Question: Represent the article for finding a single-sentence TLDR

Question: Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the ``long tail'' of this distribution requires enormous amounts of data. Representations of rare words trained directly on end tasks are usually poor, requiring us to pre-train embeddings on external data, or treat all rare words as out-of-vocabulary words with a unique representation. We provide a method for predicting embeddings of rare words on the fly from small amounts of auxiliary data with a network trained end-to-end for the downstream task. We show that this improves against baselines where embeddings are trained on the end task for reading comprehension, recognizing textual entailment and language modeling. Natural language yields a Zipfian distribution BID28 which tells us that a core set of words (at the head of the distribution) are frequent and ubiquitous, while a significantly larger number (in the long tail) are rare. Learning representations for rare words is a well-known challenge of natural language understanding, since the standard end-to-end supervised learning methods require many occurrences of each word to generalize well. The typical remedy to the rare word problem is to learn embeddings for some proportion of the head of the distribution, possibly shifted towards the domain-specific vocabulary of the dataset or task at hand, and to treat all other words as out-of-vocabulary (OOV), replacing them with an unknown word "UNK" token with a shared embedding. This essentially heuristic solution is inelegant, as words from technical domains, names of people, places, institutions, and so on will lack a specific representation unless sufficient data are available to justify their inclusion in the vocabulary. This forces model designers to rely on overly large vocabularies, as observed by BID17 BID22, which are parametrically expensive, or to employ vocabulary selection strategies BID16. In both cases, we face the issue that words in the tail of the Zipfian distribution will typically still be too rare to learn good representations for through standard embedding methods. Some models, such as in the work of BID13, have sought to deal with the open vocabulary problem by obtaining representations of words from characters. This is successful at capturing the semantics of morphological derivations (e.g. "running" from "run") but puts significant pressure on the encoder to capture semantic distinctions amongst syntactically similar but semantically unrelated words (e.g. "run" vs. "rung"). Additionally, nothing about the spelling of named entities, e.g. "The Beatles", tells you anything about their semantics (namely that they are a rock band).In this paper we propose a new method for computing embeddings "on the fly", which jointly addresses the large vocabulary problem and the paucity of data for learning representations in the long tail of the Zipfian distribution. This method, which we illustrate in FIG0, can be summarized as follows: instead of directly learning separate representations for all words in a potentially unbounded vocabulary, we train a network to predict the representations of words based on auxiliary data. Such auxiliary data need only satisfy the general requirement that it describe some aspect of the semantics of the word for which a representation is needed. Examples of such data could be dictionary definitions, Wikipedia infoboxes, linguistic descriptions of named entities obtained from Wikipedia articles, or something as simple as the spelling of a word. We will refer to the content of auxiliary data as "definitions" throughout the paper, regardless of the source. Several sources of auxiliary data can be used simultaneously as input to a neural network that will compute a combined representation. These representations can then be used for out-of-vocabulary words, or combined with withinvocabulary word embeddings directly trained on the task of interest or pretrained from an external data source BID18 BID20. Crucially, the auxiliary data encoders are trained jointly with the objective, ensuring the preservation of semantic alignment with representations of within-vocabulary words. In the present paper, we will focus on a subset of these approaches and auxiliary data sources, restricting ourselves to producing out-of-vocabulary words embeddings from dictionary data, spelling, or both. The obvious use case for our method would be datasets and tasks where there are many rare terms such as technical writing or bio/medical text BID6. On such datasets, attempting to learn global vectors-for example GloVe embeddings BID20 -from external data, would only provide coverage for common words and would be unlikely to be exposed to sufficient (or any) examples of domain-specific technical terms to learn good enough representations. However, there are no (or significantly fewer) established neural network-based baselines on these tasks, which makes it harder to validate baseline . Instead, we present on a trio of well-established tasks, namely reading comprehension, recognizing textual entailment, and a variant on language modelling. For each task, we compare baseline models with embeddings trained directly only on the task objective to those same models with our on the fly embedding method. Additionally, we report for the same models with pretrained GLoVe vectors as input which we do not update. We aim to show how the gap in between the baseline and the data-rich GLoVe-based models can be partially but substantially closed merely through the introduction of relatively small amounts of auxiliary definitions. Quantitative show that auxiliary data improves performance. Qualitative evaluation indicates our method allows models to draw and exploit connections defined in auxiliary data, along the lines of synonymy and semantic relatedness. Arguably, the most popular approach for representing rare words is by using word embeddings trained on very large corpora of raw text. BID18 BID20. Such embeddings are typically explicitly or implicitly based on word co-occurence statistics. Being a big step forward from the models that are trained from scratch only on the task at hand, the approach can be criticized for being extremely data-hungry 1. Obtaining the necessary amounts of data may be difficult, e.g. in technical domains. Besides, auxiliary training criteria used in the pretraining approaches are not guaranteed to yield representations that are useful for the task at hand. BID7 proposed to represent OOV words by fixed random vectors. While this has shown to be effective for machine comprehension, this method does not account for word semantics at all, and therefore, does not cover the same ground as the method that we propose. There have been a number of attempts to achieve out-of-vocabulary generalization by relying on the spelling. BID13 used a bidirectional LSTM to read the spelling of rare words and showed that this can be helpful for language modeling and POS tagging. We too will investigate spelling as a source of auxiliary data. In this respect, the approach presented here subsumes theirs, and can be seen as a generalization to other types of definitions. The closest to our work is the study by BID10, in which a network is trained to produce an embedding of a dictionary definition that is close to the embedding of the headword. The network is shown to be an effective