cmml"><mi id="S2.p2.14.m14.2.2.2.3.2" xref="S2.p2.14.m14.2.2.2.3.2.cmml">p</mi><mi id="S2.p2.14.m14.2.2.2.3.3" xref="S2.p2.14.m14.2.2.2.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S2.p2.14.m14.2.2.2.2" xref="S2.p2.14.m14.2.2.2.2.cmml">​</mo><mrow id="S2.p2.14.m14.2.2.2.1.1" xref="S2.p2.14.m14.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.p2.14.m14.2.2.2.1.1.2" xref="S2.p2.14.m14.2.2.2.1.1.1.cmml">(</mo><mrow id="S2.p2.14.m14.2.2.2.1.1.1" xref="S2.p2.14.m14.2.2.2.1.1.1.cmml"><mi id="S2.p2.14.m14.2.2.2.1.1.1.2" xref="S2.p2.14.m14.2.2.2.1.1.1.2.cmml">o</mi><mo fence="false" id="S2.p2.14.m14.2.2.2.1.1.1.1" xref="S2.p2.14.m14.2.2.2.1.1.1.1.cmml">|</mo><msub id="S2.p2.14.m14.2.2.2.1.1.1.3" xref="S2.p2.14.m14.2.2.2.1.1.1.3.cmml"><mi id="S2.p2.14.m14.2.2.2.1.1.1.3.2" xref="S2.p2.14.m14.2.2.2.1.1.1.3.2.cmml">π</mi><mtext id="S2.p2.14.m14.2.2.2.1.1.1.3.3" xref="S2.p2.14.m14.2.2.2.1.1.1.3.3a.cmml">nb</mtext></msub></mrow><mo stretchy="false" id="S2.p2.14.m14.2.2.2.1.1.3" xref="S2.p2.14.m14.2.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.p2.14.m14.2b"><apply id="S2.p2.14.m14.2.2.cmml" xref="S2.p2.14.m14.2.2"><gt id="S2.p2.14.m14.2.2.3.cmml" xref="S2.p2.14.m14.2.2.3"></gt><apply id="S2.p2.14.m14.1.1.1.cmml" xref="S2.p2.14.m14.1.1.1"><times id="S2.p2.14.m14.1.1.1.2.cmml" xref="S2.p2.14.m14.1.1.1.2"></times><apply id="S2.p2.14.m14.1.1.1.3.cmml" xref="S2.p2.14.m14.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.14.m14.1.1.1.3.1.cmml" xref="S2.p2.14.m14.1.1.1.3">subscript</csymbol><ci id="S2.p2.14.m14.1.1.1.3.2.cmml" xref="S2.p2.14.m14.1.1.1.3.2">𝑝</ci><ci id="S2.p2.14.m14.1.1.1.3.3.cmml" xref="S2.p2.14.m14.1.1.1.3.3">𝜃</ci></apply><apply id="S2.p2.14.m14.1.1.1.1.1.1.cmml" xref="S2.p2.14.m14.1.1.1.1.1"><csymbol cd="latexml" id="S2.p2.14.m14.1.1.1.1.1.1.1.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.1">conditional</csymbol><apply id="S2.p2.14.m14.1.1.1.1.1.1.2.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.2"><csymbol cd="ambiguous" id="S2.p2.14.m14.1.1.1.1.1.1.2.1.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.2">subscript</csymbol><ci id="S2.p2.14.m14.1.1.1.1.1.1.2.2.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.2.2">𝑜</ci><ci id="S2.p2.14.m14.1.1.1.1.1.1.2.3a.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.2.3"><mtext mathsize="70%" id="S2.p2.14.m14.1.1.1.1.1.1.2.3.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.2.3">true</mtext></ci></apply><apply id="S2.p2.14.m14.1.1.1.1.1.1.3.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.14.m14.1.1.1.1.1.1.3.1.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.3">subscript</csymbol><ci id="S2.p2.14.m14.1.1.1.1.1.1.3.2.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.3.2">𝜋</ci><ci id="S2.p2.14.m14.1.1.1.1.1.1.3.3a.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.14.m14.1.1.1.1.1.1.3.3.cmml" xref="S2.p2.14.m14.1.1.1.1.1.1.3.3">nb</mtext></ci></apply></apply></apply><apply id="S2.p2.14.m14.2.2.2.cmml" xref="S2.p2.14.m14.2.2.2"><times id="S2.p2.14.m14.2.2.2.2.cmml" xref="S2.p2.14.m14.2.2.2.2"></times><apply id="S2.p2.14.m14.2.2.2.3.cmml" xref="S2.p2.14.m14.2.2.2.3"><csymbol cd="ambiguous" id="S2.p2.14.m14.2.2.2.3.1.cmml" xref="S2.p2.14.m14.2.2.2.3">subscript</csymbol><ci id="S2.p2.14.m14.2.2.2.3.2.cmml" xref="S2.p2.14.m14.2.2.2.3.2">𝑝</ci><ci id="S2.p2.14.m14.2.2.2.3.3.cmml" xref="S2.p2.14.m14.2.2.2.3.3">𝜃</ci></apply><apply id="S2.p2.14.m14.2.2.2.1.1.1.cmml" xref="S2.p2.14.m14.2.2.2.1.1"><csymbol cd="latexml" id="S2.p2.14.m14.2.2.2.1.1.1.1.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.1">conditional</csymbol><ci id="S2.p2.14.m14.2.2.2.1.1.1.2.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.2">𝑜</ci><apply id="S2.p2.14.m14.2.2.2.1.1.1.3.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.3"><csymbol cd="ambiguous" id="S2.p2.14.m14.2.2.2.1.1.1.3.1.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.3">subscript</csymbol><ci id="S2.p2.14.m14.2.2.2.1.1.1.3.2.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.3.2">𝜋</ci><ci id="S2.p2.14.m14.2.2.2.1.1.1.3.3a.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.3.3"><mtext mathsize="70%" id="S2.p2.14.m14.2.2.2.1.1.1.3.3.cmml" xref="S2.p2.14.m14.2.2.2.1.1.1.3.3">nb</mtext></ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.14.m14.2c">p_{\theta}(o_{\text{true}}|\pi_{\text{nb}})&gt;p_{\theta}(o|\pi_{\text{nb}})</annotation></semantics></math>
where <math id="S2.p2.15.m15.1" class="ltx_Math" alttext="\pi_{\text{nb}}" display="inline"><semantics id="S2.p2.15.m15.1a"><msub id="S2.p2.15.m15.1.1" xref="S2.p2.15.m15.1.1.cmml"><mi id="S2.p2.15.m15.1.1.2" xref="S2.p2.15.m15.1.1.2.cmml">π</mi><mtext id="S2.p2.15.m15.1.1.3" xref="S2.p2.15.m15.1.1.3a.cmml">nb</mtext></msub><annotation-xml encoding="MathML-Content" id="S2.p2.15.m15.1b"><apply id="S2.p2.15.m15.1.1.cmml" xref="S2.p2.15.m15.1.1"><csymbol cd="ambiguous" id="S2.p2.15.m15.1.1.1.cmml" xref="S2.p2.15.m15.1.1">subscript</csymbol><ci id="S2.p2.15.m15.1.1.2.cmml" xref="S2.p2.15.m15.1.1.2">𝜋</ci><ci id="S2.p2.15.m15.1.1.3a.cmml" xref="S2.p2.15.m15.1.1.3"><mtext mathsize="70%" id="S2.p2.15.m15.1.1.3.cmml" xref="S2.p2.15.m15.1.1.3">nb</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.15.m15.1c">\pi_{\text{nb}}</annotation></semantics></math> is a “neighbhorhood” prompt whose target must remain unchanged from <math id="S2.p2.16.m16.1" class="ltx_Math" alttext="o_{\text{true}}" display="inline"><semantics id="S2.p2.16.m16.1a"><msub id="S2.p2.16.m16.1.1" xref="S2.p2.16.m16.1.1.cmml"><mi id="S2.p2.16.m16.1.1.2" xref="S2.p2.16.m16.1.1.2.cmml">o</mi><mtext id="S2.p2.16.m16.1.1.3" xref="S2.p2.16.m16.1.1.3a.cmml">true</mtext></msub><annotation-xml encoding="MathML-Content" id="S2.p2.16.m16.1b"><apply id="S2.p2.16.m16.1.1.cmml" xref="S2.p2.16.m16.1.1"><csymbol cd="ambiguous" id="S2.p2.16.m16.1.1.1.cmml" xref="S2.p2.16.m16.1.1">subscript</csymbol><ci id="S2.p2.16.m16.1.1.2.cmml" xref="S2.p2.16.m16.1.1.2">𝑜</ci><ci id="S2.p2.16.m16.1.1.3a.cmml" xref="S2.p2.16.m16.1.1.3"><mtext mathsize="70%" id="S2.p2.16.m16.1.1.3.cmml" xref="S2.p2.16.m16.1.1.3">true</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.16.m16.1c">o_{\text{true}}</annotation></semantics></math>
(e.g., “Macintosh File System, a product of” <math id="S2.p2.17.m17.1" class="ltx_Math" alttext="\rightarrow" display="inline"><semantics id="S2.p2.17.m17.1a"><mo stretchy="false" id="S2.p2.17.m17.1.1" xref="S2.p2.17.m17.1.1.cmml">→</mo><annotation-xml encoding="MathML-Content" id="S2.p2.17.m17.1b"><ci id="S2.p2.17.m17.1.1.cmml" xref="S2.p2.17.m17.1.1">→</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.p2.17.m17.1c">\rightarrow</annotation></semantics></math> “Apple”).
In both datasets, the final <span id="S2.p2.17.2" class="ltx_text ltx_font_bold">edit score</span> is the harmonic mean of
efficacy, generalization, and locality.</p>
</div>
<div id="S2.p3" class="ltx_para">
<p id="S2.p3.1" class="ltx_p">It is well known that naive fine-tuning, namely just optimizing</p>
</div>
<div id="S2.p4" class="ltx_para">
<table id="Sx1.EGx1" class="ltx_equationgroup ltx_eqn_align ltx_eqn_table">

<tbody id="S2.E1"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline">
<td class="ltx_eqn_cell ltx_eqn_center_padleft"></td>
<td class="ltx_td ltx_align_right ltx_eqn_cell"><math id="S2.E1.m1.1" class="ltx_Math" alttext="\displaystyle\min_{\theta}\;-\sum_{x\in\mathcal{E}}\;\log p_{\theta}(x)" display="inline"><semantics id="S2.E1.m1.1a"><mrow id="S2.E1.m1.1.2" xref="S2.E1.m1.1.2.cmml"><munder id="S2.E1.m1.1.2.2" xref="S2.E1.m1.1.2.2.cmml"><mi id="S2.E1.m1.1.2.2.2" xref="S2.E1.m1.1.2.2.2.cmml">min</mi><mi id="S2.E1.m1.1.2.2.3" xref="S2.E1.m1.1.2.2.3.cmml">θ</mi></munder><mo lspace="0.280em" id="S2.E1.m1.1.2.1" xref="S2.E1.m1.1.2.1.cmml">−</mo><mrow id="S2.E1.m1.1.2.3" xref="S2.E1.m1.1.2.3.cmml"><mstyle displaystyle="true" id="S2.E1.m1.1.2.3.1" xref="S2.E1.m1.1.2.3.1.cmml"><munder id="S2.E1.m1.1.2.3.1a" xref="S2.E1.m1.1.2.3.1.cmml"><mo movablelimits="false" id="S2.E1.m1.1.2.3.1.2" xref="S2.E1.m1.1.2.3.1.2.cmml">∑</mo><mrow id="S2.E1.m1.1.2.3.1.3" xref="S2.E1.m1.1.2.3.1.3.cmml"><mi id="S2.E1.m1.1.2.3.1.3.2" xref="S2.E1.m1.1.2.3.1.3.2.cmml">x</mi><mo id="S2.E1.m1.1.2.3.1.3.1" xref="S2.E1.m1.1.2.3.1.3.1.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S2.E1.m1.1.2.3.1.3.3" xref="S2.E1.m1.1.2.3.1.3.3.cmml">ℰ</mi></mrow></munder></mstyle><mrow id="S2.E1.m1.1.2.3.2" xref="S2.E1.m1.1.2.3.2.cmml"><mrow id="S2.E1.m1.1.2.3.2.2" xref="S2.E1.m1.1.2.3.2.2.cmml"><mi id="S2.E1.m1.1.2.3.2.2.1" xref="S2.E1.m1.1.2.3.2.2.1.cmml">log</mi><mo lspace="0.167em" id="S2.E1.m1.1.2.3.2.2a" xref="S2.E1.m1.1.2.3.2.2.cmml">⁡</mo><msub id="S2.E1.m1.1.2.3.2.2.2" xref="S2.E1.m1.1.2.3.2.2.2.cmml"><mi id="S2.E1.m1.1.2.3.2.2.2.2" xref="S2.E1.m1.1.2.3.2.2.2.2.cmml">p</mi><mi id="S2.E1.m1.1.2.3.2.2.2.3" xref="S2.E1.m1.1.2.3.2.2.2.3.cmml">θ</mi></msub></mrow><mo lspace="0em" rspace="0em" id="S2.E1.m1.1.2.3.2.1" xref="S2.E1.m1.1.2.3.2.1.cmml">​</mo><mrow id="S2.E1.m1.1.2.3.2.3.2" xref="S2.E1.m1.1.2.3.2.cmml"><mo stretchy="false" id="S2.E1.m1.1.2.3.2.3.2.1" xref="S2.E1.m1.1.2.3.2.cmml">(</mo><mi id="S2.E1.m1.1.1" xref="S2.E1.m1.1.1.cmml">x</mi><mo stretchy="false" id="S2.E1.m1.1.2.3.2.3.2.2" xref="S2.E1.m1.1.2.3.2.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.E1.m1.1b"><apply id="S2.E1.m1.1.2.cmml" xref="S2.E1.m1.1.2"><minus id="S2.E1.m1.1.2.1.cmml" xref="S2.E1.m1.1.2.1"></minus><apply id="S2.E1.m1.1.2.2.cmml" xref="S2.E1.m1.1.2.2"><csymbol cd="ambiguous" id="S2.E1.m1.1.2.2.1.cmml" xref="S2.E1.m1.1.2.2">subscript</csymbol><min id="S2.E1.m1.1.2.2.2.cmml" xref="S2.E1.m1.1.2.2.2"></min><ci id="S2.E1.m1.1.2.2.3.cmml" xref="S2.E1.m1.1.2.2.3">𝜃</ci></apply><apply id="S2.E1.m1.1.2.3.cmml" xref="S2.E1.m1.1.2.3"><apply id="S2.E1.m1.1.2.3.1.cmml" xref="S2.E1.m1.1.2.3.1"><csymbol cd="ambiguous" id="S2.E1.m1.1.2.3.1.1.cmml" xref="S2.E1.m1.1.2.3.1">subscript</csymbol><sum id="S2.E1.m1.1.2.3.1.2.cmml" xref="S2.E1.m1.1.2.3.1.2"></sum><apply id="S2.E1.m1.1.2.3.1.3.cmml" xref="S2.E1.m1.1.2.3.1.3"><in id="S2.E1.m1.1.2.3.1.3.1.cmml" xref="S2.E1.m1.1.2.3.1.3.1"></in><ci id="S2.E1.m1.1.2.3.1.3.2.cmml" xref="S2.E1.m1.1.2.3.1.3.2">𝑥</ci><ci id="S2.E1.m1.1.2.3.1.3.3.cmml" xref="S2.E1.m1.1.2.3.1.3.3">ℰ</ci></apply></apply><apply id="S2.E1.m1.1.2.3.2.cmml" xref="S2.E1.m1.1.2.3.2"><times id="S2.E1.m1.1.2.3.2.1.cmml" xref="S2.E1.m1.1.2.3.2.1"></times><apply id="S2.E1.m1.1.2.3.2.2.cmml" xref="S2.E1.m1.1.2.3.2.2"><log id="S2.E1.m1.1.2.3.2.2.1.cmml" xref="S2.E1.m1.1.2.3.2.2.1"></log><apply id="S2.E1.m1.1.2.3.2.2.2.cmml" xref="S2.E1.m1.1.2.3.2.2.2"><csymbol cd="ambiguous" id="S2.E1.m1.1.2.3.2.2.2.1.cmml" xref="S2.E1.m1.1.2.3.2.2.2">subscript</csymbol><ci id="S2.E1.m1.1.2.3.2.2.2.2.cmml" xref="S2.E1.m1.1.2.3.2.2.2.2">𝑝</ci><ci id="S2.E1.m1.1.2.3.2.2.2.3.cmml" xref="S2.E1.m1.1.2.3.2.2.2.3">𝜃</ci></apply></apply><ci id="S2.E1.m1.1.1.cmml" xref="S2.E1.m1.1.1">𝑥</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.E1.m1.1c">\displaystyle\min_{\theta}\;-\sum_{x\in\mathcal{E}}\;\log p_{\theta}(x)</annotation></semantics></math></td>
<td class="ltx_eqn_cell ltx_eqn_center_padright"></td>
<td rowspan="1" class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right"><span class="ltx_tag ltx_tag_equation ltx_align_right">(1)</span></td>
</tr></tbody>
</table>
</div>
<div id="S2.p5" class="ltx_para ltx_noindent">
<p id="S2.p5.1" class="ltx_p">results in a poor editing score. The main reason is that while it
improves efficacy and possibly even generalization, it harms locality by changing the
model’s predictions on unrelated or neighborhood prompts.
This led to the development of highly specialized editing methods,
with the implicit assumption that fine-tuning is not effective for model editing.</p>
</div>
</section>
<section id="S3" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">3 </span>Method</h2>

