Combining Entropy and Matrix Nuclear Norm for Enhanced Evaluation of Language Models

Abstract: As LLMs continue to advance, the need for precise and efficient evaluation metrics becomes more pressing. Traditional approaches, while informative, often face limitations in computational demands and interpretability. In this paper, we introduce a novel hybrid evaluation method that integrates two established techniques: entropy derived from covariance matrices and the Matrix Nuclear Norm (MNN). Our method begins by normalizing hidden states from LLMs, then computes the covariance matrix and MNN from these representations. We further calculate the entropy of the covariance matrix to capture uncertainty and redundancy in the model's outputs. By combining these metrics into a composite score, we offer a comprehensive evaluation framework that balances accuracy with computational efficiency. Additionally, our approach allows for flexibility in adjusting the weightings between entropy and MNN, tailoring the evaluation for different objectives. Through a series of experiments on various LLMs, we demonstrate the robustness and efficacy of our method, offering deeper insights into model performance. This work contributes to the ongoing development of LLM evaluation and opens avenues for future innovations in model assessment techniques.