reverse dictionary and a crossword solver. Our approach is different in that we train a dictionary reader in an end-to-end fashion for a specific task, side-stepping the potentially suboptimal auxiliary ranking cost that was used in that earlier work. Their method also relies on the availability of high-quality pretrained embeddings which might not always be feasible. Another related work by BID14 uses dictionary definitions to provide initialization to a database embedding method, which is different from directly learning to use the definitions like we do. Concurrently with this work BID24 studied dynamic integration of knowledge from a commonsense knowledge base. In another concurrent work BID15 build a new dataset for named entity prediction and show that external knowledge can be very useful for this task.. We obtain representations by retrieving external information (e.g. a dictionary definition) and embedding it, for example, with another LSTM-RNN, instead of using a catch-all "UNK" representation for out-of-vocabulary items. At a higher level our approach belongs to the a broad family of methods for conditioning neural networks on external knowledge. For example, BID12 propose to add classes to a classifier by representing them using their "descriptions". By description they meant, for example, a canonical picture of a printed character, that would represent all its possible handwritten versions. Their idea to rely on descriptions is similar to our idea to rely on definitions, however we focus on understanding complex inputs instead of adding new output classes. Enhancing word embeddings with auxiliary data from knowledge bases (including wordnet) has a long tradition BID27 BID8. Our work differs from previous approaches in essential ways. First, we use a textual form and are not restricted to knowledge represented as a graph. Second, we learn in an end to end fashion, allowing the model to pick useful information for the task of interest. In general, a neural network processes a language input by replacing its elements x i, most often words, with the respective vectors e(x i), often called embeddings BID1. Embeddings are typically either trained from scratch or pretrained. When embeddings are trained from scratch, a restricted vocabulary V train = {w 1, . . ., w n} is defined, usually based on training set frequency. Words not in V train are replaced by a special token UNK with a trainable embedding e(UNK). Unseen test-time words w / ∈ V train are then represented by e(UNK), which effectively means the specific meaning of this word is lost. Even if w had been included in V train but was very rare, its learned embedding e(w) would likely not be very informative. The approach proposed in this work, described in FIG0, is to use definitions from auxiliary data, such as dictionaries, to compute embeddings of rare words on the fly, as opposed to having a persistent embedding for each of them. More specifically, this involves fetching a definition d(w) = (x 1, . . ., x k) and feeding it into a network f that produces an embedding e d (w) = f (e (x 1),..., e (x k)). We will refer to e d (w) as a definition embedding produced by a definition reader f. One can either use the same embeddings e = e when reading the dictionary or train different ones. Likewise, one can either stick to a shared vocabulary V dict = V train, or consider two different ones. When a word x i ∈ V dict is encountered, it is replaced by UNK and the respective trainable embedding e (UNK) is used. For the function f we consider three choices: a simple mean pooling (MP) DISPLAYFORM0 where V is a trainable matrix, and lastly, using the last state of an LSTM BID11, e d (w) = LST M (e (x 1),..., e (x k)). Many words have multiple dictionary definitions. We combine embeddings for multiple definitions using mean pooling. We include all definitions whose headwords match w or any possible lemma of a lower-cased w 2. To simplify the notation, the rest of the paper assumes that there is only one definition for each word. While the primary purpose of definition embeddings e d (w) is to inform the network about the rare words, they might also contain useful information for the words in V train. When we use both, we combine the information coming from the embeddings e(w) and the definition embeddings e d (w) by computing e c (w) = e(w) + W e d (w), where W is a trainable matrix, or just by simply summing the two, e c (w) = e(w) + e d (w). Alternatively it is possible to just use e c (w) = e(w) for w from V train and e c (w) = e d (w) otherwise. When no definition is available for a word w, we posit that e d (w) is a zero vector. A crucial observation that makes an implementation of the proposed approach feasible is that the definitions d(x i) of all words x i from the input can be processed in parallel 3.To keep things simple, we limited the scope and complexity of this first incarnation of our approach as follows. First, we do not consider definitions of word combinations, such as phrasal verbs like "give up" and geographical entities like "San Francisco". Second, our definition reader could itself better handle the unknown words w / ∈ V dict by using their definition embeddings e d (w) instead e (UNK), thereby implementing a form of recursion. We will investigate both in our future work. We worked on extractive question answering, semantic entailment classification and language modelling. For each task, we picked a baseline model and a architecture from the literature which we knew would provide sensible , to explore how augmenting it with on the fly embeddings would affect performance. We explored two complementary sources of auxiliary data. First, we used word definitions from WordNet BID19. While WordNet is mostly known for its structured information about synonyms, it does contain natural language definitions for all its 147306 lemmas (this also includes multi-word headwords which we do not consider in this work) 4. Second, we experimented with the character-level spelling of words as auxiliary data. To this end, in order to fit in with our use of dictionaries, we added fake definitions of the form "Word" → "W", "o", "r", "d".In order to measure the performance of models in "data-rich" scenarios where a large amount of unlabelled language data is available for the training of word representations, we used as pretrained word embeddings 300-dimensional GLoVe vectors trained on 840 billion words BID20. We compared our auxiliary data-augmented on the fly embedding technique to baselines and models with fixed GLoVe embeddings to measure how well our technique closes the gap between a data-poor and data-rich scenario. We used the Stanford Question Answering Dataset (SQuAD) BID21 ) that consists of approximately 100000 human-generated question-answer pairs. For each pair, a paragraph from Wikipedia is provided that contains the answer as a continuous span of words. Our basic model is a simplified version of a coattention network proposed in BID26. First, we represent the context of length n and the question of length m as matrices C ∈ R n,dand Q ∈ R m,d by running them through an LSTM and a linear transform. Next, we compute the affinity scores L = CQ T ∈ R n,m. By normalizing L with row-wise and column-wise softmaxes we construct context-to-question and question-to-context attention maps A C and A Q. These are used to construct a joint question-document