<div id="S3.p1" class="ltx_para">
<p id="S3.p1.1" class="ltx_p">We propose a purely fine-tuning-based method that achieves a competitive editing score.
Our objective is a slight variation of (<a href="#S2.E1" title="In 2 Task ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">1</span></a>):</p>
</div>
<div id="S3.p2" class="ltx_para">
<table id="Sx1.EGx2" class="ltx_equationgroup ltx_eqn_align ltx_eqn_table">

<tbody id="S3.E2"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline">
<td class="ltx_eqn_cell ltx_eqn_center_padleft"></td>
<td class="ltx_td ltx_align_right ltx_eqn_cell"><math id="S3.E2.m1.3" class="ltx_Math" alttext="\displaystyle\min_{\theta}\;-\sum_{(\pi,o)\in\mathcal{E}\cup\mathcal{P}\cup\mathcal{R}}\;\log p_{\theta}(o|\pi)" display="inline"><semantics id="S3.E2.m1.3a"><mrow id="S3.E2.m1.3.3" xref="S3.E2.m1.3.3.cmml"><munder id="S3.E2.m1.3.3.3" xref="S3.E2.m1.3.3.3.cmml"><mi id="S3.E2.m1.3.3.3.2" xref="S3.E2.m1.3.3.3.2.cmml">min</mi><mi id="S3.E2.m1.3.3.3.3" xref="S3.E2.m1.3.3.3.3.cmml">θ</mi></munder><mo lspace="0.280em" id="S3.E2.m1.3.3.2" xref="S3.E2.m1.3.3.2.cmml">−</mo><mrow id="S3.E2.m1.3.3.1" xref="S3.E2.m1.3.3.1.cmml"><mstyle displaystyle="true" id="S3.E2.m1.3.3.1.2" xref="S3.E2.m1.3.3.1.2.cmml"><munder id="S3.E2.m1.3.3.1.2a" xref="S3.E2.m1.3.3.1.2.cmml"><mo movablelimits="false" id="S3.E2.m1.3.3.1.2.2" xref="S3.E2.m1.3.3.1.2.2.cmml">∑</mo><mrow id="S3.E2.m1.2.2.2" xref="S3.E2.m1.2.2.2.cmml"><mrow id="S3.E2.m1.2.2.2.4.2" xref="S3.E2.m1.2.2.2.4.1.cmml"><mo stretchy="false" id="S3.E2.m1.2.2.2.4.2.1" xref="S3.E2.m1.2.2.2.4.1.cmml">(</mo><mi id="S3.E2.m1.1.1.1.1" xref="S3.E2.m1.1.1.1.1.cmml">π</mi><mo id="S3.E2.m1.2.2.2.4.2.2" xref="S3.E2.m1.2.2.2.4.1.cmml">,</mo><mi id="S3.E2.m1.2.2.2.2" xref="S3.E2.m1.2.2.2.2.cmml">o</mi><mo stretchy="false" id="S3.E2.m1.2.2.2.4.2.3" xref="S3.E2.m1.2.2.2.4.1.cmml">)</mo></mrow><mo id="S3.E2.m1.2.2.2.3" xref="S3.E2.m1.2.2.2.3.cmml">∈</mo><mrow id="S3.E2.m1.2.2.2.5" xref="S3.E2.m1.2.2.2.5.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.E2.m1.2.2.2.5.2" xref="S3.E2.m1.2.2.2.5.2.cmml">ℰ</mi><mo id="S3.E2.m1.2.2.2.5.1" xref="S3.E2.m1.2.2.2.5.1.cmml">∪</mo><mi class="ltx_font_mathcaligraphic" id="S3.E2.m1.2.2.2.5.3" xref="S3.E2.m1.2.2.2.5.3.cmml">𝒫</mi><mo id="S3.E2.m1.2.2.2.5.1a" xref="S3.E2.m1.2.2.2.5.1.cmml">∪</mo><mi class="ltx_font_mathcaligraphic" id="S3.E2.m1.2.2.2.5.4" xref="S3.E2.m1.2.2.2.5.4.cmml">ℛ</mi></mrow></mrow></munder></mstyle><mrow id="S3.E2.m1.3.3.1.1" xref="S3.E2.m1.3.3.1.1.cmml"><mrow id="S3.E2.m1.3.3.1.1.3" xref="S3.E2.m1.3.3.1.1.3.cmml"><mi id="S3.E2.m1.3.3.1.1.3.1" xref="S3.E2.m1.3.3.1.1.3.1.cmml">log</mi><mo lspace="0.167em" id="S3.E2.m1.3.3.1.1.3a" xref="S3.E2.m1.3.3.1.1.3.cmml">⁡</mo><msub id="S3.E2.m1.3.3.1.1.3.2" xref="S3.E2.m1.3.3.1.1.3.2.cmml"><mi id="S3.E2.m1.3.3.1.1.3.2.2" xref="S3.E2.m1.3.3.1.1.3.2.2.cmml">p</mi><mi id="S3.E2.m1.3.3.1.1.3.2.3" xref="S3.E2.m1.3.3.1.1.3.2.3.cmml">θ</mi></msub></mrow><mo lspace="0em" rspace="0em" id="S3.E2.m1.3.3.1.1.2" xref="S3.E2.m1.3.3.1.1.2.cmml">​</mo><mrow id="S3.E2.m1.3.3.1.1.1.1" xref="S3.E2.m1.3.3.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E2.m1.3.3.1.1.1.1.2" xref="S3.E2.m1.3.3.1.1.1.1.1.cmml">(</mo><mrow id="S3.E2.m1.3.3.1.1.1.1.1" xref="S3.E2.m1.3.3.1.1.1.1.1.cmml"><mi id="S3.E2.m1.3.3.1.1.1.1.1.2" xref="S3.E2.m1.3.3.1.1.1.1.1.2.cmml">o</mi><mo fence="false" id="S3.E2.m1.3.3.1.1.1.1.1.1" xref="S3.E2.m1.3.3.1.1.1.1.1.1.cmml">|</mo><mi id="S3.E2.m1.3.3.1.1.1.1.1.3" xref="S3.E2.m1.3.3.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S3.E2.m1.3.3.1.1.1.1.3" xref="S3.E2.m1.3.3.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.E2.m1.3b"><apply id="S3.E2.m1.3.3.cmml" xref="S3.E2.m1.3.3"><minus id="S3.E2.m1.3.3.2.cmml" xref="S3.E2.m1.3.3.2"></minus><apply id="S3.E2.m1.3.3.3.cmml" xref="S3.E2.m1.3.3.3"><csymbol cd="ambiguous" id="S3.E2.m1.3.3.3.1.cmml" xref="S3.E2.m1.3.3.3">subscript</csymbol><min id="S3.E2.m1.3.3.3.2.cmml" xref="S3.E2.m1.3.3.3.2"></min><ci id="S3.E2.m1.3.3.3.3.cmml" xref="S3.E2.m1.3.3.3.3">𝜃</ci></apply><apply id="S3.E2.m1.3.3.1.cmml" xref="S3.E2.m1.3.3.1"><apply id="S3.E2.m1.3.3.1.2.cmml" xref="S3.E2.m1.3.3.1.2"><csymbol cd="ambiguous" id="S3.E2.m1.3.3.1.2.1.cmml" xref="S3.E2.m1.3.3.1.2">subscript</csymbol><sum id="S3.E2.m1.3.3.1.2.2.cmml" xref="S3.E2.m1.3.3.1.2.2"></sum><apply id="S3.E2.m1.2.2.2.cmml" xref="S3.E2.m1.2.2.2"><in id="S3.E2.m1.2.2.2.3.cmml" xref="S3.E2.m1.2.2.2.3"></in><interval closure="open" id="S3.E2.m1.2.2.2.4.1.cmml" xref="S3.E2.m1.2.2.2.4.2"><ci id="S3.E2.m1.1.1.1.1.cmml" xref="S3.E2.m1.1.1.1.1">𝜋</ci><ci id="S3.E2.m1.2.2.2.2.cmml" xref="S3.E2.m1.2.2.2.2">𝑜</ci></interval><apply id="S3.E2.m1.2.2.2.5.cmml" xref="S3.E2.m1.2.2.2.5"><union id="S3.E2.m1.2.2.2.5.1.cmml" xref="S3.E2.m1.2.2.2.5.1"></union><ci id="S3.E2.m1.2.2.2.5.2.cmml" xref="S3.E2.m1.2.2.2.5.2">ℰ</ci><ci id="S3.E2.m1.2.2.2.5.3.cmml" xref="S3.E2.m1.2.2.2.5.3">𝒫</ci><ci id="S3.E2.m1.2.2.2.5.4.cmml" xref="S3.E2.m1.2.2.2.5.4">ℛ</ci></apply></apply></apply><apply id="S3.E2.m1.3.3.1.1.cmml" xref="S3.E2.m1.3.3.1.1"><times id="S3.E2.m1.3.3.1.1.2.cmml" xref="S3.E2.m1.3.3.1.1.2"></times><apply id="S3.E2.m1.3.3.1.1.3.cmml" xref="S3.E2.m1.3.3.1.1.3"><log id="S3.E2.m1.3.3.1.1.3.1.cmml" xref="S3.E2.m1.3.3.1.1.3.1"></log><apply id="S3.E2.m1.3.3.1.1.3.2.cmml" xref="S3.E2.m1.3.3.1.1.3.2"><csymbol cd="ambiguous" id="S3.E2.m1.3.3.1.1.3.2.1.cmml" xref="S3.E2.m1.3.3.1.1.3.2">subscript</csymbol><ci id="S3.E2.m1.3.3.1.1.3.2.2.cmml" xref="S3.E2.m1.3.3.1.1.3.2.2">𝑝</ci><ci id="S3.E2.m1.3.3.1.1.3.2.3.cmml" xref="S3.E2.m1.3.3.1.1.3.2.3">𝜃</ci></apply></apply><apply id="S3.E2.m1.3.3.1.1.1.1.1.cmml" xref="S3.E2.m1.3.3.1.1.1.1"><csymbol cd="latexml" id="S3.E2.m1.3.3.1.1.1.1.1.1.cmml" xref="S3.E2.m1.3.3.1.1.1.1.1.1">conditional</csymbol><ci id="S3.E2.m1.3.3.1.1.1.1.1.2.cmml" xref="S3.E2.m1.3.3.1.1.1.1.1.2">𝑜</ci><ci id="S3.E2.m1.3.3.1.1.1.1.1.3.cmml" xref="S3.E2.m1.3.3.1.1.1.1.1.3">𝜋</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E2.m1.3c">\displaystyle\min_{\theta}\;-\sum_{(\pi,o)\in\mathcal{E}\cup\mathcal{P}\cup\mathcal{R}}\;\log p_{\theta}(o|\pi)</annotation></semantics></math></td>
<td class="ltx_eqn_cell ltx_eqn_center_padright"></td>
<td rowspan="1" class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right"><span class="ltx_tag ltx_tag_equation ltx_align_right">(2)</span></td>
</tr></tbody>
</table>
</div>
<div id="S3.p3" class="ltx_para ltx_noindent">
<p id="S3.p3.1" class="ltx_p">There are two small but important differences between (<a href="#S2.E1" title="In 2 Task ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">1</span></a>) and (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>).
First, we optimize the <em id="S3.p3.1.1" class="ltx_emph ltx_font_italic">conditional</em> likelihood of the edit target <math id="S3.p3.1.m1.1" class="ltx_Math" alttext="o|\pi" display="inline"><semantics id="S3.p3.1.m1.1a"><mrow id="S3.p3.1.m1.1.1" xref="S3.p3.1.m1.1.1.cmml"><mi id="S3.p3.1.m1.1.1.2" xref="S3.p3.1.m1.1.1.2.cmml">o</mi><mo fence="false" id="S3.p3.1.m1.1.1.1" xref="S3.p3.1.m1.1.1.1.cmml">|</mo><mi id="S3.p3.1.m1.1.1.3" xref="S3.p3.1.m1.1.1.3.cmml">π</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.p3.1.m1.1b"><apply id="S3.p3.1.m1.1.1.cmml" xref="S3.p3.1.m1.1.1"><csymbol cd="latexml" id="S3.p3.1.m1.1.1.1.cmml" xref="S3.p3.1.m1.1.1.1">conditional</csymbol><ci id="S3.p3.1.m1.1.1.2.cmml" xref="S3.p3.1.m1.1.1.2">𝑜</ci><ci id="S3.p3.1.m1.1.1.3.cmml" xref="S3.p3.1.m1.1.1.3">𝜋</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.p3.1.m1.1c">o|\pi</annotation></semantics></math>
rather than the full likelihood.
Our motivation is to make the training more focused (for efficacy and generalization) and minimize the damage caused by fine-tuning (for locality).</p>
</div>
<div id="S3.p4" class="ltx_para">
<p id="S3.p4.13" class="ltx_p">Second, we fine-tune not only on the requested edits <math id="S3.p4.1.m1.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S3.p4.1.m1.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.1.m1.1.1" xref="S3.p4.1.m1.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S3.p4.1.m1.1b"><ci id="S3.p4.1.m1.1.1.cmml" xref="S3.p4.1.m1.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.1.m1.1c">\mathcal{E}</annotation></semantics></math> but
also additional facts in <math id="S3.p4.2.m2.1" class="ltx_Math" alttext="\mathcal{P}" display="inline"><semantics id="S3.p4.2.m2.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.2.m2.1.1" xref="S3.p4.2.m2.1.1.cmml">𝒫</mi><annotation-xml encoding="MathML-Content" id="S3.p4.2.m2.1b"><ci id="S3.p4.2.m2.1.1.cmml" xref="S3.p4.2.m2.1.1">𝒫</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.2.m2.1c">\mathcal{P}</annotation></semantics></math> and <math id="S3.p4.3.m3.1" class="ltx_Math" alttext="\mathcal{N}" display="inline"><semantics id="S3.p4.3.m3.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.3.m3.1.1" xref="S3.p4.3.m3.1.1.cmml">𝒩</mi><annotation-xml encoding="MathML-Content" id="S3.p4.3.m3.1b"><ci id="S3.p4.3.m3.1.1.cmml" xref="S3.p4.3.m3.1.1">𝒩</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.3.m3.1c">\mathcal{N}</annotation></semantics></math>
to promote generalization and locality.
