Unlocking Tokens as Data Points for Generalization Bounds on Larger Language Models (2407.18158v1)

Abstract: LLMs with billions of parameters excel at predicting the next token in a sequence. Recent work computes non-vacuous compression-based generalization bounds for LLMs, but these bounds are vacuous for large models at the billion-parameter scale. Moreover, these bounds are obtained through restrictive compression techniques, bounding compressed models that generate low-quality text. Additionally, the tightness of these existing bounds depends on the number of IID documents in a training set rather than the much larger number of non-IID constituent tokens, leaving untapped potential for tighter bounds. In this work, we instead use properties of martingales to derive generalization bounds that benefit from the vast number of tokens in LLM training sets. Since a dataset contains far more tokens than documents, our generalization bounds not only tolerate but actually benefit from far less restrictive compression schemes. With Monarch matrices, Kronecker factorizations, and post-training quantization, we achieve non-vacuous generalization bounds for LLMs as large as LLaMA2-70B. Unlike previous approaches, our work achieves the first non-vacuous bounds for models that are deployed in practice and generate high-quality text.

• The paper introduces token-level generalization bounds by leveraging martingale properties to treat each token as an individual data point.
• It employs less restrictive compression techniques, including Monarch matrices and quantization, to obtain tighter and practical bounds.
• The paper validates its approach on large-scale models like LLaMA2-70B and GPT2, highlighting trade-offs in memorization and task performance.

Analyzing Token-Level Generalization Bounds for LLMs

The paper entitled "Unlocking Tokens as Data Points for Generalization Bounds on Larger LLMs" presents an innovative approach to deriving non-vacuous generalization bounds for LLMs. This work is remarkable for its application of martingale properties to utilize the vast number of tokens in LLM training datasets, thus facilitating tighter bounds compared to prior methods that focused on document-level generalization. The authors achieve these tighter bounds without resorting to overly restrictive compression techniques which previously limited the practical utility of the models in generating high-quality text.

Main Contributions

1. Martingale-Based Token-Level Bounds: The authors develop a novel generalization bound for LLMs that consider each token in the training dataset as an individual sample, thereby lifting the restrictive IID assumption at the document level. This is achieved through a bound derived from Azuma's inequality, addressing the non-IID nature of tokens within documents. Token-level bounds allow for a significantly higher number of data points, resulting in smaller complexity terms and non-vacuous bounds for larger models.
2. Less Restrictive Compression Techniques: With the move to token-level bounds, the paper explores several effective model compression techniques that are less restrictive compared to prior works. The explored techniques include Monarch matrices, Kronecker factorizations, and post-training quantization methods. Particularly, Monarch matrices combined with post-training quantization yielded the best bounds.
3. Evaluation on Large-Scale Models: The work successfully computes non-vacuous generalization bounds for models as large as LLaMA2-70B, a notable achievement given the model's scale. These bounds apply to models that are actively deployed in practice and generate high-quality text, unlike models bounded by earlier methods that generated low-quality text due to extreme compression.
4. Practical and Theoretical Insights: The authors provide a comprehensive evaluation of LLaMA and GPT2 models on large datasets such as Amber (1.2 trillion tokens). They show that fine-tuning models for specific tasks, like dialogue in the case of LLaMA2-Chat, results in looser generalization bounds, offering practical insights into model performance trade-offs.
5. Implications for Memorization and Generalization: Experimental results reveal that smaller, compressed models retain in-context learning capabilities for structured tasks while losing memorization ability faster for unstructured tasks. This distinction underscores the benefits of structured pattern learning in highly compressed models.

Implications for Future Developments in AI

The implications of this work are multifaceted:

• Practical Bounds: The shift to token-level bounds opens avenues for developing non-vacuous bounds for other types of deep learning models, potentially leading to more reliable and practical generalization guarantees.
• Flexible Compression Techniques: The exploration of less restrictive compression techniques indicates that combining efficient nonlinear parametrizations with post-training quantization can yield models that generalize well without sacrificing performance, thus enhancing the practicality of deploying large-scale models in resource-constrained environments.
• Robust Model Evaluation: By demonstrating that simpler, structured tasks retain performance in highly compressed models, this work suggests future research could explore adaptive compression techniques where model complexity is dynamically adjusted based on task-specific requirements.
• Bound Interpretation and Utilization: The highlight of token-level bounds being predictive of generalization on downstream tasks signifies that similar methodologies might be applied to other domains where large-scale sequence data is prevalent, such as genomics and protein folding.

Conclusion

In summary, this paper advances the understanding of generalization in LLMs through novel token-level bounds that leverage martingale properties. By achieving non-vacuous bounds for large models and emphasizing less restrictive compression techniques, this work strikes a balance between theoretical rigor and practical applicability, setting a new standard for future research in the field of AI and machine learning.