representation U 0 as a concatenation along the feature axis of the matrices C, A C Q and A C A T Q C. We transform U 0 with a bidirectional LSTM and another ReLU BID9 layer to obtain the final context-document representation U 2. Finally, two linear layers followed by a softmax assign to each position of the document probabilities of it being the beginning and the end of the answer span. We refer the reader to the work of BID26 for more details. Compared to their model, the two main simplifications that we applied is skipping the iterative inference procedure and using usual ReLU instead of the highway-maxout units. Our baseline is a model with the embeddings trained purely from scratch. We found that it performs best with a small vocabulary of 10k most common words from the training set. This can be explained by a rather moderate size of the dataset: all the models we tried tended to overfit severely. In our preliminary experiments, we found that a smaller V train of 3k words is better for the models using auxiliary data, and that combining the information from definitions and word embeddings is helpful. Unless otherwise specified, we use summation preceded by a linear transformation for composing word embedding with definition embeddings: e c (w) = e(w) + W e d (w).We tried different models (MP and LSTM) for reading the dictionary and used an LSTM for reading the spelling. In addition to using either the spelling or the dictionary definitions, we tried mixing the dictionary definitions with the spelling. When both dictionary and spelling were used, we found that using a LSTM for reading the spelling and MP-L for reading dictionary definitions works best. As mentioned in Section 3 our dictionary lookup procedure involves lowercasing and lemmatization. In order to estimate the contribution of these steps we add to the comparison a model that fetches the spelling of a lemmatized and lowercased version of each word. The last model in our comparison is trained with the GLoVe embeddings. Except for GloVe embeddings, all vectors, such as word embeddings and LSTM states, have d=200 dimensions in all models. The are reported in TAB0. We report the exact match ratio as computed by the evaluation tools provided with the dataset, which is basically the accuracy of selecting the right answer. We report the average over multiple runs on the development set. Looking at the one can see that adding any external information in a significant improvement over the baseline model (B) (3.7 -10.5 points). When the dictionary alone is used, mean pooling (D3) performs similarly to LSTM (D4). For the model with mean pooling, we verified that the matrix W in computing e c (w) is necessary for best (see model D2), and back-propagating through the process of reading definition is helpful (see model D1). We thereby establish that our method is preferable to the one by BID14, which prescribes mean pooling of available embeddings without end-to-end training. We found that adding the spelling (S) helps more than adding a dictionary (D) (3 points difference), possibly due to relatively lower coverage of our dictionary. However, the model that uses both (SD) has a 1.1 point advantage over the model that uses just the spelling (S), demonstrating that combining several forms of auxiliary data allows the model to exploit the complementary information they provide. The model with GLoVe embeddings (G) is still ahead with a 1.1 point margin, but the gap has been shrunk. Finally, we evaluated the models S, SL and SD on the test set. The parameters for test evaluation were selected based on the development set 5. The test set confirm the benefit of using dictionary definitions (SD has a 1 point advantage over S). Lastly, the model that uses lemmatization and lowercasing (SL) to retrieve spelling does not outperform S, which shows that the advantage of SD over S is not due to the normalization procedures and that SD must be using the dictionary definitions in a non-trivial way. To understand how our model successfully uses the dictionary and what prevents it from using it better, we conducted a qualitative investigation on selected examples. Namely, we considered examples on which SD selected the correct answer span and S did not, and from them we chose the ones with the largest difference of log-likelihoods that S and SD assigned to the correct answer. Figure 2 shows the attention maps A C for both models for one of the examples. We can see that S has no clue that "overseas" may be an answer to an question about location, whereas SD is aware of that, presumably thanks to the definition "overseas -> in a foreign country". In a similar manner we observed SD being able to match "direction" and "eastwards", "where" and "outdoors". Another pattern that we saw is that the model with the dictionary was able to answer questions of the form "which scientist" or "which actress" better. Both words "scientist" and "actress" were not frequent enough to make it to V train, but the definitions "actress -> a female actor" "scientist -> a person with advanced knowledge of one or more sciences" apparently provided enough information about these words that the model could start matching them with named entities in the passage. Figure 2: The attention maps A C of the models with (on the left) and without the dictionary (on the right). The rows correspond to words of the context and the columns to the words of the question. One can see how with the help of the dictionary the model starts considering "overseas" as a candidate answer to "where".Furthermore, we compared the models G and SD in a similar way. We found that often SD simply was missing a definition. For a example, it was not able to match "XBox" and "console", "Mark Twain" and "author", "most-watched" and "most watched". We also saw cases where the definition was available but was not used, seemingly because the key word in the definition was outside V train = V dict. For example, "arrow" was defined as "a projectile with a straight thin shaft", and the word "projectile" was quite rare in the training corpus. As a consequence, the model had no chances to understand that an arrow is a weapon and match the word "arrow" in the context with the word "weapon" in the question. Likewise, "Earth" was defined as "planet", but "planet" was outside V train. Finally, we saw cases where inferring important aspects of meaning from the dictionary would be non-trivial, for example, guessing that "historian" is a "profession" from the definition "a person who is an authority on history and who studies it and writes about it" would involve serious common sense reasoning. We used the Stanford Natural Language Inference (SNLI) corpus BID3, which consists of around 500k pairs of sentences (hypothesis and premise) and the task is to predict the logical relation (contradiction, neutral or entailment) between them. In addition we used the MultiGenre Natural Language Inference (MultiNLI) corpus BID25, which effectively is a more recent and more diverse version of SNLI of approximately the same size. A key distinction of MultiNLI from SNLI is the availability of a "matched" and a "mismatched" development and test set. The matched test and development sets contain data from the same domains as the training set, whereas the mismatched ones were intentionally collected using data from different domains. We implemented a variant (replacing