<math id="S3.p4.4.m4.1" class="ltx_Math" alttext="\mathcal{P}" display="inline"><semantics id="S3.p4.4.m4.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.4.m4.1.1" xref="S3.p4.4.m4.1.1.cmml">𝒫</mi><annotation-xml encoding="MathML-Content" id="S3.p4.4.m4.1b"><ci id="S3.p4.4.m4.1.1.cmml" xref="S3.p4.4.m4.1.1">𝒫</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.4.m4.1c">\mathcal{P}</annotation></semantics></math> is pseudo-paraphrases of the prompts in <math id="S3.p4.5.m5.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S3.p4.5.m5.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.5.m5.1.1" xref="S3.p4.5.m5.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S3.p4.5.m5.1b"><ci id="S3.p4.5.m5.1.1.cmml" xref="S3.p4.5.m5.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.5.m5.1c">\mathcal{E}</annotation></semantics></math>
generated by appending text generated by the (unedited) model.
More specifically, for each <math id="S3.p4.6.m6.2" class="ltx_Math" alttext="(\pi,o)\in\mathcal{E}" display="inline"><semantics id="S3.p4.6.m6.2a"><mrow id="S3.p4.6.m6.2.3" xref="S3.p4.6.m6.2.3.cmml"><mrow id="S3.p4.6.m6.2.3.2.2" xref="S3.p4.6.m6.2.3.2.1.cmml"><mo stretchy="false" id="S3.p4.6.m6.2.3.2.2.1" xref="S3.p4.6.m6.2.3.2.1.cmml">(</mo><mi id="S3.p4.6.m6.1.1" xref="S3.p4.6.m6.1.1.cmml">π</mi><mo id="S3.p4.6.m6.2.3.2.2.2" xref="S3.p4.6.m6.2.3.2.1.cmml">,</mo><mi id="S3.p4.6.m6.2.2" xref="S3.p4.6.m6.2.2.cmml">o</mi><mo stretchy="false" id="S3.p4.6.m6.2.3.2.2.3" xref="S3.p4.6.m6.2.3.2.1.cmml">)</mo></mrow><mo id="S3.p4.6.m6.2.3.1" xref="S3.p4.6.m6.2.3.1.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S3.p4.6.m6.2.3.3" xref="S3.p4.6.m6.2.3.3.cmml">ℰ</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.p4.6.m6.2b"><apply id="S3.p4.6.m6.2.3.cmml" xref="S3.p4.6.m6.2.3"><in id="S3.p4.6.m6.2.3.1.cmml" xref="S3.p4.6.m6.2.3.1"></in><interval closure="open" id="S3.p4.6.m6.2.3.2.1.cmml" xref="S3.p4.6.m6.2.3.2.2"><ci id="S3.p4.6.m6.1.1.cmml" xref="S3.p4.6.m6.1.1">𝜋</ci><ci id="S3.p4.6.m6.2.2.cmml" xref="S3.p4.6.m6.2.2">𝑜</ci></interval><ci id="S3.p4.6.m6.2.3.3.cmml" xref="S3.p4.6.m6.2.3.3">ℰ</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.6.m6.2c">(\pi,o)\in\mathcal{E}</annotation></semantics></math> we generate
<math id="S3.p4.7.m7.4" class="ltx_Math" alttext="((z,\pi),o)\in\mathcal{P}" display="inline"><semantics id="S3.p4.7.m7.4a"><mrow id="S3.p4.7.m7.4.4" xref="S3.p4.7.m7.4.4.cmml"><mrow id="S3.p4.7.m7.4.4.1.1" xref="S3.p4.7.m7.4.4.1.2.cmml"><mo stretchy="false" id="S3.p4.7.m7.4.4.1.1.2" xref="S3.p4.7.m7.4.4.1.2.cmml">(</mo><mrow id="S3.p4.7.m7.4.4.1.1.1.2" xref="S3.p4.7.m7.4.4.1.1.1.1.cmml"><mo stretchy="false" id="S3.p4.7.m7.4.4.1.1.1.2.1" xref="S3.p4.7.m7.4.4.1.1.1.1.cmml">(</mo><mi id="S3.p4.7.m7.1.1" xref="S3.p4.7.m7.1.1.cmml">z</mi><mo id="S3.p4.7.m7.4.4.1.1.1.2.2" xref="S3.p4.7.m7.4.4.1.1.1.1.cmml">,</mo><mi id="S3.p4.7.m7.2.2" xref="S3.p4.7.m7.2.2.cmml">π</mi><mo stretchy="false" id="S3.p4.7.m7.4.4.1.1.1.2.3" xref="S3.p4.7.m7.4.4.1.1.1.1.cmml">)</mo></mrow><mo id="S3.p4.7.m7.4.4.1.1.3" xref="S3.p4.7.m7.4.4.1.2.cmml">,</mo><mi id="S3.p4.7.m7.3.3" xref="S3.p4.7.m7.3.3.cmml">o</mi><mo stretchy="false" id="S3.p4.7.m7.4.4.1.1.4" xref="S3.p4.7.m7.4.4.1.2.cmml">)</mo></mrow><mo id="S3.p4.7.m7.4.4.2" xref="S3.p4.7.m7.4.4.2.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S3.p4.7.m7.4.4.3" xref="S3.p4.7.m7.4.4.3.cmml">𝒫</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.p4.7.m7.4b"><apply id="S3.p4.7.m7.4.4.cmml" xref="S3.p4.7.m7.4.4"><in id="S3.p4.7.m7.4.4.2.cmml" xref="S3.p4.7.m7.4.4.2"></in><interval closure="open" id="S3.p4.7.m7.4.4.1.2.cmml" xref="S3.p4.7.m7.4.4.1.1"><interval closure="open" id="S3.p4.7.m7.4.4.1.1.1.1.cmml" xref="S3.p4.7.m7.4.4.1.1.1.2"><ci id="S3.p4.7.m7.1.1.cmml" xref="S3.p4.7.m7.1.1">𝑧</ci><ci id="S3.p4.7.m7.2.2.cmml" xref="S3.p4.7.m7.2.2">𝜋</ci></interval><ci id="S3.p4.7.m7.3.3.cmml" xref="S3.p4.7.m7.3.3">𝑜</ci></interval><ci id="S3.p4.7.m7.4.4.3.cmml" xref="S3.p4.7.m7.4.4.3">𝒫</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.7.m7.4c">((z,\pi),o)\in\mathcal{P}</annotation></semantics></math> where <math id="S3.p4.8.m8.1" class="ltx_Math" alttext="z\sim p_{\theta}" display="inline"><semantics id="S3.p4.8.m8.1a"><mrow id="S3.p4.8.m8.1.1" xref="S3.p4.8.m8.1.1.cmml"><mi id="S3.p4.8.m8.1.1.2" xref="S3.p4.8.m8.1.1.2.cmml">z</mi><mo id="S3.p4.8.m8.1.1.1" xref="S3.p4.8.m8.1.1.1.cmml">∼</mo><msub id="S3.p4.8.m8.1.1.3" xref="S3.p4.8.m8.1.1.3.cmml"><mi id="S3.p4.8.m8.1.1.3.2" xref="S3.p4.8.m8.1.1.3.2.cmml">p</mi><mi id="S3.p4.8.m8.1.1.3.3" xref="S3.p4.8.m8.1.1.3.3.cmml">θ</mi></msub></mrow><annotation-xml encoding="MathML-Content" id="S3.p4.8.m8.1b"><apply id="S3.p4.8.m8.1.1.cmml" xref="S3.p4.8.m8.1.1"><csymbol cd="latexml" id="S3.p4.8.m8.1.1.1.cmml" xref="S3.p4.8.m8.1.1.1">similar-to</csymbol><ci id="S3.p4.8.m8.1.1.2.cmml" xref="S3.p4.8.m8.1.1.2">𝑧</ci><apply id="S3.p4.8.m8.1.1.3.cmml" xref="S3.p4.8.m8.1.1.3"><csymbol cd="ambiguous" id="S3.p4.8.m8.1.1.3.1.cmml" xref="S3.p4.8.m8.1.1.3">subscript</csymbol><ci id="S3.p4.8.m8.1.1.3.2.cmml" xref="S3.p4.8.m8.1.1.3.2">𝑝</ci><ci id="S3.p4.8.m8.1.1.3.3.cmml" xref="S3.p4.8.m8.1.1.3.3">𝜃</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.8.m8.1c">z\sim p_{\theta}</annotation></semantics></math>.
<math id="S3.p4.9.m9.1" class="ltx_Math" alttext="\mathcal{R}" display="inline"><semantics id="S3.p4.9.m9.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.9.m9.1.1" xref="S3.p4.9.m9.1.1.cmml">ℛ</mi><annotation-xml encoding="MathML-Content" id="S3.p4.9.m9.1b"><ci id="S3.p4.9.m9.1.1.cmml" xref="S3.p4.9.m9.1.1">ℛ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.9.m9.1c">\mathcal{R}</annotation></semantics></math> is a set of facts that should not be altered
by editing on <math id="S3.p4.10.m10.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S3.p4.10.m10.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.10.m10.1.1" xref="S3.p4.10.m10.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S3.p4.10.m10.1b"><ci id="S3.p4.10.m10.1.1.cmml" xref="S3.p4.10.m10.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.10.m10.1c">\mathcal{E}</annotation></semantics></math>.
There are many ways to obtain <math id="S3.p4.11.m11.1" class="ltx_Math" alttext="\mathcal{R}" display="inline"><semantics id="S3.p4.11.m11.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p4.11.m11.1.1" xref="S3.p4.11.m11.1.1.cmml">ℛ</mi><annotation-xml encoding="MathML-Content" id="S3.p4.11.m11.1b"><ci id="S3.p4.11.m11.1.1.cmml" xref="S3.p4.11.m11.1.1">ℛ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.11.m11.1c">\mathcal{R}</annotation></semantics></math>, but we find taking
<em id="S3.p4.13.1" class="ltx_emph ltx_font_italic">random</em> facts from the training split to be simple and effective.
We filter <math id="S3.p4.12.m12.1" class="ltx_Math" alttext="x\in\mathcal{R}" display="inline"><semantics id="S3.p4.12.m12.1a"><mrow id="S3.p4.12.m12.1.1" xref="S3.p4.12.m12.1.1.cmml"><mi id="S3.p4.12.m12.1.1.2" xref="S3.p4.12.m12.1.1.2.cmml">x</mi><mo id="S3.p4.12.m12.1.1.1" xref="S3.p4.12.m12.1.1.1.cmml">∈</mo><mi class="ltx_font_mathcaligraphic" id="S3.p4.12.m12.1.1.3" xref="S3.p4.12.m12.1.1.3.cmml">ℛ</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.p4.12.m12.1b"><apply id="S3.p4.12.m12.1.1.cmml" xref="S3.p4.12.m12.1.1"><in id="S3.p4.12.m12.1.1.1.cmml" xref="S3.p4.12.m12.1.1.1"></in><ci id="S3.p4.12.m12.1.1.2.cmml" xref="S3.p4.12.m12.1.1.2">𝑥</ci><ci id="S3.p4.12.m12.1.1.3.cmml" xref="S3.p4.12.m12.1.1.3">ℛ</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.12.m12.1c">x\in\mathcal{R}</annotation></semantics></math> to ensure that <math id="S3.p4.13.m13.1" class="ltx_Math" alttext="x" display="inline"><semantics id="S3.p4.13.m13.1a"><mi id="S3.p4.13.m13.1.1" xref="S3.p4.13.m13.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S3.p4.13.m13.1b"><ci id="S3.p4.13.m13.1.1.cmml" xref="S3.p4.13.m13.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p4.13.m13.1c">x</annotation></semantics></math> does not include
the subject-relation-object triple used in evaluation.</p>
</div>
<div id="S3.p5" class="ltx_para">
<p id="S3.p5.3" class="ltx_p">We emphasize that the augmented sets <math id="S3.p5.1.m1.1" class="ltx_Math" alttext="\mathcal{P}" display="inline"><semantics id="S3.p5.1.m1.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p5.1.m1.1.1" xref="S3.p5.1.m1.1.1.cmml">𝒫</mi><annotation-xml encoding="MathML-Content" id="S3.p5.1.m1.1b"><ci id="S3.p5.1.m1.1.1.cmml" xref="S3.p5.1.m1.1.1">𝒫</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p5.1.m1.1c">\mathcal{P}</annotation></semantics></math> and <math id="S3.p5.2.m2.1" class="ltx_Math" alttext="\mathcal{R}" display="inline"><semantics id="S3.p5.2.m2.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p5.2.m2.1.1" xref="S3.p5.2.m2.1.1.cmml">ℛ</mi><annotation-xml encoding="MathML-Content" id="S3.p5.2.m2.1b"><ci id="S3.p5.2.m2.1.1.cmml" xref="S3.p5.2.m2.1.1">ℛ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p5.2.m2.1c">\mathcal{R}</annotation></semantics></math>
do not use the evaluation facts (otherwise it is trivial).
Given the requested edits <math id="S3.p5.3.m3.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S3.p5.3.m3.1a"><mi class="ltx_font_mathcaligraphic" id="S3.p5.3.m3.1.1" xref="S3.p5.3.m3.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S3.p5.3.m3.1b"><ci id="S3.p5.3.m3.1.1.cmml" xref="S3.p5.3.m3.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.p5.3.m3.1c">\mathcal{E}</annotation></semantics></math>, we perform the data augmentation
and finetune the model according to (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>).</p>
</div>
<section id="S3.SS0.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Contrastive learning.</h4>

