Excess Description Length of Learning Generalizable Predictors

2026-01-08

arXiv.org

AI Summary

This study addresses the fundamental question of whether fine-tuning large language models elicits pre-existing capabilities or imparts genuinely new ones, and quantifies the source of their generalization ability. To this end, the authors develop an information-theoretic framework grounded in preorder encoding and introduce the Excess Description Length (EDL) metric to measure the amount of predictive structure extracted from data and encoded into model parameters. Theoretical analysis establishes that EDL is non-negative and converges to the redundant description length, thereby providing a rigorous upper bound on generalization gain. Empirical validation on synthetic tasks demonstrates EDL’s explanatory power regarding phenomena such as label noise sensitivity, rare input handling, and format learning. This work further reveals an essential distinction between capability elicitation and instructional learning in scaling behavior, clarifying several misconceptions about information acquisition during fine-tuning.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Understanding whether fine-tuning elicits latent capabilities or teaches new ones is a fundamental question for language model evaluation and safety. We develop a formal information-theoretic framework for quantifying how much predictive structure fine-tuning extracts from the train dataset and writes into a model's parameters. Our central quantity, Excess Description Length (EDL), is defined via prequential coding and measures the gap between the bits required to encode training labels sequentially using an evolving model (trained online) and the residual encoding cost under the final trained model. We establish that EDL is non-negative in expectation, converges to surplus description length in the infinite-data limit, and provides bounds on expected generalization gain. Through a series of toy models, we clarify common confusions about information in learning: why random labels yield EDL near zero, how a single example can eliminate many bits of uncertainty about the underlying rule(s) that describe the data distribution, why structure learned on rare inputs contributes proportionally little to expected generalization, and how format learning creates early transients distinct from capability acquisition. This framework provides rigorous foundations for the empirical observation that capability elicitation and teaching exhibit qualitatively distinct scaling signatures.

Problem

• fine-tuning
• latent capabilities
• generalization
• language model evaluation
• model safety

Innovation

• Excess Description Length
• prequential coding
• generalization
• fine-tuning
• information theory