TreeLSTM by biLSTM) of Enhanced Sequential Inference Model (ESIM) BID5 that achieves close to SOTA accuracy. Similarly to the model used in the SQuAD experiments, this model represents hypothesis and premise as H ∈ R n,d and P ∈ R m,d matrices by encoding them using a bidirectional LSTM. Analogously, alignment matrices A H and A P are computed by normalizing affinity scores. These alignment matrices are used to form joint hypothesis-premise representations. For the hypothesis we compute and concatenate H, A H P, H − A H P and H A H P, yielding a h ∈ R n,4d sentence embedding, and proceed similarly for the premise. The ing sentence representations are then processed in parallel by a bidirectional LSTM and the final states of the LSTMs are concatenated and processed by a single layer Tanh MLP to predict entailment. Similarly to the SQuAD experiments, we found that the baseline model performs best with a larger vocabulary (5k words for SNLI, 20k words for MultiNLI) than the model that uses auxiliary information (3k words). Differently from SQuAD, we found it helpful to use a different vocabulary V dict = V train. We built V dict by collecting the 11000 words that occur most often in the definitions, where each definition is weighted with the frequency of its headword in the training data. While in theory it would still be possible to share word embeddings between the main model and the definition reader even when they have different vocabularies, we opted for the simpler option of using separate word embeddings e and e. Since with separate word embeddings having a subsequent linear transformations would be redundant, we simply add the of mean pooling k i=1 e (x i)/k to e(w). We use an LSTM for reading the spelling, but unlike the SQuAD experiments, we found that simply adding the last hidden state of the spelling LSTM to e(w) worked better. We also tried to use a LSTM for reading definitions but it did no better than the simpler mean pooling. Our last model used pretrained GloVe embeddings. 300-dimensional ESIM performed best for the baseline and GloVe models, whereas using just 100 dimensions worked better for the models using auxiliary information. All runs were repeated 3 times and scores are averaged. Results on SNLI and MultiNLI are presented in TAB1. Using dictionary definitions allows us to bridge ≈40% of the gap between training from scratch and using embeddings pretrained on 840 billion words, and this improvement is consistent on both datasets. Compared to the SQuAD , an important difference is that spelling was not as useful on SNLI and MultiNLI. We also note that we tried using fixed random embeddings for OOV words as proposed by BID7, and that this method did not bring a significant advantage over the baseline. In order to gain some insights on the performance of our entailment recognition models, in FIG1 we plot a t-SNE (van der) visualization of word embeddings computed for the words from BLESS dataset BID0. Specifically, we used embeddings produced by the definition encoder of our best SNLI model using Wordnet definitions. The BLESS dataset contains three categories of words: fruits, tools and vehicles. One can see that fruit words tend to be separated from tool and vehicle words. FIG1 shows that, as expected, dictionary-enabled models significantly outperform baseline models for sentences containing rare words. Experiments in the previous sections used datasets of moderate size. To get an idea of how useful different auxiliary data sources will be for datasets of various sizes, we also apply our approach to the One Billion Words (OBW) language modelling task BID4. In the first round of experiments, we use only 1% of the training data (∼ 10 7 words) and in the second we train our models on the whole training set (∼ 10 9 words). Similarly to prior work on using the spelling BID13 we restrict the softmax output layer to only predict probabilities of the 10k most common words, however, we do not impose such a constraint when the model processes the words from the input context. We want to assess thereby if having a definition of an observed word helps the model to predict the following ones from a restricted vocabulary. Our baseline model is an LSTM with 500 units and with trainable input embeddings for the 10k most frequent input words. This covers around 90.24% of all word occurrences. We consider computing embeddings of the less frequent input words from their dictionary definitions, GloVe vectors and spellings. These sources of auxiliary information were available for 63.35%, 97.43% and 100% of the rest of occurrences respectively. In order to compare how helpful these sources are when they are available, we run additional set of experiments with "restricted" inputs. Specifically, we only use auxiliary information for a word if it has both a GloVe embedding and a dictionary definition. When the word does not have any of these, we replace it with "UNK". We report for three variants of dictionary-enabled models. The first variant (dict1) uses the same LSTM for reading the text and the definitions. The second one (dict2) has two separate LSTMs but the word embeddings are shared 6. The third variant (dict+spelling) adds spelling to our best dictionary model. Lastly, we trained a model that used the lowercased lemma of the word as the definition. The training was early-stopped using a development set. We report the test perplexities in TAB2. Similarly to our other experiments, using external information to compute embeddings of unknown words helps in all cases. We observe a significant gain even for dict1, which is remarkable as this model has the same architecture and parameters as the baseline. We note that lemma+lowercase performs worse than any model with the dictionary, which suggests that dictionary definitions are used in a non-trivial way. Adding spelling consistently helps more than adding dictionary definitions. In our experiments with restricted inputs ((R) in TAB2 ), spelling and dict2 show similar performance, which suggests that this difference is mostly due to the complete coverage of spelling. Using both dictionary and spelling is consistently slightly better than using just spelling, and the improvement is more pronounced in the restricted setting. Using GloVe embeddings in the best perplexity. Switching to the full training set shrank all the gaps. To zoom in on how the models deal with rare words, we look at the perplexities of the words that appear right after out-of-vocabulary words (PPL after OOV). We can see that the ranking of different models mostly stays the same, yet the differences in performance become larger. For example, on the 1% version of the dataset, in the restricted setting, adding definitions to the spelling helps to bridge half of the 6 points PPL after OOV gap between spelling and GloVe. This is in line with our expectations that when definitions are available they should be helpful for handling rare words. We showed how different sources of auxiliary information, such as the spelling and a dictionary of definitions can be used to produce on the fly useful embeddings for rare words. While it was known before that adding the spelling information to the model is helpful, it is often hard or not possible to infer the meaning directly from the characters, as confirmed by our entailment recognition experiments. Our more general approach offers endless possibilities