<div id="S3.SS0.SSS0.Px1.p1" class="ltx_para">
<p id="S3.SS0.SSS0.Px1.p1.6" class="ltx_p">Given that our goal in <span id="S3.SS0.SSS0.Px1.p1.6.1" class="ltx_text ltx_font_smallcaps">CounterFact</span> is to achieve
<math id="S3.SS0.SSS0.Px1.p1.1.m1.2" class="ltx_Math" alttext="p_{\theta}(o|\pi)&gt;p_{\theta}(o_{\text{true}}|\pi)" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.1.m1.2a"><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.2.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.cmml"><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.cmml"><msub id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.cmml"><mi id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.2.cmml">p</mi><mi id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.2.cmml">​</mo><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.cmml"><mi id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.2.cmml">o</mi><mo fence="false" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.1.cmml">|</mo><mi id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.3.cmml">&gt;</mo><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.cmml"><msub id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.cmml"><mi id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.2.cmml">p</mi><mi id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.3.cmml">θ</mi></msub><mo lspace="0em" rspace="0em" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.2.cmml">​</mo><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.cmml">(</mo><mrow id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.cmml"><msub id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.cmml"><mi id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.2" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.2.cmml">o</mi><mtext id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3a.cmml">true</mtext></msub><mo fence="false" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.1" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.1.cmml">|</mo><mi id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.3.cmml">π</mi></mrow><mo stretchy="false" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.3" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.1.m1.2b"><apply id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2"><gt id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.3"></gt><apply id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1"><times id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.2"></times><apply id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3"><csymbol cd="ambiguous" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3">subscript</csymbol><ci id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.2">𝑝</ci><ci id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.3.3">𝜃</ci></apply><apply id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1"><csymbol cd="latexml" id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.1">conditional</csymbol><ci id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.2">𝑜</ci><ci id="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.1.1.1.1.1.1.3">𝜋</ci></apply></apply><apply id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2"><times id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.2"></times><apply id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3"><csymbol cd="ambiguous" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3">subscript</csymbol><ci id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.2">𝑝</ci><ci id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.3.3">𝜃</ci></apply><apply id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1"><csymbol cd="latexml" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.1">conditional</csymbol><apply id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2"><csymbol cd="ambiguous" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.1.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2">subscript</csymbol><ci id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.2.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.2">𝑜</ci><ci id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3a.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3"><mtext mathsize="70%" id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.2.3">true</mtext></ci></apply><ci id="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.1.m1.2.2.2.1.1.1.3">𝜋</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.1.m1.2c">p_{\theta}(o|\pi)&gt;p_{\theta}(o_{\text{true}}|\pi)</annotation></semantics></math>
where <math id="S3.SS0.SSS0.Px1.p1.2.m2.1" class="ltx_Math" alttext="o" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.2.m2.1a"><mi id="S3.SS0.SSS0.Px1.p1.2.m2.1.1" xref="S3.SS0.SSS0.Px1.p1.2.m2.1.1.cmml">o</mi><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.2.m2.1b"><ci id="S3.SS0.SSS0.Px1.p1.2.m2.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.2.m2.1.1">𝑜</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.2.m2.1c">o</annotation></semantics></math> is the new object to enforce over the original <math id="S3.SS0.SSS0.Px1.p1.3.m3.1" class="ltx_Math" alttext="o_{\text{true}}" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.3.m3.1a"><msub id="S3.SS0.SSS0.Px1.p1.3.m3.1.1" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.cmml"><mi id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.2" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.2.cmml">o</mi><mtext id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3a.cmml">true</mtext></msub><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.3.m3.1b"><apply id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1"><csymbol cd="ambiguous" id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1">subscript</csymbol><ci id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.2">𝑜</ci><ci id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3a.cmml" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3"><mtext mathsize="70%" id="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.3.m3.1.1.3">true</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.3.m3.1c">o_{\text{true}}</annotation></semantics></math> for a given prompt <math id="S3.SS0.SSS0.Px1.p1.4.m4.1" class="ltx_Math" alttext="\pi" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.4.m4.1a"><mi id="S3.SS0.SSS0.Px1.p1.4.m4.1.1" xref="S3.SS0.SSS0.Px1.p1.4.m4.1.1.cmml">π</mi><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.4.m4.1b"><ci id="S3.SS0.SSS0.Px1.p1.4.m4.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.4.m4.1.1">𝜋</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.4.m4.1c">\pi</annotation></semantics></math>,
it is natural to consider a contrastive objective.
We experimented with DPO <cite class="ltx_cite ltx_citemacro_citep">(Rafailov et al., <a href="#bib.bib10" title="" class="ltx_ref">2023</a>)</cite>
where we frame <math id="S3.SS0.SSS0.Px1.p1.5.m5.1" class="ltx_Math" alttext="o|\pi" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.5.m5.1a"><mrow id="S3.SS0.SSS0.Px1.p1.5.m5.1.1" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.cmml"><mi id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.2" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.2.cmml">o</mi><mo fence="false" id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.1" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.1.cmml">|</mo><mi id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.3" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.3.cmml">π</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.5.m5.1b"><apply id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1"><csymbol cd="latexml" id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.1">conditional</csymbol><ci id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.2">𝑜</ci><ci id="S3.SS0.SSS0.Px1.p1.5.m5.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.5.m5.1.1.3">𝜋</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.5.m5.1c">o|\pi</annotation></semantics></math> as the “preferred” response
over <math id="S3.SS0.SSS0.Px1.p1.6.m6.1" class="ltx_Math" alttext="o_{\text{true}}|\pi" display="inline"><semantics id="S3.SS0.SSS0.Px1.p1.6.m6.1a"><mrow id="S3.SS0.SSS0.Px1.p1.6.m6.1.1" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.cmml"><msub id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.cmml"><mi id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.2" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.2.cmml">o</mi><mtext id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3a.cmml">true</mtext></msub><mo fence="false" id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.1" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.1.cmml">|</mo><mi id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.3" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.3.cmml">π</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.SS0.SSS0.Px1.p1.6.m6.1b"><apply id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1"><csymbol cd="latexml" id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.1.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.1">conditional</csymbol><apply id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2"><csymbol cd="ambiguous" id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.1.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2">subscript</csymbol><ci id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.2.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.2">𝑜</ci><ci id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3a.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3"><mtext mathsize="70%" id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.2.3">true</mtext></ci></apply><ci id="S3.SS0.SSS0.Px1.p1.6.m6.1.1.3.cmml" xref="S3.SS0.SSS0.Px1.p1.6.m6.1.1.3">𝜋</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS0.SSS0.Px1.p1.6.m6.1c">o_{\text{true}}|\pi</annotation></semantics></math>, optimizing the DPO loss
jointly with (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>).
However, we found that prompt masking and data augmentation are already
effective and do not benefit from contrastive learning.</p>
</div>
<figure id="S3.T2" class="ltx_table">
<table id="S3.T2.1" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S3.T2.1.1.1" class="ltx_tr">
<th id="S3.T2.1.1.1.1" class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;"></th>
<th id="S3.T2.1.1.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;" colspan="4">ZsRE</th>
<th id="S3.T2.1.1.1.3" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;" colspan="4"><span id="S3.T2.1.1.1.3.1" class="ltx_text ltx_font_smallcaps">CounterFact</span></th>
</tr>
<tr id="S3.T2.1.2.2" class="ltx_tr">
<th id="S3.T2.1.2.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">Editor</th>
<th id="S3.T2.1.2.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Score</th>
<th id="S3.T2.1.2.2.3" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Efficacy</th>
<th id="S3.T2.1.2.2.4" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Generalization</th>
<th id="S3.T2.1.2.2.5" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r" style="padding:1pt 3.0pt;">Locality</th>
<th id="S3.T2.1.2.2.6" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Score</th>
<th id="S3.T2.1.2.2.7" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Efficacy</th>
<th id="S3.T2.1.2.2.8" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Generalization</th>
<th id="S3.T2.1.2.2.9" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Locality</th>
</tr>
<tr id="S3.T2.1.3.3" class="ltx_tr">
<th id="S3.T2.1.3.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">— (original GPT-J)</th>
<th id="S3.T2.1.3.3.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">26.4</th>
<th id="S3.T2.1.3.3.3" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">26.4 (0.6)</th>
<th id="S3.T2.1.3.3.4" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">25.8 (0.5)</th>
<th id="S3.T2.1.3.3.5" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">27.0 (0.5)</th>
<th id="S3.T2.1.3.3.6" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">22.4</th>
<th id="S3.T2.1.3.3.7" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">15.2 (0.7)</th>
<th id="S3.T2.1.3.3.8" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">17.7 (0.6)</th>
<th id="S3.T2.1.3.3.9" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">83.5 (0.5)</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S3.T2.1.4.1" class="ltx_tr">
<th id="S3.T2.1.4.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">FT-W (21st layer w/ weight decay)</th>
<td id="S3.T2.1.4.1.2" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">42.1</td>
<td id="S3.T2.1.4.1.3" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">69.6 (0.6)</td>
<td id="S3.T2.1.4.1.4" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">64.8 (0.6)</td>
<td id="S3.T2.1.4.1.5" class="ltx_td ltx_align_center ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">24.1 (0.6)</td>
<td id="S3.T2.1.4.1.6" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">67.6</td>
<td id="S3.T2.1.4.1.7" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">99.4 (0.1)</td>
<td id="S3.T2.1.4.1.8" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">77.0 (0.7)</td>
<td id="S3.T2.1.4.1.9" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">46.9 (0.6)</td>
</tr>
<tr id="S3.T2.1.5.2" class="ltx_tr">
<th id="S3.T2.1.5.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEND</th>
<td id="S3.T2.1.5.2.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">20.0</td>
<td id="S3.T2.1.5.2.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">19.4 (0.5)</td>
<td id="S3.T2.1.5.2.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">18.6 (0.5)</td>
<td id="S3.T2.1.5.2.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">22.4 (0.5)</td>
<td id="S3.T2.1.5.2.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">23.1</td>
<td id="S3.T2.1.5.2.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">15.7 (0.7)</td>
<td id="S3.T2.1.5.2.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">18.5 (0.7)</td>
<td id="S3.T2.1.5.2.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">83.0 (0.5)</td>
</tr>
<tr id="S3.T2.1.6.3" class="ltx_tr">
<th id="S3.T2.1.6.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">ROME</th>
<td id="S3.T2.1.6.3.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">2.6</td>
<td id="S3.T2.1.6.3.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">21.0 (0.7)</td>
<td id="S3.T2.1.6.3.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">19.6 (0.7)</td>
<td id="S3.T2.1.6.3.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">0.9 (0.1)</td>
<td id="S3.T2.1.6.3.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">50.3</td>
<td id="S3.T2.1.6.3.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">50.2 (1.0)</td>
<td id="S3.T2.1.6.3.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">50.4 (0.8)</td>
<td id="S3.T2.1.6.3.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">50.2 (0.6)</td>
</tr>
<tr id="S3.T2.1.7.4" class="ltx_tr">
<th id="S3.T2.1.7.4.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEMIT</th>
<td id="S3.T2.1.7.4.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">50.7</td>
<td id="S3.T2.1.7.4.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">96.7 (0.3)</td>
<td id="S3.T2.1.7.4.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">89.7 (0.5)</td>
<td id="S3.T2.1.7.4.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">26.6 (0.5)</td>
<td id="S3.T2.1.7.4.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">85.8</td>
<td id="S3.T2.1.7.4.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">98.9 (0.2)</td>
<td id="S3.T2.1.7.4.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">88.6 (0.5)</td>
<td id="S3.T2.1.7.4.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.7.4.9.1" class="ltx_text ltx_font_bold">73.7</span> (0.5)</td>
</tr>
<tr id="S3.T2.1.8.5" class="ltx_tr">
<th id="S3.T2.1.8.5.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">FT</th>
<td id="S3.T2.1.8.5.2" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">44.8</td>
<td id="S3.T2.1.8.5.3" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.8.5.3.1" class="ltx_text ltx_font_bold">99.9</span> (0.03)</td>
<td id="S3.T2.1.8.5.4" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.8.5.4.1" class="ltx_text ltx_font_bold">98.9</span> (0.2)</td>
<td id="S3.T2.1.8.5.5" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">21.4 (0.5)</td>
<td id="S3.T2.1.8.5.6" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">52.8</td>
<td id="S3.T2.1.8.5.7" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">79.6 (0.8)</td>
<td id="S3.T2.1.8.5.8" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">58.5 (0.8)</td>
<td id="S3.T2.1.8.5.9" class="ltx_td ltx_align_center ltx_border_t" style="padding:1pt 3.0pt;">36.8 (0.7)</td>
</tr>
<tr id="S3.T2.1.9.6" class="ltx_tr">
<th id="S3.T2.1.9.6.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT (21st layer)</th>
<td id="S3.T2.1.9.6.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">42.9</td>
<td id="S3.T2.1.9.6.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.9.6.3.1" class="ltx_text ltx_font_bold">99.9</span> (0.0)</td>
<td id="S3.T2.1.9.6.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">87.4 (0.5)</td>
<td id="S3.T2.1.9.6.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">20.5 (0.5)</td>
<td id="S3.T2.1.9.6.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">60.5</td>
<td id="S3.T2.1.9.6.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">99.9 (0.04)</td>
<td id="S3.T2.1.9.6.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">63.3 (0.8)</td>
<td id="S3.T2.1.9.6.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">42.0 (0.6)</td>
</tr>
<tr id="S3.T2.1.10.7" class="ltx_tr">
<th id="S3.T2.1.10.7.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask</th>
<td id="S3.T2.1.10.7.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">58.3</td>
<td id="S3.T2.1.10.7.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">97.6 (0.3)</td>
<td id="S3.T2.1.10.7.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">91.7 (0.5)</td>
<td id="S3.T2.1.10.7.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">32.9 (0.6)</td>
<td id="S3.T2.1.10.7.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">54.3</td>
<td id="S3.T2.1.10.7.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">97.1 (0.3)</td>
<td id="S3.T2.1.10.7.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">62.1 (0.8)</td>
<td id="S3.T2.1.10.7.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">34.7 (0.6)</td>
</tr>
<tr id="S3.T2.1.11.8" class="ltx_tr">
<th id="S3.T2.1.11.8.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask + Para</th>
<td id="S3.T2.1.11.8.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">56.1</td>
<td id="S3.T2.1.11.8.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.11.8.3.1" class="ltx_text ltx_font_bold">99.9</span> (0.0)</td>
<td id="S3.T2.1.11.8.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">98.7 (0.2)</td>
<td id="S3.T2.1.11.8.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">29.9 (0.5)</td>
<td id="S3.T2.1.11.8.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">63.7</td>
<td id="S3.T2.1.11.8.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.11.8.7.1" class="ltx_text ltx_font_bold">100.0</span> (0.0)</td>
<td id="S3.T2.1.11.8.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">92.5 (0.4)</td>
<td id="S3.T2.1.11.8.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">38.0 (0.6)</td>
</tr>
<tr id="S3.T2.1.12.9" class="ltx_tr">
<th id="S3.T2.1.12.9.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask + Para + Rand</th>
<td id="S3.T2.1.12.9.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S3.T2.1.12.9.2.1" class="ltx_text ltx_font_bold">62.0</span></td>
<td id="S3.T2.1.12.9.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.12.9.3.1" class="ltx_text ltx_font_bold">99.9</span> (0.0)</td>
<td id="S3.T2.1.12.9.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">97.0 (0.3)</td>
<td id="S3.T2.1.12.9.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.12.9.5.1" class="ltx_text ltx_font_bold">35.6</span> (0.6)</td>
<td id="S3.T2.1.12.9.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S3.T2.1.12.9.6.1" class="ltx_text ltx_font_bold">86.5</span></td>
<td id="S3.T2.1.12.9.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">98.8 (0.2)</td>
<td id="S3.T2.1.12.9.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S3.T2.1.12.9.8.1" class="ltx_text ltx_font_bold">93.6</span> (0.4)</td>
<td id="S3.T2.1.12.9.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">72.0 (0.6)</td>
</tr>
<tr id="S3.T2.1.13.10" class="ltx_tr">
<th id="S3.T2.1.13.10.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask + Para + Rand + DPO</th>
<td id="S3.T2.1.13.10.2" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">—</td>
<td id="S3.T2.1.13.10.3" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">—</td>
<td id="S3.T2.1.13.10.4" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">—</td>
<td id="S3.T2.1.13.10.5" class="ltx_td ltx_align_center ltx_border_b ltx_border_r" style="padding:1pt 3.0pt;">—</td>
<td id="S3.T2.1.13.10.6" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">85.5</td>
<td id="S3.T2.1.13.10.7" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">98.8 (0.2)</td>
<td id="S3.T2.1.13.10.8" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">93.4 (0.4)</td>
<td id="S3.T2.1.13.10.9" class="ltx_td ltx_align_center ltx_border_b" style="padding:1pt 3.0pt;">70.1 (0.6)</td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">Table 2: </span>Mass-editing results on ZsRE and <span id="S3.T2.5.1" class="ltx_text ltx_font_smallcaps">CounterFact</span> (10,000 edits each) with GPT-J. The results of the specialized methods (FT-W, MEND, ROME, MEMIT) are from <cite class="ltx_cite ltx_citemacro_citet">Meng et al. (<a href="#bib.bib7" title="" class="ltx_ref">2023</a>)</cite>. FT denotes naive fine-tuning on the requested edits; FT (21st layer) denotes FT only on the 21st layer. “+ Mask” means we mask the prompt. “+ Para” means we augment the data with model-generated paraphrases of the requested edits. “+ Rand” means we augment the data with <em id="S3.T2.6.2" class="ltx_emph ltx_font_italic">random</em> facts from the training split (not overlapping with any evaluation facts). “+ DPO” means we additionally optimize the DPO loss term using the changed target as the preferred response over the original target (which is supplied in <span id="S3.T2.7.3" class="ltx_text ltx_font_smallcaps">CounterFact</span>).
</figcaption>
</figure>
</section>
</section>
<section id="S4" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">4 </span>Related Work</h2>

