Schrodinger's Memory: Large Language Models (2409.10482v3)

Abstract: Memory is the foundation of all human activities; without memory, it would be nearly impossible for people to perform any task in daily life. With the development of LLMs, their language capabilities are becoming increasingly comparable to those of humans. But do LLMs have memory? Based on current performance, LLMs do appear to exhibit memory. So, what is the underlying mechanism of this memory? Previous research has lacked a deep exploration of LLMs' memory capabilities and the underlying theory. In this paper, we use Universal Approximation Theorem (UAT) to explain the memory mechanism in LLMs. We also conduct experiments to verify the memory capabilities of various LLMs, proposing a new method to assess their abilities based on these memory ability. We argue that LLM memory operates like Schr\"odinger's memory, meaning that it only becomes observable when a specific memory is queried. We can only determine if the model retains a memory based on its output in response to the query; otherwise, it remains indeterminate. Finally, we expand on this concept by comparing the memory capabilities of the human brain and LLMs, highlighting the similarities and differences in their operational mechanisms.

• The paper demonstrates that LLM memory is a dynamic phenomenon that becomes observable only when specifically queried.
• It applies the Universal Approximation Theorem to Transformer models, revealing near-perfect recall for concise inputs.
• The study draws parallels with human memory, suggesting pathways for developing modular AI architectures with advanced cognitive functions.

Schrödinger's Memory: LLMs

Abstract Overview

The paper by Wei Wang and Qing Li explores the concept of memory within LLMs through the lens of the Universal Approximation Theorem (UAT). The paper introduces the notion of "Schrödinger's memory," positing that the memory within these models only becomes observable upon querying. This work aims to bridge the gap in understanding the memory mechanism in LLMs and draws comparisons between human and machine memory capabilities.

Introduction

The authors present a crucial question: do LLMs possess memory? The paper underscores the significance of memory in human activities, drawing an analogy to LLMs' capabilities. Though LLMs have demonstrated superior performance in various language tasks, the understanding of their memory mechanisms remains insufficient. Existing research primarily focuses on expanding context length or integrating external memory systems, yet fails to delve deeply into the intrinsic memory functionalities of LLMs. This paper utilizes UAT to elucidate the memory attributes of LLMs and introduces an objective method for evaluating these capabilities.

UAT and LLMs

Universal Approximation Theorem (UAT)

The UAT posits that neural networks can approximate any continuous function with sufficient capacity. This foundational theorem in deep learning suggests that with a sufficiently large number of neurons or layers, a neural network can fit any function given ample data. The adaptation of UAT to LLMs indicates that these models, particularly Transformers, can be viewed as dynamic systems that fit functions based on input data.

The UAT Format of Transformer-Based LLMs

The authors describe the mathematical structure of multi-layer Transformers aligned with UAT, emphasizing their dynamic adjustment to input data. The Transformer's attention mechanism and its varying parameters enable the model to handle dynamic input, explaining the memory phenomenon through UAT.

Memory in LLMs

Definition of Memory

The paper provides a refined definition of memory, framing it as the ability to produce specific output based on previous learning and current input, not merely static storage and retrieval of information. This dynamic aspect is critical for understanding how LLMs generate outputs based on incomplete inputs.

Experimental Validation

Through experiments using CN Poems and ENG Poems datasets, the authors demonstrate that LLMs can memorize and recall entire poems based on minimal input information. This is accomplished by fine-tuning various LLMs, including Qwen and bloom models, and evaluating their performance. The results reveal impressive memory capabilities, with some models recalling nearly 100% of the input poems.

The Token Length Effect

The paper also examines the impact of input text length on the memory performance of LLMs, concluding that longer texts pose greater challenges for accurate recall. The experiments affirm that the ability to remember is inversely proportional to input length, thus impacting the model's memory efficiency.

Comparison Between Human and LLM Memory

The paper draws comparisons between human cognitive abilities and LLMs, proposing that both systems function as dynamic models that fit inputs to produce corresponding outputs. The similarities are highlighted, particularly the idea that both brains and LLMs require specific inputs to trigger memory and generate appropriate responses. The discussion extends to other cognitive abilities like reasoning, social skills, and creativity, framing them as advanced forms of dynamic fitting based on prior knowledge.

Implications and Future Developments

The research has significant implications for the future development of AI:

• Enhanced Model Architectures: The paper suggests that future models could benefit from modular architectures, similar to the human brain, with specialized units for different tasks.
• Data and Training: Improving data quality and quantity remains crucial for enhancing the performance of LLMs.
• Advanced Dynamic Models: The exploration of more advanced dynamic fitting models could lead to the development of more sophisticated AI capable of higher-level cognitive functions.

Conclusion

The paper provides a compelling argument that LLMs possess a form of memory analogous to human memory, driven by the dynamic capabilities of Transformer models as outlined by the UAT. The concept of "Schrödinger's memory" aptly captures the conditional nature of memory in LLMs, which only manifests upon specific input queries. This framework opens new avenues for understanding and evaluating the memory and reasoning capabilities of LLMs, drawing fascinating parallels with human cognition and suggesting pathways for future AI advancements.