Schrodinger's Memory: Large Language Models
Large Language Models' Memory
I provided sources on mathematical modeling in Cognitive Science in another reply. The question of how memory is stored in human brain is not a mathematical question, but an empirical one. I don't see any value of me listing hundreds of possible sources here. If the authors are genuinely interested in the subject, I suggest starting with the concept of "grandmother cell" (https://en.wikipedia.org/wiki/Grandmother_cell) or "memory" more generally (https://en.wikipedia.org/wiki/Memory). There are numerous sources on the matter linked in the corresponding Wikipedia pages.

**A:**First, I would like to point out that this aligns with what I mentioned earlier: communication of thoughts between individuals can be quite challenging. You view memory as an empirical question, while I believe that memory can fundamentally be expressed mathematically. 

Let me explain why I hold this view:

First, the initial neural network can be considered a perceptron, which was designed based on human neurons. However, due to subsequent changes in form, it is no longer seen as having a direct relationship with the brain. In my work, I reconnect deep learning with the brain, and therefore, I believe that whether considering the original design principles of neural networks or the phenomena exhibited by modern LLMs, they can be regarded as simulations of the brain.
Sources
#### See my reply "About a mathematical theory of memory" where I give a more general reply.

#### Briefly, on this issue specifically: overfitting can be seen as a type of memory. But a) The opposite is not true. Memory is more than overfitting, we can generalize when we retrieve information from memory, while overfitting, by definition, is associated with poor generalization. b) Regardless of the relationship between memory and overfitting, running a new experiment to show that LLMs can overfit is neither novel nor valuable (it's an extremely well-known fact already).

**A:**  a) First, we never claimed that memory is necessarily overfitting. Instead, we use the overfitting phenomenon in LLMs to illustrate the concept of memory. Second, to some extent  our brains are overfitting to the real world we encounter, and the resulting phenomenon is generalization. 

For example, why can't an expert in mathematics generalize from one or two examples to the entire field of physics? While this example is somewhat extreme, a simpler one illustrates the point better: why can't a long-distance runner with excellent jumping ability achieve the same jumping standards as a professional jumper after just one or two training sessions? The reason is that they need to overfit to the specific task. 

The key point is that because we overfit to the real world, the result appears as generalization. 

**A:**  b) Our goal has never been to overfit; rather, our goal is to explain the phenomenon of memory.
Replied in another comment
#### Line "472" refers to a middle of the author list in an OpenAI paper in your citations. Line 427 offers a short paragraph near the very end of your paper about the role of hippocampus in human memory. It is a vastly insufficient discussion for something that is a central theme of the paper. It also contradicts the author's earlier claim that "the brain does not have a structure analogous to a database for storing information," because in some ways, hippocampus can be seen as analogous to such a database (though of course it's not a perfect analogy).

**A:** I believe there might be a misunderstanding. In my paper, I clearly state that the hippocampus acts as a switch for long-term memory, not as a database. If it were a database, individuals with hippocampal damage would lose their long-term memories entirely. However, he still retains his long-term memories, which supports my argument. Therefore, I believe the case I presented is valid.
On human memory discussion
#### It is possible to provide a mathematical description of anything, it does not make the description valuable. The mathematical description needs to predict new, unexpected empirical data to be valuable (think Einstein's prediction of Mercury's perihelion), or to simplify the description of some known models/observations (e.g. Newton's first-principles explanations of planetary motion). Unfortunately, your paper only provides a new way to formalize already known phenomena, but it does not offer and meaningful simplifications or insightful predictions.

First, thank you for your guidance. I have learned a lot from this review, your comments and those of many other reviewers are very valuable, and I will correct them later.

1. To begin, since the issue is complex, I’ll first present a viewpoint and then address your question. I’m not certain if my explanation below will clearly convey my thoughts, but **I want to emphasize that this is purely an academic discussion, with no intention whatsoever of contradicting your perspective.**

2.  **Viewpoint 1**: The human brain can be considered a large, dynamic fitting function, continually adjusting its internal "weights" through interaction with the real world. In this process, some of these adaptations are accurate, while others are not. However, since these adjustments are grounded in real-world experience, whether correct or incorrect, they remain bounded by the constraints of reality. For instance, people cannot imagine something they have never encountered in some form. Take Picasso, for example: while his work is regarded as innovative, it’s possible that it simply stemmed from his exposure to distorted perspectives through mirrors or other natural distortions, which he then exaggerated and developed into his distinctive style. Yet fundamentally, his work did not transcend the bounds of his experiences with reality.