<div id="S4.p1" class="ltx_para">
<p id="S4.p1.1" class="ltx_p">We discuss some prominent model editing methods and the different assumptions they require to highlight the simplicity of our fine-tuning approach; we refer to <cite class="ltx_cite ltx_citemacro_citet">Zhang et al. (<a href="#bib.bib14" title="" class="ltx_ref">2024</a>)</cite> for an in-depth survey.</p>
</div>
<div id="S4.p2" class="ltx_para">
<p id="S4.p2.1" class="ltx_p">MEND <cite class="ltx_cite ltx_citemacro_citep">(Mitchell et al., <a href="#bib.bib8" title="" class="ltx_ref">2022</a>)</cite> is a meta-learning method <cite class="ltx_cite ltx_citemacro_citep">(Sinitsin et al., <a href="#bib.bib12" title="" class="ltx_ref">2020</a>; De Cao et al., <a href="#bib.bib2" title="" class="ltx_ref">2021</a>)</cite> that predicts the change in the gradient.
Similar to our approach, it also involves an explicit training stage (on the training split of ZsRE).
It uses a special rank-one decomposition of the gradient for parameter efficiency.
In our case, we achieve parameter efficiency without special considerations
simply by leveraging PEFT methods.
MEND works poorly for mass-editing.</p>
</div>
<div id="S4.p3" class="ltx_para">
<p id="S4.p3.1" class="ltx_p">ROME <cite class="ltx_cite ltx_citemacro_citep">(Meng et al., <a href="#bib.bib6" title="" class="ltx_ref">2022</a>)</cite> is a locate-then-edit method <cite class="ltx_cite ltx_citemacro_citep">(Geva et al., <a href="#bib.bib3" title="" class="ltx_ref">2021</a>; Dai et al., <a href="#bib.bib1" title="" class="ltx_ref">2022</a>)</cite>
that first uses causal tracing to identify the feedforward layer to change, and then applies
a rank-one update to the layer’s weight matrix.
While it does not involve an explicit training stage, it
does require an explicit knowledge of the subject <math id="S4.p3.1.m1.1" class="ltx_Math" alttext="s" display="inline"><semantics id="S4.p3.1.m1.1a"><mi id="S4.p3.1.m1.1.1" xref="S4.p3.1.m1.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="S4.p3.1.m1.1b"><ci id="S4.p3.1.m1.1.1.cmml" xref="S4.p3.1.m1.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p3.1.m1.1c">s</annotation></semantics></math> in the edit
and its vector representation (which is heuristically induced).
It also relies on Wikipedia to estimate the covariance matrix of
the subject embeddings (needed in the rank-one update).
ROME works well on single-editing but poorly on mass-editing.
MEMIT <cite class="ltx_cite ltx_citemacro_citep">(Meng et al., <a href="#bib.bib7" title="" class="ltx_ref">2023</a>)</cite> extends ROME to multiple edits
by carefully spreading updates to multiple layers.
Like ROME, it requires layer specification, subject embeddings,
and covariance statistics obtained from Wikipedia.
MEMIT is very effective for mass-editing and is our strongest baseline.</p>
</div>
<div id="S4.p4" class="ltx_para">
<p id="S4.p4.1" class="ltx_p">IKE <cite class="ltx_cite ltx_citemacro_citep">(Zheng et al., <a href="#bib.bib15" title="" class="ltx_ref">2023</a>)</cite> proposes in-context learning for model editing. While it similarly uses demonstrations, it is critically limited to single-editing. It also requires an initial model that is capable of effective in-context learning. Consequently, IKE focuses on single-editing with large-scale LLMs, making their results not comparable to ours.</p>
</div>
<div id="S4.p5" class="ltx_para">
<p id="S4.p5.1" class="ltx_p">We define our scope as achieving a competitive edit score through pure fine-tuning.
In particular, we do not focus on preserving general capabilities of the model being edited.
Existing methods consider basic metrics such as <math id="S4.p5.1.m1.1" class="ltx_Math" alttext="n" display="inline"><semantics id="S4.p5.1.m1.1a"><mi id="S4.p5.1.m1.1.1" xref="S4.p5.1.m1.1.1.cmml">n</mi><annotation-xml encoding="MathML-Content" id="S4.p5.1.m1.1b"><ci id="S4.p5.1.m1.1.1.cmml" xref="S4.p5.1.m1.1.1">𝑛</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p5.1.m1.1c">n</annotation></semantics></math>-gram repetition,
but recent work shows that performance on a variety of downstream tasks
drops to zero under any editor <cite class="ltx_cite ltx_citemacro_citep">(Gu et al., <a href="#bib.bib4" title="" class="ltx_ref">2024</a>)</cite>.
We leave preserving the general capabilities of an LLM with a fine-tuning editor
as the next step of our work.</p>
</div>
<figure id="S4.T3" class="ltx_table">
<table id="S4.T3.1" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S4.T3.1.1.1" class="ltx_tr">
<th id="S4.T3.1.1.1.1" class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;"></th>
<th id="S4.T3.1.1.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;" colspan="4">ZsRE</th>
<th id="S4.T3.1.1.1.3" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;" colspan="4"><span id="S4.T3.1.1.1.3.1" class="ltx_text ltx_font_smallcaps">CounterFact</span></th>
</tr>
<tr id="S4.T3.1.2.2" class="ltx_tr">
<th id="S4.T3.1.2.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">Editor</th>
<th id="S4.T3.1.2.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Score</th>
<th id="S4.T3.1.2.2.3" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Efficacy</th>
<th id="S4.T3.1.2.2.4" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Generalization</th>
<th id="S4.T3.1.2.2.5" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r" style="padding:1pt 3.0pt;">Locality</th>
<th id="S4.T3.1.2.2.6" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Score</th>
<th id="S4.T3.1.2.2.7" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Efficacy</th>
<th id="S4.T3.1.2.2.8" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Generalization</th>
<th id="S4.T3.1.2.2.9" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding:1pt 3.0pt;">Locality</th>
</tr>
<tr id="S4.T3.1.3.3" class="ltx_tr">
<th id="S4.T3.1.3.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">— (original GPT-2 XL)</th>
<th id="S4.T3.1.3.3.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">22.5</th>
<th id="S4.T3.1.3.3.3" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">22.2 (0.5)</th>
<th id="S4.T3.1.3.3.4" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">21.3 (0.5)</th>
<th id="S4.T3.1.3.3.5" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">24.2 (0.5)</th>
<th id="S4.T3.1.3.3.6" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">30.5</th>
<th id="S4.T3.1.3.3.7" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">22.2 (0.9)</th>
<th id="S4.T3.1.3.3.8" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">24.7 (0.8)</th>
<th id="S4.T3.1.3.3.9" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">78.1 (0.6)</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S4.T3.1.4.1" class="ltx_tr">
<th id="S4.T3.1.4.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">FT</th>
<td id="S4.T3.1.4.1.2" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">45.9</td>
<td id="S4.T3.1.4.1.3" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">99.6 (0.1)</td>
<td id="S4.T3.1.4.1.4" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">82.1 (0.1)</td>
<td id="S4.T3.1.4.1.5" class="ltx_td ltx_align_center ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">23.2 (0.5)</td>
<td id="S4.T3.1.4.1.6" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">65.1</td>
<td id="S4.T3.1.4.1.7" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.4.1.7.1" class="ltx_text ltx_font_bold">100.0</span> (0.0)</td>
<td id="S4.T3.1.4.1.8" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">87.9 (0.6)</td>
<td id="S4.T3.1.4.1.9" class="ltx_td ltx_align_center ltx_border_tt" style="padding:1pt 3.0pt;">40.4 (0.7)</td>
</tr>
<tr id="S4.T3.1.5.2" class="ltx_tr">
<th id="S4.T3.1.5.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT-L</th>
<td id="S4.T3.1.5.2.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">40.1</td>
<td id="S4.T3.1.5.2.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">92.3 (0.4)</td>
<td id="S4.T3.1.5.2.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">47.2 (0.7)</td>
<td id="S4.T3.1.5.2.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">23.4 (0.5)</td>
<td id="S4.T3.1.5.2.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">66.9</td>
<td id="S4.T3.1.5.2.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">99.1 (0.2)</td>
<td id="S4.T3.1.5.2.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">48.7 (1.0)</td>
<td id="S4.T3.1.5.2.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">70.3 (0.7)</td>
</tr>
<tr id="S4.T3.1.6.3" class="ltx_tr">
<th id="S4.T3.1.6.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">KN</th>
<td id="S4.T3.1.6.3.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">-</td>
<td id="S4.T3.1.6.3.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">-</td>
<td id="S4.T3.1.6.3.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">-</td>
<td id="S4.T3.1.6.3.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">-</td>
<td id="S4.T3.1.6.3.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">35.6</td>
<td id="S4.T3.1.6.3.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">28.7 (1.0)</td>
<td id="S4.T3.1.6.3.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">28.0 (0.9)</td>
<td id="S4.T3.1.6.3.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">72.9 (0.7)</td>
</tr>
<tr id="S4.T3.1.7.4" class="ltx_tr">
<th id="S4.T3.1.7.4.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">KE</th>
<td id="S4.T3.1.7.4.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">41.8</td>
<td id="S4.T3.1.7.4.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">65.5 (0.6)</td>
<td id="S4.T3.1.7.4.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">61.4 (0.6)</td>
<td id="S4.T3.1.7.4.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">24.9 (0.5)</td>
<td id="S4.T3.1.7.4.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">52.2</td>
<td id="S4.T3.1.7.4.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">84.3 (0.8)</td>
<td id="S4.T3.1.7.4.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">75.4 (0.8)</td>
<td id="S4.T3.1.7.4.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">30.9 (0.7)</td>
</tr>
<tr id="S4.T3.1.8.5" class="ltx_tr">
<th id="S4.T3.1.8.5.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEND</th>
<td id="S4.T3.1.8.5.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">42.9</td>
<td id="S4.T3.1.8.5.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">75.9 (0.5)</td>
<td id="S4.T3.1.8.5.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">65.3 (0.6)</td>
<td id="S4.T3.1.8.5.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">24.1 (0.5)</td>
<td id="S4.T3.1.8.5.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">57.9</td>
<td id="S4.T3.1.8.5.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">99.1 (0.2)</td>
<td id="S4.T3.1.8.5.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">65.4 (0.9)</td>
<td id="S4.T3.1.8.5.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">37.9 (0.7)</td>
</tr>
<tr id="S4.T3.1.9.6" class="ltx_tr">
<th id="S4.T3.1.9.6.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">ROME</th>
<td id="S4.T3.1.9.6.2" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">47.9</td>
<td id="S4.T3.1.9.6.3" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">99.8 (0.0)</td>
<td id="S4.T3.1.9.6.4" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">88.1 (0.5)</td>
<td id="S4.T3.1.9.6.5" class="ltx_td ltx_align_center ltx_border_r" style="padding:1pt 3.0pt;">24.2 (0.5)</td>
<td id="S4.T3.1.9.6.6" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;"><span id="S4.T3.1.9.6.6.1" class="ltx_text ltx_font_bold">89.2</span></td>
<td id="S4.T3.1.9.6.7" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">100 (0.1)</td>
<td id="S4.T3.1.9.6.8" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.9.6.8.1" class="ltx_text ltx_font_bold">96.4</span> (0.3)</td>
<td id="S4.T3.1.9.6.9" class="ltx_td ltx_align_center" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.9.6.9.1" class="ltx_text ltx_font_bold">75.4</span> (0.7)</td>
</tr>
<tr id="S4.T3.1.10.7" class="ltx_tr">
<th id="S4.T3.1.10.7.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">FT + Mask + Para + Sim</th>
<td id="S4.T3.1.10.7.2" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;"><span id="S4.T3.1.10.7.2.1" class="ltx_text ltx_font_bold">51.4</span></td>
<td id="S4.T3.1.10.7.3" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.10.7.3.1" class="ltx_text ltx_font_bold">100.0</span> (0.0)</td>
<td id="S4.T3.1.10.7.4" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.10.7.4.1" class="ltx_text ltx_font_bold">99.9</span> (0.0)</td>
<td id="S4.T3.1.10.7.5" class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">
<span id="S4.T3.1.10.7.5.1" class="ltx_text ltx_font_bold">26.1</span> (0.8)</td>
<td id="S4.T3.1.10.7.6" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">83.1</td>
<td id="S4.T3.1.10.7.7" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">98.6 (0.3)</td>
<td id="S4.T3.1.10.7.8" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">87.3 (0.7)</td>
<td id="S4.T3.1.10.7.9" class="ltx_td ltx_align_center ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">69.0 (0.7)</td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">Table 3: </span>Single-editing results on ZsRE (10,000 edits) and <span id="S4.T3.3.1" class="ltx_text ltx_font_smallcaps">CounterFact</span> (7,500 edits) with GPT-2 XL. “+ Sim” means we include similar facts (measured by Sentence-BERT) instead of random facts for locality supervision.
</figcaption>
</figure>
<figure id="S4.T4" class="ltx_table">
<table id="S4.T4.1" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S4.T4.1.1.1" class="ltx_tr">
<th id="S4.T4.1.1.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">Editor</th>
<th id="S4.T4.1.1.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">Score</th>
<th id="S4.T4.1.1.1.3" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">Fluency</th>
<th id="S4.T4.1.1.1.4" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">Consistency</th>
</tr>
<tr id="S4.T4.1.2.2" class="ltx_tr">
<th id="S4.T4.1.2.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">— (original GPT-J)</th>
<th id="S4.T4.1.2.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">22.4</th>
<th id="S4.T4.1.2.2.3" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">622.4 (0.3)</th>
<th id="S4.T4.1.2.2.4" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">29.4 (0.2)</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S4.T4.1.3.1" class="ltx_tr">
<th id="S4.T4.1.3.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">FT-W</th>
<th id="S4.T4.1.3.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">67.6</th>
<td id="S4.T4.1.3.1.3" class="ltx_td ltx_align_right ltx_border_tt" style="padding:1pt 3.0pt;">293.9 (2.4)</td>
<td id="S4.T4.1.3.1.4" class="ltx_td ltx_align_right ltx_border_tt" style="padding:1pt 3.0pt;">15.9 (0.3)</td>
</tr>
<tr id="S4.T4.1.4.2" class="ltx_tr">
<th id="S4.T4.1.4.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEND</th>
<th id="S4.T4.1.4.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">20.0</th>
<td id="S4.T4.1.4.2.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">618.4 (0.3)</td>
<td id="S4.T4.1.4.2.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">31.1 (0.2)</td>
</tr>
<tr id="S4.T4.1.5.3" class="ltx_tr">
<th id="S4.T4.1.5.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">ROME</th>
<th id="S4.T4.1.5.3.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">50.3</th>
<td id="S4.T4.1.5.3.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">589.6 (0.5)</td>
<td id="S4.T4.1.5.3.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">3.3 (0.0)</td>
</tr>
<tr id="S4.T4.1.6.4" class="ltx_tr">
<th id="S4.T4.1.6.4.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEMIT</th>
<th id="S4.T4.1.6.4.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">85.8</th>
<td id="S4.T4.1.6.4.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">619.9 (0.3)</td>
<td id="S4.T4.1.6.4.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">40.1 (0.2)</td>
</tr>
<tr id="S4.T4.1.7.5" class="ltx_tr">
<th id="S4.T4.1.7.5.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">FT</th>
<th id="S4.T4.1.7.5.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">52.8</th>
<td id="S4.T4.1.7.5.3" class="ltx_td ltx_align_right ltx_border_t" style="padding:1pt 3.0pt;">626.1 (0.4)</td>
<td id="S4.T4.1.7.5.4" class="ltx_td ltx_align_right ltx_border_t" style="padding:1pt 3.0pt;">31.0 (0.2)</td>
</tr>
<tr id="S4.T4.1.8.6" class="ltx_tr">
<th id="S4.T4.1.8.6.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask</th>
<th id="S4.T4.1.8.6.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">54.3</th>
<td id="S4.T4.1.8.6.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">563.6 (0.5)</td>
<td id="S4.T4.1.8.6.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">6.1 (0.1)</td>
</tr>
<tr id="S4.T4.1.9.7" class="ltx_tr">
<th id="S4.T4.1.9.7.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask + Para</th>
<th id="S4.T4.1.9.7.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">63.7</th>
<td id="S4.T4.1.9.7.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">550.7 (0.6)</td>
<td id="S4.T4.1.9.7.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">4.7 (0.1)</td>
</tr>
<tr id="S4.T4.1.10.8" class="ltx_tr">
<th id="S4.T4.1.10.8.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_r" style="padding:1pt 3.0pt;">FT + Mask + Para + Rand</th>
<th id="S4.T4.1.10.8.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" style="padding:1pt 3.0pt;">86.5</th>
<td id="S4.T4.1.10.8.3" class="ltx_td ltx_align_right ltx_border_b" style="padding:1pt 3.0pt;">352.0 (1.5)</td>
<td id="S4.T4.1.10.8.4" class="ltx_td ltx_align_right ltx_border_b" style="padding:1pt 3.0pt;">5.2 (0.2)</td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">Table 4: </span>Fluency and consistency with mass-editing on <span id="S4.T4.3.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>.</figcaption>
</figure>
</section>
<section id="S5" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">5 </span>Experiments</h2>