of adding other data sources and learning end-to-end to extract the relevant bits of information from them. Our experiments with a dictionary of definitions show the feasibility of the approach, as we report improvements over using just the spelling on question answering and semantic entailment classification tasks. Our qualitative investigations on the question answering data confirms our intuition on where the improvement comes from. It is also clear from them that adding more auxiliary data would help, and that it would probably be also useful to add definitions not just for words, but also for phrases (see "Mark Twain" from Section 4.1). We are planning to add more data sources (e.g. first sentences from Wikipedia articles) and better use the available ones (WordNet has definitions of phrasal verbs like "come across") in our future work. An important question that we did not touch in this paper is how to deal with rare words in the auxiliary information, such as dictionary definitions. Based on our qualitative investigations (see the example with "arrow" and "weapon" in Section 4.1), we believe that better handling rare words in the auxiliary information could substantially improve the proposed method. It would be natural to use on the fly embeddings similarly to the ones that we produce for words from the input, but the straight-forward approach of computing them on request would be very computation and memory hungry. One would furthermore have to resolve cyclical dependencies, which are unfortunately common in dictionary data (when e.g. "entertainment" is defined using "diverting" and "diverting" is defined using "entertainment"). In our future work we want to investigate asynchronous training of on the fly embeddings and the main model. In this paper, we have shown that introducing relatively small amounts of auxiliary data and a method for computing embeddings on the fly using that data bridges the gap between data-poor setups, where embeddings need to be learned directly from the end task, and data-rich setups, where embeddings can be pretrained and sufficient external data exists to ensure in-domain lexical coverage. A large representative corpus to pretrain word embeddings is not always available and our method is applicable when one has access only to limited auxiliary data. Learning end-to-end from auxiliary sources can be extremely data efficient when these sources represent compressed relevant information about the word, as dictionary definitions do. A related desirable aspect of our approach is that it may partially return the control over what a language processing system does into the hands of engineers or even users: when dissatisfied with the output, they may edit or add auxiliary information to the system to make it perform as desired. Furthermore, domain adaptation with our method could be carried out simply by using other sources of auxiliary knowledge, for example definitions of domain-specific technical terms in order to understand medical texts. Overall, the aforementioned properties of our method make it a promising alternative to the existing approaches to handling rare words.

We propose a method to deal with rare words by computing their embedding from definitions.

Represent this text to find a much much longer article about it with say hundreds-thousands of words!

This work aims to provide quantitative answers to the relative importance of concepts of interest via concept activation vectors (CAV). In particular, this framework enables non-machine learning experts to express concepts of interest and test hypotheses using examples (e.g., a set of pictures that illustrate  the concept). We show that CAV can be learned given a relatively small set of examples. Hypothesis testing with CAV can answer whether a particular concept (e.g., gender) is more important in predicting a given class (e.g., doctor) than other sets of concepts. Interpreting networks with CAV does not require any retraining or modification of the network.


Question: Represent the article for finding a single-sentence TLDR

Question: The capability of reliably detecting out-of-distribution samples is one of the key factors in deploying a good classifier, as the test distribution always does not match with the training distribution in most real-world applications. In this work, we propose a deep generative classifier which is effective to detect out-of-distribution samples as well as classify in-distribution samples, by integrating the concept of Gaussian discriminant analysis into deep neural networks. Unlike the discriminative (or softmax) classifier that only focuses on the decision boundary partitioning its latent space into multiple regions, our generative classifier aims to explicitly model class-conditional distributions as separable Gaussian distributions. Thereby, we can define the confidence score by the distance between a test sample and the center of each distribution. Our empirical evaluation on multi-class images and tabular data demonstrate that the generative classifier achieves the best performances in distinguishing out-of-distribution samples, and also it can be generalized well for various types of deep neural networks. Out-of-distribution (OOD) detection, also known as novelty detection, refers to the task of identifying the samples that differ in some respect from the training samples. Recently, deep neural networks (DNNs) turned out to show unpredictable behaviors in case of mismatch between the training and testing data distributions; for example, they tend to make high confidence prediction for the samples that are drawn from OOD or belong to unseen classes . For this reason, accurately measuring the distributional uncertainty of DNNs becomes one of the important challenges in many real-world applications where we can hardly control the testing data distribution. Several recent studies have tried to simply detect OOD samples using the confidence score defined by softmax probability or Mahalanobis distance from class means , and they showed promising even without re-training the model. However, all of them employ the DNNs designed for a discriminative (or softmax) classifier, which has limited power to locate OOD samples distinguishable with in-distribution (ID) samples in their latent space. To be specific, the softmax classifier is optimized to learn the discriminative latent space where the training samples are aligned along their corresponding class weight vectors, maximizing the softmax probability for the target classes. As pointed out in , OOD samples are more likely to have small values of the softmax probability for all known classes, which means that their latent vectors get closer to the origin. As a , there could be a large overlap between two sets of ID and OOD samples in the latent space (Figure 1), which eventually reduces the gap between their confidence scores and degrades the performance as well. In addition, most of existing confidence scores adopt additional calibration techniques ) to enhance the reliability of the detection, but they include several hyperparameters whose optimal values vary depending on the testing data distribution. In this situation, they utilized a small portion of each test set (containing both ID and OOD samples) for validation, and reported the evaluated on the rest by using the optimal hyperparameter values for each test case. Considering the