 **Viewpoint 2**: It’s important to emphasize that the second viewpoint also describes the way the brain processes thoughts; it’s absolutely not directed at you personally, as I am one of those who experiences this phenomenon too. Because our brains learn based on interactions with the real world, we develop our own "fixed weights" through extensive learning, creating an equation like *y = f(x)*. This means that if others have a different perspective or produce a different output from the same input, we tend to reject their viewpoint. This is also why it’s often difficult to persuade others to see things our way.

**Anwers**： When you refer to the “description of some known models/observations,” why can’t this mathematical model serve as a representation or simplification of the brain itself? In many ways, LLMs already seem remarkably close to human cognitive processes, and we have here provided a mathematical description alongside a comparison to memory phenomena in the brain.
About a mathematical theory of memory
First, I would like to express my sincere gratitude to the reviewer for the prompt response. 

Regarding this issue, it appears that the citation I used may have caused some confusion. The article in question seems to have been updated after my initial reference, which led to an inconsistency in the publication year. Alternatively, there may have been an error in my citation source itself. In either case, it is indeed the same article, and I have made the necessary corrections. Thank you very much for bringing this to my attention.
Clarification
I provided sources on mathematical modeling in Cognitive Science in another reply. The question of how memory is stored in human brain is not a mathematical question, but an empirical one. I don't see any value of me listing hundreds of possible sources here. If the authors are genuinely interested in the subject, I suggest starting with the concept of "grandmother cell" (https://en.wikipedia.org/wiki/Grandmother_cell) or "memory" more generally (https://en.wikipedia.org/wiki/Memory). There are numerous sources on the matter linked in the corresponding Wikipedia pages.
Sources
See my reply "About a mathematical theory of memory" where I give a more general reply.

Briefly, on this issue specifically: overfitting can be seen as a type of memory. But 
a) The opposite is not true. Memory is more than overfitting, we can generalize when we retrieve information from memory, while overfitting, by definition, is associated with poor generalization.
b) Regardless of the relationship between memory and overfitting, running a new experiment to show that LLMs can overfit is neither novel nor valuable (it's an extremely well-known fact already).
Replied in another comment
Line "472" refers to a middle of the author list in an OpenAI paper in your citations. Line 427 offers a short paragraph near the very end of your paper about the role of hippocampus in human memory. It is a vastly insufficient discussion for something that is a central theme of the paper. It also contradicts the author's earlier claim that "the brain does not have a structure analogous to a database for storing information," because in some ways, hippocampus can be seen as analogous to such a database (though of course it's not a perfect analogy).
On human memory discussion
It is possible to provide a mathematical description of anything, it does not make the description valuable. The mathematical description needs to predict new, unexpected empirical data to be valuable (think Einstein's prediction of Mercury's perihelion), or to simplify the description of some known models/observations (e.g. Newton's first-principles explanations of planetary motion). Unfortunately, your paper only provides a new way to formalize already known phenomena, but it does not offer and meaningful simplifications or insightful predictions.

Overall, I believe that a lot of the questions I received from the authors stem from a fundamental misunderstanding of scientific methodology & the relationship between mathematical theorizing/modeling and empirical studies.

I still highly suggest turning to the scientific community for pee-to-peer guidance. Alternatively/additinally, I highly suggest "Computational Modeling in Cognition: Principles and Practice" by S.Lewandowsky and S.Farrell, which would be a good foundational text on the matter, that, if studied in depth, will provide a good foundation for both the role and the use of models in Cognitive Science, and will give a good overview of existing mathematical models of various cognitive processes (including memory).

I hope that the authors take the unanimous and, at present, negative feedback from the reviewers as a learning opportunity and try to improve their approach in the future. As of now, unfortunately, I see little evidence of that. The (short) time between when the reviews became visible and the author replies shows that they did not meaningfully engage with the references I provided. Their claim "I did not find a concrete mathematical theory in the content you provided" means exactly what it states - they did not find it; it does not mean that there are no mathematical theories of memory psychology, neuroscience, or Cognitive Science. To clarify: the sources I provided were given as a starting point in a more comprehensive literature review, not an exhaustive list.
About a mathematical theory of memory
It was confusing because when you cite a publication from 2007 as the work that introduced UAT, while in the next sentence you refer to another work about UAT from 1989.
Clarification