<section id="S5.SS1" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">5.1 </span>Mass-Editing</h3>

<div id="S5.SS1.p1" class="ltx_para">
<p id="S5.SS1.p1.4" class="ltx_p">Our main results are on mass-editing with on ZsRE and <span id="S5.SS1.p1.4.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>, following the same setting in <cite class="ltx_cite ltx_citemacro_citet">Meng et al. (<a href="#bib.bib7" title="" class="ltx_ref">2023</a>)</cite>.
Each dataset provides 10,000 requested edits (i.e., <math id="S5.SS1.p1.1.m1.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S5.SS1.p1.1.m1.1a"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p1.1.m1.1.1" xref="S5.SS1.p1.1.m1.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p1.1.m1.1b"><ci id="S5.SS1.p1.1.m1.1.1.cmml" xref="S5.SS1.p1.1.m1.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p1.1.m1.1c">\mathcal{E}</annotation></semantics></math>).
As described in Section <a href="#S3" title="3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>, we
augment the fine-tuning data with pseudo-paraphrases of the edit prompts <math id="S5.SS1.p1.2.m2.1" class="ltx_Math" alttext="\mathcal{P}" display="inline"><semantics id="S5.SS1.p1.2.m2.1a"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p1.2.m2.1.1" xref="S5.SS1.p1.2.m2.1.1.cmml">𝒫</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p1.2.m2.1b"><ci id="S5.SS1.p1.2.m2.1.1.cmml" xref="S5.SS1.p1.2.m2.1.1">𝒫</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p1.2.m2.1c">\mathcal{P}</annotation></semantics></math> for generalization supervision and random facts <math id="S5.SS1.p1.3.m3.1" class="ltx_Math" alttext="\mathcal{R}" display="inline"><semantics id="S5.SS1.p1.3.m3.1a"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p1.3.m3.1.1" xref="S5.SS1.p1.3.m3.1.1.cmml">ℛ</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p1.3.m3.1b"><ci id="S5.SS1.p1.3.m3.1.1.cmml" xref="S5.SS1.p1.3.m3.1.1">ℛ</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p1.3.m3.1c">\mathcal{R}</annotation></semantics></math>
for locality supervision.
More specifically, for each edit in <math id="S5.SS1.p1.4.m4.1" class="ltx_Math" alttext="\mathcal{E}" display="inline"><semantics id="S5.SS1.p1.4.m4.1a"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p1.4.m4.1.1" xref="S5.SS1.p1.4.m4.1.1.cmml">ℰ</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p1.4.m4.1b"><ci id="S5.SS1.p1.4.m4.1.1.cmml" xref="S5.SS1.p1.4.m4.1.1">ℰ</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p1.4.m4.1c">\mathcal{E}</annotation></semantics></math> we generate
15 paraphrases and take 20 facts from the training split
while ensuring that they do not contain any evaluation facts.
Thus the total number of facts we fine-tune on is 360,000.
We fine-tune GPT-J (6B) <cite class="ltx_cite ltx_citemacro_citep">(Wang and Komatsuzaki, <a href="#bib.bib13" title="" class="ltx_ref">2021</a>)</cite> with LoRA <cite class="ltx_cite ltx_citemacro_citep">(Hu et al., <a href="#bib.bib5" title="" class="ltx_ref">2022</a>)</cite> for computational efficiency.
We optimize (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>). The training takes around 7 hours on 8 GPUs.</p>
</div>
<div id="S5.SS1.p2" class="ltx_para">
<p id="S5.SS1.p2.1" class="ltx_p">We give the results in Table <a href="#S3.T2" title="Table 2 ‣ Contrastive learning. ‣ 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>
where the row “FT + Mask + Para + Rand” corresponds to our final method.
We show various ablations to illustrate the effect of
individual components.
We can make the following observations.
First, the proposed prompt masking in (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>) (FT + Mask)
improves the performance of vanilla fine-tuning (FT),
supporting the intuition that minimizing the model update is beneficial.
In fact, on ZsRE this already outperforms MEMIT without any data augmentation.
Second, augmenting the data with paraphrased prompts substantially improves generalization (FT + Mask + Para).
Third, augmenting the data with random facts further improves locality
(FT + Mask + Para + Rand), allowing pure fine-tuning to match the
performance of MEMIT on <span id="S5.SS1.p2.1.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>.
We find that adding the DPO loss on top of the final method does not yield improvements.</p>
</div>
</section>
<section id="S5.SS2" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">5.2 </span>Single-Editing</h3>

<div id="S5.SS2.p1" class="ltx_para">
<p id="S5.SS2.p1.1" class="ltx_p">To compare with existing methods developed for single-editing (i.e., updating the model for a single fact),
we consider optimizing (<a href="#S3.E2" title="In 3 Method ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>) one edit at a time.
We follow the setting in ROME and use GPT-2 XL (1.5B) <cite class="ltx_cite ltx_citemacro_cite">Radford et al. (<a href="#bib.bib9" title="" class="ltx_ref">2019</a>)</cite>.
The training takes around 1.4 seconds per edit on average.
We give the results in Table <a href="#S4.T3" title="Table 3 ‣ 4 Related Work ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>.
We find that it is helpful to include similar facts instead of random facts for locality
supervision, presumably because fine-tuning is more sensitive with small data size
thus requiring more care in the selection of demonstrations.
We use Sentence-BERT embeddings <cite class="ltx_cite ltx_citemacro_citep">(Reimers and Gurevych, <a href="#bib.bib11" title="" class="ltx_ref">2019</a>)</cite> and take 15 nearest facts as <math id="S5.SS2.p1.1.m1.1" class="ltx_Math" alttext="\mathcal{R}" display="inline"><semantics id="S5.SS2.p1.1.m1.1a"><mi class="ltx_font_mathcaligraphic" id="S5.SS2.p1.1.m1.1.1" xref="S5.SS2.p1.1.m1.1.1.cmml">ℛ</mi><annotation-xml encoding="MathML-Content" id="S5.SS2.p1.1.m1.1b"><ci id="S5.SS2.p1.1.m1.1.1.cmml" xref="S5.SS2.p1.1.m1.1.1">ℛ</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS2.p1.1.m1.1c">\mathcal{R}</annotation></semantics></math>.
On ZsRE, our method outperforms all existing single-edit methods.
On <span id="S5.SS2.p1.1.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>, our method lags behind ROME which is specifically optimized for single-editing,
but still achieves the second-best edit score.</p>
</div>
<figure id="S5.T5" class="ltx_table">
<table id="S5.T5.1" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S5.T5.1.1.1" class="ltx_tr">
<th id="S5.T5.1.1.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">Editor</th>
<th id="S5.T5.1.1.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">Score</th>
<th id="S5.T5.1.1.1.3" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">Fluency</th>
<th id="S5.T5.1.1.1.4" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">Consistency</th>
</tr>
<tr id="S5.T5.1.2.2" class="ltx_tr">
<th id="S5.T5.1.2.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">— (original GPT-2 XL)</th>
<th id="S5.T5.1.2.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">30.5</th>
<th id="S5.T5.1.2.2.3" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">626.6 (0.3)</th>
<th id="S5.T5.1.2.2.4" class="ltx_td ltx_align_right ltx_th ltx_th_column ltx_border_t" style="padding:1pt 3.0pt;">31.9 (0.2)</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S5.T5.1.3.1" class="ltx_tr">
<th id="S5.T5.1.3.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">FT</th>
<th id="S5.T5.1.3.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_tt" style="padding:1pt 3.0pt;">65.1</th>
<td id="S5.T5.1.3.1.3" class="ltx_td ltx_align_right ltx_border_tt" style="padding:1pt 3.0pt;">607.1 (1.1)</td>
<td id="S5.T5.1.3.1.4" class="ltx_td ltx_align_right ltx_border_tt" style="padding:1pt 3.0pt;">40.5 (0.3)</td>
</tr>
<tr id="S5.T5.1.4.2" class="ltx_tr">
<th id="S5.T5.1.4.2.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">FT-L</th>
<th id="S5.T5.1.4.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">66.9</th>
<td id="S5.T5.1.4.2.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">621.4 (1.0)</td>
<td id="S5.T5.1.4.2.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">37.4 (0.3)</td>
</tr>
<tr id="S5.T5.1.5.3" class="ltx_tr">
<th id="S5.T5.1.5.3.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">KN</th>
<th id="S5.T5.1.5.3.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">35.6</th>
<td id="S5.T5.1.5.3.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">570.4 (2.3)</td>
<td id="S5.T5.1.5.3.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">30.3 (0.3)</td>
</tr>
<tr id="S5.T5.1.6.4" class="ltx_tr">
<th id="S5.T5.1.6.4.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">KE</th>
<th id="S5.T5.1.6.4.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">52.2</th>
<td id="S5.T5.1.6.4.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">586.6 (2.1)</td>
<td id="S5.T5.1.6.4.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">31.2 (0.3)</td>
</tr>
<tr id="S5.T5.1.7.5" class="ltx_tr">
<th id="S5.T5.1.7.5.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">MEND</th>
<th id="S5.T5.1.7.5.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">57.9</th>
<td id="S5.T5.1.7.5.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">624.2 (0.4)</td>
<td id="S5.T5.1.7.5.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">34.8 (0.3)</td>
</tr>
<tr id="S5.T5.1.8.6" class="ltx_tr">
<th id="S5.T5.1.8.6.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">ROME</th>
<th id="S5.T5.1.8.6.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" style="padding:1pt 3.0pt;">89.2</th>
<td id="S5.T5.1.8.6.3" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">621.9 (0.5)</td>
<td id="S5.T5.1.8.6.4" class="ltx_td ltx_align_right" style="padding:1pt 3.0pt;">41.9 (0.3)</td>
</tr>
<tr id="S5.T5.1.9.7" class="ltx_tr">
<th id="S5.T5.1.9.7.1" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_b ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">FT + Mask + Para + Sim</th>
<th id="S5.T5.1.9.7.2" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r ltx_border_t" style="padding:1pt 3.0pt;">83.1</th>
<td id="S5.T5.1.9.7.3" class="ltx_td ltx_align_right ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">557.0 (1.8)</td>
<td id="S5.T5.1.9.7.4" class="ltx_td ltx_align_right ltx_border_b ltx_border_t" style="padding:1pt 3.0pt;">15.2 (0.3)</td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">Table 5: </span>Fluency and consistency with single-editing on <span id="S5.T5.3.1" class="ltx_text ltx_font_smallcaps">CounterFact</span>.</figcaption>
</figure>
</section>
<section id="S5.SS3" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">5.3 </span>Generative metrics</h3>

<div id="S5.SS3.p1" class="ltx_para">
<p id="S5.SS3.p1.1" class="ltx_p">We report results on generative metrics in Table <a href="#S4.T4" title="Table 4 ‣ 4 Related Work ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">4</span></a> and <a href="#S5.T5" title="Table 5 ‣ 5.2 Single-Editing ‣ 5 Experiments ‣ Model Editing by Pure Fine-Tuning" class="ltx_ref"><span class="ltx_text ltx_ref_tag">5</span></a>
for completeness.
Following prior work <cite class="ltx_cite ltx_citemacro_citep">(Meng et al., <a href="#bib.bib6" title="" class="ltx_ref">2022</a>, <a href="#bib.bib7" title="" class="ltx_ref">2023</a>)</cite>,
we report fluency (entropy of <math id="S5.SS3.p1.1.m1.1" class="ltx_Math" alttext="n" display="inline"><semantics id="S5.SS3.p1.1.m1.1a"><mi id="S5.SS3.p1.1.m1.1.1" xref="S5.SS3.p1.1.m1.1.1.cmml">n</mi><annotation-xml encoding="MathML-Content" id="S5.SS3.p1.1.m1.1b"><ci id="S5.SS3.p1.1.m1.1.1.cmml" xref="S5.SS3.p1.1.m1.1.1">𝑛</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS3.p1.1.m1.1c">n</annotation></semantics></math>-gram distributions) and
consistency (similarity score with a reference text).
Our fine-tuning methods take a hit on these metrics while improving the
edit score, showing that more work is needed to go beyond classification.
However, recent work shows that <em id="S5.SS3.p1.1.1" class="ltx_emph ltx_font_italic">none</em> of the compared editors preserves
downstream performance <cite class="ltx_cite ltx_citemacro_citep">(Gu et al., <a href="#bib.bib4" title="" class="ltx_ref">2024</a>)</cite>,
thus achieving this goal meaningfully is still an open problem.</p>
</div>
</section>
</section>
<section id="S6" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">6 </span>Conclusions</h2>

<div id="S6.p1" class="ltx_para">
<p id="S6.p1.1" class="ltx_p">We have demonstrated that pure fine-tuning is sufficient to obtain strong edit performance
with a slight modification: optimizing the conditional likelihood and augmenting the data
with additional facts.
Our results challenge the assumption that fine-tuning is ineffective as a model editor, suggesting that model editing could become part of standard training.</p>
</div>
</section>
<section id="Sx1" class="ltx_section">
<h2 class="ltx_title ltx_title_section">Limitations</h2>

<div id="Sx1.p1" class="ltx_para">
<p id="Sx1.p1.1" class="ltx_p">Our scope is deliberately limited to the classification aspect of model editing
rather than the generative aspect to demonstrate the viability of a fine-tuning editor.
Thus our approach is currently unable to preserve the LLM’s general capabilities,
as is the case with all existing mass editors.</p>
</div>
</section>
<section id="bib" class="ltx_bibliography">
<h2 class="ltx_title ltx_title_bibliography">References</h2>

<ul class="ltx_biblist">
<li id="bib.bib1" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Dai et al. (2022)</span>
<span class="ltx_bibblock">
Damai Dai, Li Dong, Yaru Hao, Zhifang Sui, Baobao Chang, and Furu Wei. 2022.