motivation of OOD detection that prior knowledge of test distributions is not available before we encounter them, such process of tuning the hyperparameters for each test case is not practical when deploying the DNNs in practice. In this paper, we propose a novel objective to train DNNs with a generative (or distance) classifier which is capable of effectively identifying OOD test samples. The main difference of our deep generative classifier is to learn separable class-conditional distributions in the latent space, by explicitly modeling them as a DNN layer. The generative classifier places OOD samples further apart from the distributions of all given classes, without utilizing OOD samples for its validation. Thus, based on the Euclidean distance between a test sample and the centers of the obtained class-conditional distributions, we can calculate how likely and how confidently the sample belongs to each class. This can be interpreted as a multi-class extension of unsupervised anomaly detection , and Gaussian discriminant analysis provides the theoretical for incorporating the generative classifier into the DNNs. Our extensive experiments on images and tabular data demonstrate that the proposed classifier distinguishes OOD samples more accurately than the state-of-the-art method, while maintaining the classification accuracy for ID samples. We introduce a novel objective for training deep neural networks (DNNs) with a generative classifier, which is able to effectively detect out-of-distribution samples as well as classify in-distribution samples into known classes. We first derive the learning objective from the Gaussian discriminant analysis, and propose the distance-based confidence score for out-of-distribution sample detection. Metric learning objective for classification. The key idea of our objective is to optimize the deep learning model so that the latent representations (i.e., the outputs of the last layer) of data samples in the same class gather together thereby form an independent sphere. In other words, it aims to learn each class-conditional distribution in the latent space to follow a normal distribution that is entirely separable from other class-conditional distributions. Using the obtained distributions, we can calculate the class-conditional probabilities that indicate how likely an input sample is generated from each distribution, and this probability can serve as a good measure of the confidence. We define the two terms based on the Euclidean distance between the data representations obtained by the DNNs, denoted by f (x), and the center of each class-conditional distribution, denoted by c k. Given N training samples {(x 1, y 1),..., (x N, y N)} from K different classes, the objective is described as follows. The objective includes three types of trainable parameters: the weights of DNNs W, the class centers c 1,..., c K and biases b 1,..., b K. All of them can be effectively optimized by stochastic gradient descent (SGD) and back-propagation, which are widely used in deep learning. Note that we directly optimize the latent space induced by the DNNs using Euclidean distance, similarly to other metric learning objectives. Existing deep metric learning based on the triplet loss learns the distance among training samples utilizing their label information to capture their similarities into the metric space for a variety of retrieval tasks. On the other hand, our objective focuses on the distance between the samples and their target class centers for the accurate modeling of class-conditional distributions. Derivation from Gaussian discriminant analysis. Our objective for the generative classifier can be understood from the perspective of Gaussian discriminant analysis (GDA) . The generative classifier defines the posterior distribution P (y|x) by using the class-conditional distribution P (x|y) and class prior P (y). In case of GDA, each class-conditional distribution is assumed to follow the multivariate Gaussian distribution (i.e., P (x|y = k) = N (x|µ k, Σ k)) and the class prior is assumed to follow the Bernoulli distribution (i.e., P (y = k) = To simply fuse GDA with DNNs, we further fix all the class covariance matrices to the identity matrix (i.e., Σ k = I). Then, the posterior probability that a sample f (x) belongs to the class k is described as Considering µ k and log β k as the class center c k and bias b k respectively, the first term of our objective is equivalent to the negative log posterior probability. That is, the objective eventually trains the classifier by maximizing the posterior probability for training samples. However, the direct optimization of the DNNs and other parameters by its gradient does not guarantee that the class-conditional distributions become the Gaussian distributions and the class centers are the actual class means of training samples. Thus, to enforce our GDA assumption, we minimize the Kullback-Leibler (KL) divergence between the k-th empirical class-conditional distribution and the Gaussian distribution whose mean and covariance are c k and I, respectively. The empirical class-conditional distribution is represented by the average of the dirac delta functions for all training samples of a target class, i.e., where N k is the number of the training samples of the class k. Then, the KL divergence is formulated as The entropy term of the empirical class-conditional distribution can be calculated by using the definition of the dirac measure . By minimizing this KL divergence for all the classes, we can approximate the K class-conditional Gaussian distributions. Finally, we complete our objective by combining this KL term with the posterior term using the λ-weighted sum in order to control the effect of the regularization. We remark that λ is the hyperparameter used for training the model, which depends on only ID, not OOD; thus it does not need to be tuned for different test distributions. In-distribution classification. Since our objective maximizes the posterior probability for the target class of each sample P (y = y i |x), we can predict the class label of an input sample to the class that has the highest posterior probability as follows. In terms of DNNs, our proposed classifier replaces the fully-connected layer (fc-layer) computing the final classification score by w k · f (x) + b k with the distance metric layer (dm-layer) computing the distance from each center by − f (x) − c k 2 + b k. In other words, the class label is mainly predicted by the distance from each class center, so we use the terms "distance classifier" and "generative classifier" interchangeably in the rest of this paper. The dm-layer contains the exactly same number of model parameters with the fully-connected layer, because only the weight matrix K×d is replaced with the class center matrix Out-of-distribution detection. Using the trained generative classifier (i.e., class-conditional distributions obtained from the classifier), the confidence score of each sample can be computed based on the class-conditional probability P (x|y = k). Taking the log of the probability, we simply define the confidence score D(x) using the Euclidean distance between a test sample and the center of the closest class-conditional distribution in the latent space, This distance-based confidence score yields discriminative values between ID and OOD samples. In the experiment section, we show that the