Unlocking Tokens as Data Points for Generalization Bounds on Larger Language Models

Summary

The paper proposes token-level generalization bounds for large language models (LLMs), such as LLaMA2-70B, using less restrictive compression techniques like Monarch matrices, Kronecker factorizations, and post-training quantization. The authors argue that traditional document-level bounds are vacuous at this scale and introduce a method leveraging martingales for deriving tighter bounds, which not only hold theoretically but are also demonstrated through empirical validation.

Strengths

1. **Originality**: The paper introduces a novel approach to computing generalization bounds at the token level, which is a significant departure from the document-level bounds prevalent in prior works. 2. **Technical Soundness**: The use of martingales and non-restrictive compression methods to derive generalization bounds is both innovative and robust, providing a solid theoretical framework backed by empirical results. 3. **Significance**: The ability to provide non-vacuous generalization bounds for LLMs as large as 70 billion parameters is highly significant, as it pushes the boundary of what is understood about LLM generalization in practical settings. 4. **Clarity**: The paper is well-written, with clear explanations of the methods and their implications, making it accessible to readers who may not be experts in the specific sub-field of machine learning.

Weaknesses

No major weaknesses

Questions

Can the generalization bounds proposed be integrated into the training regimen to enhance model generalization directly?

Rating

7

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

The paper lacks intuitive explanations for the proposed bounds, which might hinder understanding for readers not familiar with advanced statistical concepts in machine learning.

Summary

This paper develops nonvacuous generalization bounds for modern language models. Specifically, this paper proves a token-level generalization bound, and applies different techniques (LoRA, 2 Kronecker Product, Monarch Matrices, and post-training quantization) to control the capacity of model class.

Strengths

This paper is well-written: Theorem 3.1 is clean, and many compression techniques (parameter-efficient tuning, post-training quantization,etc.) and modern language models (GPT, LLAMA, etc.) are analyzed. I believe these are nice contributions.

Weaknesses

The main weakness in my opinion is the left-hand side of eq. (2), since it uses contexts from the training data. I agree it is still a meaningful result, but it is also a little hard to interpret. Line 190 claims that "This figure confirms our intuition that the next token distribution is particularly diffuse at the beginning of a sentence, while it decreases for later tokens but remains relatively high. Given how diffuse the distribution is and the large number of possible sentences, it is broadly infeasible to make predictions on new resampled tokens from the empirical distribution alone." I am not fully convinced by this, since we can add some fixed prompt and only measure generalization error for the generated part.

Questions

Figure 2 (right) claims that the left-hand side of eq. (2) is correlated with downstream performance. Specifically, the left y-axis plots accuracies of GPT-2 models, while the y-axis uses samples from the LLAMA model; if I understand correctly, the LLAMA model is treated as an oracle model here, since we do not know the true data-generation process. However, I feel this is a little indirect; can you instead compare downstream performance with your generalization bound (i.e., right-hand side of eq. (2)) for the same model? If this also works, then we can claim that not only the quantity we try to bound is meaningful, but the bound itself is also meaningful.

Rating

6

Confidence

4

Soundness

3

Presentation

4

Contribution

3

Limitations

N/A

Summary

This paper presents a novel approach that computes non-vacuous compression-based generalization bounds for LLMs at the billion-parameter scale. Prior works could only achieve vacuous bounds for these large-scale models and rely on the assumption of IID documents. By leveraging the vast number of tokens in LLM training sets and properties of martingales, the authors derive non-vacuous bounds for LLMs that generate high-quality texts. Further, they showcase the tightness of the bounds by examining compression schemes including Monarch matrices and Kronecker factorizations, and post-training quantization techniques.

Strengths

1. The paper tackles an important problem that aims to give guarantees on the generalization abilities of LLMs, which are getting more powerful but the good performance is extremely hard to interpret and assess. 2. Prior works compute non-vacuous bounds on LLMs but rely on assumptions of IID documents and therefore can only be applied to those that generate poor text quality. This work presents a novel approach based on properties of martingales and gives much tighter bounds on LLMs of much more practical capabilities. Further, it does not require altering the pretraining pipeline of the LLMs being analyzed. 3. It investigates the generalizations by examining compression schemes including Monarch matrices and Kronecker factorizations, and post-training quantization techniques. The results also give interesting insights for practitioners.

Weaknesses

1. Since the utilization of martingales is one main theoretical contribution of the work, I feel some background and proof sketch on how they are being used would be better included in the main text. 2. The main models being examined are of the LLaMA and GPT-2 family of models. In particular, the experiment on the chat version of LLaMA is interesting as the generalization gets worse from the supervised finetuning. It would be interesting to see if this is generally true and why this is the case. More experiments on other finetuned LLMs would provide more evidence. 3. From table 2 and 3, it seems that given larger model sizes, the derived bounds get closer to random guess performance. Why is this the case and does it mean the bound would potentially be no-longer meaningful if the model gets large enough? Maybe I misunderstood something and would appreciate some clarification on this point.

Questions

Stated in the prior part.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors note the limitations of the current work.