</span>
<span class="ltx_bibblock">Knowledge neurons in pretrained transformers.

</span>
<span class="ltx_bibblock">In <em id="bib.bib1.1.1" class="ltx_emph ltx_font_italic">Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)</em>, pages 8493–8502.

</span>
</li>
<li id="bib.bib2" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">De Cao et al. (2021)</span>
<span class="ltx_bibblock">
Nicola De Cao, Wilker Aziz, and Ivan Titov. 2021.

</span>
<span class="ltx_bibblock">Editing factual knowledge in language models.

</span>
<span class="ltx_bibblock">In <em id="bib.bib2.1.1" class="ltx_emph ltx_font_italic">Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing</em>, pages 6491–6506.

</span>
</li>
<li id="bib.bib3" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Geva et al. (2021)</span>
<span class="ltx_bibblock">
Mor Geva, Roei Schuster, Jonathan Berant, and Omer Levy. 2021.

</span>
<span class="ltx_bibblock">Transformer feed-forward layers are key-value memories.

</span>
<span class="ltx_bibblock">In <em id="bib.bib3.1.1" class="ltx_emph ltx_font_italic">Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing</em>, pages 5484–5495.

</span>
</li>
<li id="bib.bib4" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Gu et al. (2024)</span>
<span class="ltx_bibblock">
Jia-Chen Gu, Hao-Xiang Xu, Jun-Yu Ma, Pan Lu, Zhen-Hua Ling, Kai-Wei Chang, and Nanyun Peng. 2024.

</span>
<span class="ltx_bibblock">Model editing can hurt general abilities of large language models.

</span>
<span class="ltx_bibblock"><em id="bib.bib4.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2401.04700</em>.

</span>
</li>
<li id="bib.bib5" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Hu et al. (2022)</span>
<span class="ltx_bibblock">
Edward J Hu, yelong shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. 2022.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://openreview.net/forum?id=nZeVKeeFYf9" title="" class="ltx_ref ltx_href">LoRA: Low-rank adaptation of large language models</a>.

</span>
<span class="ltx_bibblock">In <em id="bib.bib5.1.1" class="ltx_emph ltx_font_italic">International Conference on Learning Representations</em>.

</span>
</li>
<li id="bib.bib6" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Meng et al. (2022)</span>
<span class="ltx_bibblock">
Kevin Meng, David Bau, Alex Andonian, and Yonatan Belinkov. 2022.

</span>
<span class="ltx_bibblock">Locating and editing factual associations in gpt.

</span>
<span class="ltx_bibblock"><em id="bib.bib6.1.1" class="ltx_emph ltx_font_italic">Advances in Neural Information Processing Systems</em>, 35:17359–17372.

</span>
</li>
<li id="bib.bib7" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Meng et al. (2023)</span>
<span class="ltx_bibblock">
Kevin Meng, Arnab Sen Sharma, Alex J Andonian, Yonatan Belinkov, and David Bau. 2023.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://openreview.net/forum?id=MkbcAHIYgyS" title="" class="ltx_ref ltx_href">Mass-editing memory in a transformer</a>.

</span>
<span class="ltx_bibblock">In <em id="bib.bib7.1.1" class="ltx_emph ltx_font_italic">The Eleventh International Conference on Learning Representations</em>.

</span>
</li>
<li id="bib.bib8" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Mitchell et al. (2022)</span>
<span class="ltx_bibblock">
Eric Mitchell, Charles Lin, Antoine Bosselut, Chelsea Finn, and Christopher D Manning. 2022.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://openreview.net/forum?id=0DcZxeWfOPt" title="" class="ltx_ref ltx_href">Fast model editing at scale</a>.

</span>
<span class="ltx_bibblock">In <em id="bib.bib8.1.1" class="ltx_emph ltx_font_italic">International Conference on Learning Representations</em>.

</span>
</li>
<li id="bib.bib9" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Radford et al. (2019)</span>
<span class="ltx_bibblock">
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. 2019.

</span>
<span class="ltx_bibblock">Language models are unsupervised multitask learners.

</span>
<span class="ltx_bibblock"><em id="bib.bib9.1.1" class="ltx_emph ltx_font_italic">OpenAI blog</em>, 1(8):9.

</span>
</li>
<li id="bib.bib10" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Rafailov et al. (2023)</span>
<span class="ltx_bibblock">
Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. 2023.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://openreview.net/forum?id=HPuSIXJaa9" title="" class="ltx_ref ltx_href">Direct preference optimization: Your language model is secretly a reward model</a>.

</span>
<span class="ltx_bibblock">In <em id="bib.bib10.1.1" class="ltx_emph ltx_font_italic">Thirty-seventh Conference on Neural Information Processing Systems</em>.

</span>
</li>
<li id="bib.bib11" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Reimers and Gurevych (2019)</span>
<span class="ltx_bibblock">
Nils Reimers and Iryna Gurevych. 2019.

</span>
<span class="ltx_bibblock">Sentence-bert: Sentence embeddings using siamese bert-networks.

</span>
<span class="ltx_bibblock">In <em id="bib.bib11.1.1" class="ltx_emph ltx_font_italic">Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)</em>, pages 3982–3992.

</span>
</li>
<li id="bib.bib12" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Sinitsin et al. (2020)</span>
<span class="ltx_bibblock">
Anton Sinitsin, Vsevolod Plokhotnyuk, Dmitry Pyrkin, Sergei Popov, and Artem Babenko. 2020.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://openreview.net/forum?id=HJedXaEtvS" title="" class="ltx_ref ltx_href">Editable neural networks</a>.

</span>
<span class="ltx_bibblock">In <em id="bib.bib12.1.1" class="ltx_emph ltx_font_italic">International Conference on Learning Representations</em>.

</span>
</li>
<li id="bib.bib13" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Wang and Komatsuzaki (2021)</span>
<span class="ltx_bibblock">
Ben Wang and Aran Komatsuzaki. 2021.

</span>
<span class="ltx_bibblock">GPT-J-6B: A 6 Billion Parameter Autoregressive Language Model.

</span>
<span class="ltx_bibblock"><a target="_blank" href="https://github.com/kingoflolz/mesh-transformer-jax" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://github.com/kingoflolz/mesh-transformer-jax</a>.

</span>
</li>
<li id="bib.bib14" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zhang et al. (2024)</span>
<span class="ltx_bibblock">
Ningyu Zhang, Yunzhi Yao, Bozhong Tian, Peng Wang, Shumin Deng, Mengru Wang, Zekun Xi, Shengyu Mao, Jintian Zhang, Yuansheng Ni, et al. 2024.

</span>
<span class="ltx_bibblock">A comprehensive study of knowledge editing for large language models.

</span>
<span class="ltx_bibblock"><em id="bib.bib14.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2401.01286</em>.

</span>
</li>
<li id="bib.bib15" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zheng et al. (2023)</span>
<span class="ltx_bibblock">
Ce Zheng, Lei Li, Qingxiu Dong, Yuxuan Fan, Zhiyong Wu, Jingjing Xu, and Baobao Chang. 2023.

</span>
<span class="ltx_bibblock">Can we edit factual knowledge by in-context learning?

</span>
<span class="ltx_bibblock"><em id="bib.bib15.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2305.12740</em>.

</span>
</li>
</ul>
</section>
</article>
</div>
<div class="ar5iv-footer"><a href="/html/2402.11077" class="ar5iv-nav-button ar5iv-nav-button-prev">◄</a>
    <a class="ar5iv-home-button" href="/"><img height="40" alt="ar5iv homepage" src="/assets/ar5iv.png"></a>
    <a href="/feeling_lucky" class="ar5iv-text-button">Feeling<br>lucky?</a>
    <a href="/log/2402.11078" class="ar5iv-text-button ar5iv-severity-warning">Conversion<br>report</a>
    <a class="ar5iv-text-button" target="_blank" href="https://github.com/dginev/ar5iv/issues/new?template=improve-article--arxiv-id-.md&title=Improve+article+2402.11078">Report<br>an issue</a>
    <a href="https://arxiv.org/abs/2402.11078" class="ar5iv-text-button arxiv-ui-theme">View&nbsp;original<br>on&nbsp;arXiv</a><a href="/html/2402.11079" class="ar5iv-nav-button ar5iv-nav-button-next">►</a>
</div><footer class="ltx_page_footer">
<a class="ar5iv-toggle-color-scheme" href="javascript:toggleColorScheme()" title="Toggle ar5iv color scheme"><span class="color-scheme-icon"></span></a>
<a class="ar5iv-footer-button" href="https://arxiv.org/help/license" target="_blank">Copyright</a>
<a class="ar5iv-footer-button" href="https://arxiv.org/help/policies/privacy_policy" target="_blank">Privacy Policy</a>

<div class="ltx_page_logo">Generated  on Tue Mar  5 16:50:50 2024 by <a target="_blank" href="http://dlmf.nist.gov/LaTeXML/" class="ltx_LaTeXML_logo"><span style="letter-spacing:-0.2em; margin-right:0.1em;">L<span class="ltx_font_smallcaps" style="position:relative; bottom:2.2pt;">a</span>T<span class="ltx_font_smallcaps" style="font-size:120%;position:relative; bottom:-0.2ex;">e</span></span><span style="font-size:90%; position:relative; bottom:-0.2ex;">XML</span><img src="data:image/png;base64,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" alt="Mascot Sammy"></a>
</div></footer>
</div>

    <script>
      var canMathML = typeof(MathMLElement) == "function";
      if (!canMathML) {
        var body = document.querySelector("body");
        body.firstElementChild.setAttribute('style', 'opacity: 0;');
        var loading = document.createElement("div");
        loading.setAttribute("id", "mathjax-loading-spinner");
        var message = document.createElement("div");
        message.setAttribute("id", "mathjax-loading-message");
        message.innerText = "Typesetting Equations...";
        body.prepend(loading);
        body.prepend(message);

        var el = document.createElement("script");
        el.src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js";
        document.querySelector("head").appendChild(el);

        window.MathJax = {
          startup: {
            pageReady: () => {
              return MathJax.startup.defaultPageReady().then(() => {
                body.removeChild(loading);
                body.removeChild(message);
                body.firstElementChild.removeAttribute('style');
              }); } } };
      }
    </script>
    <script>
    // Auxiliary function, building the preview feature when
    // an inline citation is clicked
    function clicked_cite(e) {
      e.preventDefault();
      let cite = this.closest('.ltx_cite');
      let next = cite.nextSibling;
      if (next && next.nodeType == Node.ELEMENT_NODE && next.getAttribute('class') == "ar5iv-bibitem-preview") {
        next.remove();
        return; }
      // Before adding a preview modal,
      // cleanup older previews, in case they're still open
      document.querySelectorAll('span.ar5iv-bibitem-preview').forEach(function(node) {
        node.remove();
      })

      // Create the preview
      preview = document.createElement('span');
      preview.setAttribute('class','ar5iv-bibitem-preview');
      let target = document.getElementById(this.getAttribute('href').slice(1));
      target.childNodes.forEach(function (child) {
        preview.append(child.cloneNode(true));
      });
      let close_x = document.createElement('button');
      close_x.setAttribute("aria-label","Close modal for bibliography item preview");
      close_x.textContent = "×";
      close_x.setAttribute('class', 'ar5iv-button-close-preview');
      close_x.setAttribute('onclick','this.parentNode.remove()');
      preview.append(close_x);
      preview.querySelectorAll('.ltx_tag_bibitem').forEach(function(node) {
        node.remove();
      });
      cite.parentNode.insertBefore(preview, cite.nextSibling);
      return;
    }
    // Global Document initialization:
    // - assign the preview feature to all inline citation links
    document.querySelectorAll(".ltx_cite .ltx_ref").forEach(function (link) {
      link.addEventListener("click", clicked_cite);
    });
    </script>
    </body>
</html>