Euclidean distance in the latent space of our distance classifier is more effective to detect the samples not belonging to the K classes, compared to the Mahalanobis distance in the latent space of the softmax classifier. Moreover, it does not require further computation to obtain the class means and covariance matrix, and the predictive uncertainty can be measured by a single DNN inference. Relationship to deep one-class classifier. Recent studies on one-class classification, which have been mainly applied to anomaly detection, try to employ DNNs in order to effectively model the normality of a single class. Inspired by early work on one-class classification including one-class support vector machine (OC-SVM) (Schölkopf et al., 2001) and support vector data description (SVDD) , Ruff et al. (2018; 2019) proposed a simple yet powerful deep learning objective, DeepSVDD. It trains the DNNs to map samples of the single known class close to its class center in the latent space, showing that it finds a hypersphere of minimum volume with the center c: Our DNNs with the distance classifier can be interpreted as an extension of DeepSVDD for multiclass classification, which incorporates K one-class classifiers into a single network. In the proposed objective, the first term makes the K classifiers distinguishable for the multi-class setting, and the second term learns each classifier by gathering the training samples into their corresponding center, as done in DeepSVDD. The purpose of the one-class classifier is to determine whether a test sample belong to the target class or not, thus training it for each class is useful for detecting out-of-distribution samples in our task as well. In this section, we present experimental that support the superiority of the proposed model. Using tabular and image datasets, we compare the performance of our distance classifier (i.e., DNNs with dm-layer) with that of the softmax classifier (i.e., DNNs with fc-layer) in terms of both ID classification and OOD detection. We also provide empirical analysis on the effect of our regularization term. Our code and preprocessed datasets will be publicly available for reproducibility. Experimental settings. We first evaluate our distance classifier using four multi-class tabular datasets with real-valued attributes: GasSensor, Shuttle, DriveDiagnosis, and MNIST. They are downloaded from UCI Machine Learning repository 1, and we use them after preprocessing all the attributes using z-score normalization. Table 1 summarizes the details of the datasets. To simulate the scenario that the test distribution includes both ID and OOD samples, we build the training and test set by regarding one of classes as the OOD class and the rest of them as the ID classes. We exclude the samples of the OOD class from the training set, then train the DNNs using only the ID samples for classifying inputs into the K-1 classes. The test set contains all samples of the OOD class as well as the ID samples that are left out for testing. The evaluations are repeated while alternately changing the OOD class, thus we consider K scenarios for each dataset. For all the scenarios, we perform 5-fold cross validation and report the average . The multi-layer perceptron (MLP) with three hidden layers is chosen as the DNNs for training the tabular data. For fair comparisons, we employ the same architecture of MLP (# Input attributes ×128 × 128 × 128× # Classes) for both the softmax classifier and the distance classifier. We use the Adam optimizer with the initial learning rate η = 0.01, and set the maximum number of epochs to 100. In case of tabular data, we empirically found that the regularization coefficient λ hardly affects the performance of our model, so fix it to 1.0 without further hyperparameter tuning. We consider two competing methods using the DNNs optimized for the softmax classifier: 1) the baseline method uses a maximum value of softmax posterior probability as the confidence score, max k, and 2) the state-of-the-art method defines the score based on the Mahalanobis distance using empirical class meansμ k and covariance matrixΣ, which is max Note that any OOD samples are not available at training time, so we do not consider advanced calibration techniques for all the methods; for example, temperature scaling, input perturbation , and regression-based feature ensemble . We measure the classification accuracy for ID test samples 2, as well as three performance metrics for OOD detection: the true negative rate (TNR) at 85% true positive rate (TPR), the area under the receiver operating characteristic curve (AUROC), and the detection accuracy. Experimental . In Table 2, our proposed method (i.e., distance-based confidence score) using the distance classifier considerably outperforms the other competing methods using the softmax classifier in most scenarios. Compared to the baseline method, the Mahalanobis distance-based confidence score sometimes performs better, and sometimes worse. This strongly indicates that the empirical data distribution in the latent space does not always take the form of Gaussian distribution for each class, in case of the softmax classifier. For this reason, our explicit modeling of class-conditional Gaussian distributions using the dm-layer guarantees the GDA assumption, and it eventually helps to distinguish OOD samples from ID samples. Moreover, the distance classifier shows almost the same classification accuracy with the softmax classifier; that is, it improves the performance of OOD detection without compromising the performance of ID classification. For qualitative comparison on the latent spaces of the softmax classifier and distance classifier, we plot the 2D latent space after training the DNNs whose size of latent dimension is set to 2. Figure 1 illustrates the training and test distributions of the GasSensor dataset, where the class 3 (i.e., Ammonia) is considered as the OOD class. Our DNNs successfully learn the latent space so that ID and OOD samples are separated more clearly than the DNNs of the softmax classifier. Notably, in case of the softmax classifier, the covariance matrices of all the classes are not identical, which violates the necessary condition for the Mahalanobis distance-based confidence score to be effective in detecting OOD samples. 