reviews: 
Comments: This work explores the memory capabilities of LLMs using the Universal Approximation Theorem (UAT). The authors introduce the concept of "Schrödinger's memory" - suggesting that LLMs' memory only becomes observable when queried and remains indeterminate otherwise. The paper presents experimental results comparing different models' ability to memorize Chinese and English poems and draws comparisons between LLMs and human memory mechanisms.
Strengths: The paper tries to address an important and timely question about the memory mechanisms in LLMs;  
The choice of structured datasets (particularly poetry) is suited for testing memory recall in LLMs and evaluating the relationship between model architecture and memory capacity;  
The attempt to connect UAT with LLMs memory is interesting and provides a mathematical basis for discussing dynamic response mechanisms in LLMs;  
The comparison between human and LLM memory provides insights that could bridge cognitive science and AI.
Weaknesses: 1.The paper claims to use UAT to explain LLMs' memory abilities, but the connection between Eq. (3) and the memory mechanism is not rigorously established. The authors need to prove how the dynamic fitting capability directly relates to memory retention. This connection might be strengthened by providing a step-by-step derivation linking Eq. (3) to specific memory processes, or designing an experiment that directly tests the relationship between dynamic fitting and memory retention.  
2.While the paper develops an extensive theoretical framework using UAT in Section 2, the experiments in Section 3 do not directly validate or connect to this theory. This gap might be addressed by quantitatively relate the parameters in Eq. (3) to the observed memory performance in the experiments.  
3.Section 3.3 proposes using memory ability as an objective measure of LLM capabilities but does not relate this metric to standard benchmarks. The authors should demonstrate how their memory assessment correlates with or complements existing evaluation methods.  
4.The output length effect analysis in Section 3.4 only tests up to 512 characters. The authors should investigate how memory performance degrades with sequence length and compare this with theoretical predictions from their UAT framework.   
5.The paper fails to examine an essential aspect of memory systems - their ability to recognize unknown information. Specifically, there are no experiments testing whether models can reliably indicate when they encounter previously unseen poems, nor is there a comparison between "memorized" vs. "hallucinated" outputs' characteristics. The paper could benefit from adding specific experimental designs to test the models' ability to distinguish between known and unknown information. This might be achieved by including a set of previously unseen poems in the test set, or evaluating how the models distinguish between known and unknown information.  
6.The experiments only measure binary success (correct/incorrect recitation) without examining the deviations as metioned in Section 3.1.  
7.The comparison between human and LLM memory is largely speculative and lacks scientific rigor. Many claims about human memory mechanisms are made without proper citations or empirical support. This could be improved by designing experiments to more rigorously compare human and LLM memory, perhaps drawing on established methods from cognitive psychology.
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 2
Clarity: 3