2402.11078
Fine-tuning is dismissed as not effective for model editing
due to its poor performance compared to more specialized methods.
However, fine-tuning is simple, agnostic to the architectural details of the model being edited,
and able to leverage ongoing advances in standard training methods (e.g., PEFT) ,
making it an appealing choice for a model editor.
In this work, we show that pure fine-tuning can be a viable approach to model editing.
We propose a slight modification of naive fine-tuning with two key ingredients.
First, we optimize the conditional likelihood rather than the full likelihood.
Second, we augment the data with random paraphrases and facts to encourage generalization and locality.
Our experiments on ZsRE andCounterFactshow that this simple modification
allows fine-tuning to often match or outperform specialized editors in the edit score.
abstract
Model Editing by Pure Fine-Tuning
Abstract
2402.11078
1IntroductionModel editing is a promising approach to combating incorrect or otherwise unwanted knowledge in LLMs.
It assumes a set of edits that assert desired information
and aims to alter the model so that it not only succeeds in memorizing
the edits (efficacy) , but also applying the asserted information
to new prompts (generalization) ,withoutaffecting
inference that should remain unchanged (locality) .
There is clearly a trade-off between these metrics.
At one extreme, the model can achieve high efficacy by
memorizing the edits, but it will fail in generalization and locality.
At another extreme, the model can achieve high locality by
staying unmodified, but it will fail in efficacy and generalization.A straightforward approach of fine-tuning the model on the requested edits
is well known to perform poorly, especially in locality.
This motivated researchers to dismiss fine-tuning as an ineffective solution
to model editing and develop very specialized methods
such as MEND, ROME,
and MEMIT.
A central theme of these methods is “minimally invasive modification”,
typically involving a careful selection of weights and rank-one updates.
While technically interesting, they require a suite of assumptions
which may not be satisfied in other contexts (e.g., with a different model architecture) .
In contrast, fine-tuning is simple, completely agnostic to the details of the model,
and can take advantage of advances in standard training such as
parameter-efficient fine-tuning (PEFT)  techniques.EditorStandardmodel?Batchededits?Notraining?Effectiveedits?Naive fine-tuning✓✓✓✗MEND✗✓✗✓ROME✗✗✓✓MEMIT✗✓✓✓Our fine-tuning✓✓✗✓Table 1:Conceptual comparisons of model editors.In this work, we show that fine-tuning can be a viable approach to model editing,
focusing primarily on improving the edit score.
We shift the focus from models and algorithms to
training objectives and data augmentation.
See Table1for conceptual comparisons between our approach and other editors.
Our method is a slight variation on naive fine-tuning with two small but important differences.
First, in line with the theme of minimal modification, we optimize theconditionallikelihood (i.e., mask all tokens except the edited target) .
Second, we augment the data with self-induced paraphrases of the prompt
and arbitrary unrelated facts to encourage generalization and locality.
This simple change is sufficient for pure fine-tuning to match or outperform
specialized editors in mass-editing
and also perform respectably in single-editing.
introduction
Model Editing by Pure Fine-Tuning
1Introduction
2402.11078
2TaskWe consider the task of mass-editing.
Letdenote the vocabulary.
Afactis a sentencethat expresses
a subject-relation-object triplein natural language.
We follow the convention in the model editing literature and assume that
the objectis the lasttokens of.
The prefixexpressesand is denoted as theprompt.
Letdenote a set of facts to enforce (i.e., requested edits) .
Our goal is to edit a pretrained language model so that
it upholds the relations expressed inwithout changing its behavior on other facts.
In ZsRE,consists of 10,000 factual statements
(e.g., “The artwork Gideon’s Way was by who? John Creasey”) .
InCounterFact,consists of 10,000 counterfactual statements (e.g., “TextEdit, a product of Nintendo”) .An editor is evaluated by three competing metrics: efficacy, generalization, and locality.
Letdenote a language model edited on.
In ZsRE, efficacy is the accuracy offor;
generalization is the accuracy ofwhereis some paraphrase of;
locality is the accuracy ofwhereis an unrelated fact.
InCounterFact, efficacy and generalization measure the accuracy ofandwhereis a true object for(e.g., “Apple” in “TextEdit, a product of Nintendo”) .
Locality measures the accuracy ofwhereis a “neighbhorhood” prompt whose target must remain unchanged from(e.g., “Macintosh File System, a product of”“Apple”) .
In both datasets, the finaledit scoreis the harmonic mean of
efficacy, generalization, and locality.It is well known that naive fine-tuning, namely just optimizing(1) results in a poor editing score. The main reason is that while it
improves efficacy and possibly even generalization, it harms locality by changing the
model’s predictions on unrelated or neighborhood prompts.
This led to the development of highly specialized editing methods,
with the implicit assumption that fine-tuning is not effective for model editing.
body
Model Editing by Pure Fine-Tuning
2Task
2402.11078
3MethodWe propose a purely fine-tuning-based method that achieves a competitive editing score.
Our objective is a slight variation of (1) :(2) There are two small but important differences between (1)  and (2) .
First, we optimize theconditionallikelihood of the edit targetrather than the full likelihood.
Our motivation is to make the training more focused (for efficacy and generalization)  and minimize the damage caused by fine-tuning (for locality) .Second, we fine-tune not only on the requested editsbut
also additional facts inandto promote generalization and locality.is pseudo-paraphrases of the prompts ingenerated by appending text generated by the (unedited)  model.
More specifically, for eachwe generatewhere.is a set of facts that should not be altered
by editing on.
There are many ways to obtain, but we find takingrandomfacts from the training split to be simple and effective.
We filterto ensure thatdoes not include
the subject-relation-object triple used in evaluation.We emphasize that the augmented setsanddo not use the evaluation facts (otherwise it is trivial) .
Given the requested edits, we perform the data augmentation
and finetune the model according to (2) .Contrastive learning.Given that our goal inCounterFactis to achievewhereis the new object to enforce over the originalfor a given prompt,
it is natural to consider a contrastive objective.
We experimented with DPOwhere we frameas the “preferred” response
over, optimizing the DPO loss
jointly with (2) .
However, we found that prompt masking and data augmentation are already
effective and do not benefit from contrastive learning.ZsRECounterFactEditorScoreEfficacyGeneralizationLocalityScoreEfficacyGeneralizationLocality— (original GPT-J) 26.426.4 (0.6) 25.8 (0.5) 27.0 (0.5) 22.415.2 (0.7) 17.7 (0.6) 83.5 (0.5) FT-W (21st layer w/ weight decay) 42.169.6 (0.6) 64.8 (0.6) 24.1 (0.6) 67.699.4 (0.1) 77.0 (0.7) 46.9 (0.6) MEND20.019.4 (0.5) 18.6 (0.5) 22.4 (0.5) 23.115.7 (0.7) 18.5 (0.7) 83.0 (0.5) ROME2.621.0 (0.7) 19.6 (0.7) 0.9 (0.1) 50.350.2 (1.0) 50.4 (0.8) 50.2 (0.6) MEMIT50.796.7 (0.3) 89.7 (0.5) 26.6 (0.5) 85.898.9 (0.2) 88.6 (0.5) 73.7(0.5) FT44.899.9(0.03) 98.9(0.2) 21.4 (0.5) 52.879.6 (0.8) 58.5 (0.8) 36.8 (0.7) FT (21st layer) 42.999.9(0.0) 87.4 (0.5) 20.5 (0.5) 60.599.9 (0.04) 63.3 (0.8) 42.0 (0.6) FT + Mask58.397.6 (0.3) 91.7 (0.5) 32.9 (0.6) 54.397.1 (0.3) 62.1 (0.8) 34.7 (0.6) FT + Mask + Para56.199.9(0.0) 98.7 (0.2) 29.9 (0.5) 63.7100.0(0.0) 92.5 (0.4) 38.0 (0.6) FT + Mask + Para + Rand62.099.9(0.0) 97.0 (0.3) 35.6(0.6) 86.598.8 (0.2) 93.6(0.4) 72.0 (0.6) FT + Mask + Para + Rand + DPO————85.598.8 (0.2) 93.4 (0.4) 70.1 (0.6) Table 2:Mass-editing results on ZsRE andCounterFact(10,000 edits each)  with GPT-J. The results of the specialized methods (FT-W, MEND, ROME, MEMIT)  are from. FT denotes naive fine-tuning on the requested edits; FT (21st layer)  denotes FT only on the 21st layer. “+ Mask” means we mask the prompt. “+ Para” means we augment the data with model-generated paraphrases of the requested edits. “+ Rand” means we augment the data withrandomfacts from the training split (not overlapping with any evaluation facts) . “+ DPO” means we additionally optimize the DPO loss term using the changed target as the preferred response over the original target (which is supplied inCounterFact) .
body
Model Editing by Pure Fine-Tuning
3Method
2402.11078
4Related WorkWe discuss some prominent model editing methods and the different assumptions they require to highlight the simplicity of our fine-tuning approach; we refer tofor an in-depth survey.MENDis a meta-learning methodthat predicts the change in the gradient.
Similar to our approach, it also involves an explicit training stage (on the training split of ZsRE) .
It uses a special rank-one decomposition of the gradient for parameter efficiency.
In our case, we achieve parameter efficiency without special considerations
simply by leveraging PEFT methods.
MEND works poorly for mass-editing.ROMEis a locate-then-edit methodthat first uses causal tracing to identify the feedforward layer to change, and then applies
a rank-one update to the layer’s weight matrix.
While it does not involve an explicit training stage, it
does require an explicit knowledge of the subjectin the edit
and its vector representation (which is heuristically induced) .
It also relies on Wikipedia to estimate the covariance matrix of
the subject embeddings (needed in the rank-one update) .
ROME works well on single-editing but poorly on mass-editing.
MEMITextends ROME to multiple edits
by carefully spreading updates to multiple layers.
Like ROME, it requires layer specification, subject embeddings,
and covariance statistics obtained from Wikipedia.
MEMIT is very effective for mass-editing and is our strongest baseline.IKEproposes in-context learning for model editing. While it similarly uses demonstrations, it is critically limited to single-editing. It also requires an initial model that is capable of effective in-context learning. Consequently, IKE focuses on single-editing with large-scale LLMs, making their results not comparable to ours.We define our scope as achieving a competitive edit score through pure fine-tuning.
In particular, we do not focus on preserving general capabilities of the model being edited.
Existing methods consider basic metrics such as-gram repetition,
but recent work shows that performance on a variety of downstream tasks
drops to zero under any editor.
We leave preserving the general capabilities of an LLM with a fine-tuning editor
as the next step of our work.ZsRECounterFactEditorScoreEfficacyGeneralizationLocalityScoreEfficacyGeneralizationLocality— (original GPT-2 XL) 22.522.2 (0.5) 21.3 (0.5) 24.2 (0.5) 30.522.2 (0.9) 24.7 (0.8) 78.1 (0.6) FT45.999.6 (0.1) 82.1 (0.1) 23.2 (0.5) 65.1100.0(0.0) 87.9 (0.6) 40.4 (0.7) FT-L40.192.3 (0.4) 47.2 (0.7) 23.4 (0.5) 66.999.1 (0.2) 48.7 (1.0) 70.3 (0.7) KN----35.628.7 (1.0) 28.0 (0.9) 72.9 (0.7) KE41.865.5 (0.6) 61.4 (0.6) 24.9 (0.5) 52.284.3 (0.8) 75.4 (0.8) 30.9 (0.7) MEND42.975.9 (0.5) 65.3 (0.6) 24.1 (0.5) 57.999.1 (0.2) 65.4 (0.9) 37.9 (0.7) ROME47.999.8 (0.0) 88.1 (0.5) 24.2 (0.5) 89.2100 (0.1) 96.4(0.3) 75.4(0.7) FT + Mask + Para + Sim51.4100.0(0.0) 99.9(0.0) 26.1(0.8) 83.198.6 (0.3) 87.3 (0.7) 69.0 (0.7) Table 3:Single-editing results on ZsRE (10,000 edits)  andCounterFact(7,500 edits)  with GPT-2 XL. “+ Sim” means we include similar facts (measured by Sentence-BERT)  instead of random facts for locality supervision.EditorScoreFluencyConsistency— (original GPT-J) 22.4622.4 (0.3) 29.4 (0.2) FT-W67.6293.9 (2.4) 15.9 (0.3) MEND20.0618.4 (0.3) 31.1 (0.2) ROME50.3589.6 (0.5) 3.3 (0.0) MEMIT85.8619.9 (0.3) 40.1 (0.2) FT52.8626.1 (0.4) 31.0 (0.2) FT + Mask54.3563.6 (0.5) 6.1 (0.1) FT + Mask + Para63.7550.7 (0.6) 4.7 (0.1) FT + Mask + Para + Rand86.5352.0 (1.5) 5.2 (0.2) Table 4:Fluency and consistency with mass-editing onCounterFact.
body
Model Editing by Pure Fine-Tuning
4Related Work
2402.11078
5Experiments5.1Mass-EditingOur main results are on mass-editing with on ZsRE andCounterFact, following the same setting in.
Each dataset provides 10,000 requested edits (i.e.,) .
As described in Section3, we
augment the fine-tuning data with pseudo-paraphrases of the edit promptsfor generalization supervision and random factsfor locality supervision.
More specifically, for each edit inwe generate
15 paraphrases and take 20 facts from the training split
while ensuring that they do not contain any evaluation facts.
Thus the total number of facts we fine-tune on is 360,000.
We fine-tune GPT-J (6B) with LoRAfor computational efficiency.
We optimize (2) . The training takes around 7 hours on 8 GPUs.We give the results in Table2where the row “FT + Mask + Para + Rand” corresponds to our final method.
We show various ablations to illustrate the effect of
individual components.
We can make the following observations.
First, the proposed prompt masking in (2)  (FT + Mask) 
improves the performance of vanilla fine-tuning (FT) ,
supporting the intuition that minimizing the model update is beneficial.
In fact, on ZsRE this already outperforms MEMIT without any data augmentation.
Second, augmenting the data with paraphrased prompts substantially improves generalization (FT + Mask + Para) .
Third, augmenting the data with random facts further improves locality
(FT + Mask + Para + Rand) , allowing pure fine-tuning to match the
performance of MEMIT onCounterFact.
We find that adding the DPO loss on top of the final method does not yield improvements.5.2Single-EditingTo compare with existing methods developed for single-editing (i.e., updating the model for a single fact) ,
we consider optimizing (2)  one edit at a time.
We follow the setting in ROME and use GPT-2 XL (1.5B) .
The training takes around 1.4 seconds per edit on average.
We give the results in Table3.
We find that it is helpful to include similar facts instead of random facts for locality
supervision, presumably because fine-tuning is more sensitive with small data size
thus requiring more care in the selection of demonstrations.
We use Sentence-BERT embeddingsand take 15 nearest facts as.
On ZsRE, our method outperforms all existing single-edit methods.
OnCounterFact, our method lags behind ROME which is specifically optimized for single-editing,
but still achieves the second-best edit score.EditorScoreFluencyConsistency— (original GPT-2 XL) 30.5626.6 (0.3) 31.9 (0.2) FT65.1607.1 (1.1) 40.5 (0.3) FT-L66.9621.4 (1.0) 37.4 (0.3) KN35.6570.4 (2.3) 30.3 (0.3) KE52.2586.6 (2.1) 31.2 (0.3) MEND57.9624.2 (0.4) 34.8 (0.3) ROME89.2621.9 (0.5) 41.9 (0.3) FT + Mask + Para + Sim83.1557.0 (1.8) 15.2 (0.3) Table 5:Fluency and consistency with single-editing onCounterFact.5.3Generative metricsWe report results on generative metrics in Table4and5for completeness.
Following prior work,
we report fluency (entropy of-gram distributions)  and
consistency (similarity score with a reference text) .
Our fine-tuning methods take a hit on these metrics while improving the
edit score, showing that more work is needed to go beyond classification.
However, recent work shows thatnoneof the compared editors preserves
downstream performance,
thus achieving this goal meaningfully is still an open problem.
body
Model Editing by Pure Fine-Tuning
5Experiments
2402.11078
6ConclusionsWe have demonstrated that pure fine-tuning is sufficient to obtain strong edit performance
with a slight modification: optimizing the conditional likelihood and augmenting the data
with additional facts.
Our results challenge the assumption that fine-tuning is ineffective as a model editor, suggesting that model editing could become part of standard training.
body
Model Editing by Pure Fine-Tuning
6Conclusions
2402.11078
LimitationsOur scope is deliberately limited to the classification aspect of model editing
rather than the generative aspect to demonstrate the viability of a fine-tuning editor.
Thus our approach is currently unable to preserve the LLM’s general capabilities,
as is the case with all existing mass editors.
conclusion
Model Editing by Pure Fine-Tuning
Limitations