4 In this sense, the proposed score does not require such assumption any longer, because our objective makes the latent space satisfy the GDA assumption. Experimental settings. We validate the effectiveness of the distance classifier on OOD image detection as well. Two types of deep convolutional neural networks (CNNs) are utilized: ResNet with 100 layers and DenseNet with 34 layers. Specifically, we train ResNet and DenseNet for classifying three image datasets: CIFAR-10, CIFAR-100 , and SVHN . Each dataset used for training the models is considered as ID samples, and the others are considered as OOD samples. To consider a variety of OOD samples at test time, we measure the performance by additionally using TinyImageNet (randomly cropped image patches of size 32 × 32 from ImageNet dataset) and LSUN as test OOD samples. All CNNs are trained with stochastic gradient descent with Nesterov momentum , and we follow the training configuration (e.g., the number of epochs, batch size, learning rate and its scheduling, and momentum) suggested by . The regularization coefficient λ of the distance classifier is set to 0.1. Experimental . Table 3 shows that our distance classifier also can be generalized well for deeper and more complicated models such as ResNet and DenseNet. Similarly to tabular data, our confidence score achieves the best performance for most test cases, and significantly improves the detection performance over the state-of-the-art method. Interestingly, the distance classifier achieves better ID classification accuracy than the softmax classifier in Table 4. These show the possibility that any existing DNNs can improve their classification power by adopting the dmlayer, which learns the class centers instead of the class weights. From the experiments, we can conclude that our proposed objective is helpful to accurately classify ID samples as well as identify OOD samples from unknown test distributions. We further investigate the effects of our regularization term on the performance and the data distributions in the latent space. We first evaluate the distance classifier, using the DNNs trained with different λ values from 10 −3 to 10 3. Figure 2 presents the performance changes with respect to the λ value. In terms of ID classification, the classifier cannot be trained properly when λ grows beyond 10 2, because the regularization term is weighted too much compared to the log posterior term in our objective which learns the decision boundary. On the other hand, we observe that the OOD detection performances are not much affected by the regularization coefficient, unless we set λ too small or too large; any values in the range (0.1, 10) are fine enough to obtain the model working well. We also visualize the 2D latent space where the training distribution of MNIST are represented, varying the value of λ ∈ {0.01, 0.1, 1, 10}. In Figure 3, even with a small value of λ, we can find the decision boundary that partitions the space into K regions, whereas the class centers (plotted as black circles) do not match with the actual class means and the samples are spread over the entire space. As λ increases, the class centers approach to the actual class means, and simultaneously the samples get closer to its corresponding class center thereby form multiple spheres. As discussed in Section 2, the regularization term enforces the empirical class-conditional distributions to approximate the Gaussian distribution with the mean c k. In , the proper value of λ makes the DNNs place the class-conditional Gaussian distributions far apart from each other, so the OOD samples are more likely to be located in the rest of the space. As DNNs have become the dominant approach to a wide range of real-world applications and the cost of their errors increases rapidly, many studies have been carried out on measuring the uncertainty of a model's prediction, especially for non-Bayesian DNNs . defined several types of uncertainty, and among them, distributional uncertainty occurs by the discrepancy between the training and test distributions. In this sense, the OOD detection task can be understood as modeling the distributional uncertainty, and a variety of approaches have been attempted, including the parameterization of a prior distribution over predictive distributions and training multiple classifiers for an ensemble method . The baseline method is the first work to define the confidence score by the softmax probability based on a given DNN classifier. To enhance the reliability of detection, ODIN applies two calibration techniques, i.e., temperature scaling and input perturbation, to the baseline method, which can push the softmax scores of ID and OOD samples further apart from each other. uses the Mahalanobis distance from class means instead of the softmax score, assuming that samples of each class follows the Gaussian distribution in the latent space. However, all of them utilize the DNNs for the discriminative (i.e, softmax) classifier, only optimized for classifying ID samples. Our approach differs from the existing methods in that it explicitly learns the class-conditional Gaussian distributions and computes the score based on the Euclidean distance from class centers. This paper introduces a deep learning objective to learn the multi-class generative classifier, by fusing the concept of Gaussian discriminant analysis with DNNs. Unlike the conventional softmax classifier, our generative (or distance) classifier learns the class-conditional distributions to be separated from each other and follow the Gaussian distribution at the same time, thus it is able to effectively distinguish OOD samples from ID samples. We empirically show that our confidence score beats other competing methods in detecting both OOD tabular data and OOD images, and also the distance classifier can be easily combined with various types of DNNs to further improve their performances.

This paper proposes a deep generative classifier which is effective to detect out-of-distribution samples as well as classify in-distribution samples, by integrating the concept of Gaussian discriminant analysis into deep neural networks.

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For instance, <<The Wave-U-Net architecture, recently introduced by Stoller et al for music source separation, is highly effective for speech enhancement, beating the state of the art.>>  to <<We study the use of the Wave-U-Net architecture for speech enhancement, a model introduced by Stoller et al for the separation of music vocals and accompaniment. This end-to-end learning method for audio source separation operates directly in the time domain, permitting the integrated modelling of phase information and being able to take large temporal contexts into account. Our experiments show that the proposed method improves several metrics, namely PESQ, CSIG, CBAK, COVL and SSNR, over the state-of-the-art with respect to the speech enhancement task on the Voice Bank corpus (VCTK) dataset. We find that a reduced number of hidden layers is sufficient for speech enhancement in comparison to the original system designed for singing voice separation in music. We see this initial as an encouraging signal to further explore speech enhancement in the time-domain, both as an end in itself and as a pre-processing step to speech recognition systems. The remainder of this paper is structured as follows. In section 2, we briefly review related work 27 from the literature. In section 3, we introduce briefly the Wave-U-Net architecture and its application architectures like that of BID0. Recently, the U-Net architecture on magnitude spectrograms has for each prediction and is based on the repeated application of dilated convolutions with exponentially increasing dilation factors to factor in context information. yield an estimate of the target sources, a tanh nonlinearity follows, succeeded by a final LeakyReLU. In applying the Wave-U-Net architecture to the application of speech enhancement, our objective 58 is to separate a mixture waveform DISPLAYFORM0 To evaluate and compare the quality of the enhanced speech yielded by the Wave-U-Net, we mirror filter sizes, to the task and expanding to multi-channel audio and multi-source-separation.>>

We propose a method based on the adversarial training strategy to learn discriminative features unbiased and invariant to the confounder(s) by incorporating a loss function that encourages a vanished correlation between the bias and learned features.