The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?
arXiv:2604.06192v1 Announce Type: new Abstract: Recent work uses entropy-based signals at multiple representation levels to study reasoning in large language models, but the field remains largely empirical. A central unresolved puzzle is why internal entropy dynamics, defined under the predictive distribution of a model, correlate so robustly with external correctness given by the ground-truth answer. In this paper, we argue that this correlation arises because autoregressive models reason correctly when they accumulate information about the true answer via answer-informative prefixes. We formalize this intuition via the Stepwise Informativeness Assumption (SIA), which states that reasoning prefixes accumulate answer-relevant information in expectation as generation progresses. We show that SIA naturally emerges from maximum-likelihood optimization on human reasoning traces and is reinforced by standard fine-tuning and reinforcement-learning pipelines. We then derive observable signat
arXiv:2604.06192v1 Announce Type: new Abstract: Recent work uses entropy-based signals at multiple representation levels to study reasoning in large language models, but the field remains largely empirical. A central unresolved puzzle is why internal entropy dynamics, defined under the predictive distribution of a model, correlate so robustly with external correctness given by the ground-truth answer. In this paper, we argue that this correlation arises because autoregressive models reason correctly when they accumulate information about the true answer via answer-informative prefixes. We formalize this intuition via the Stepwise Informativeness Assumption (SIA), which states that reasoning prefixes accumulate answer-relevant information in expectation as generation progresses. We show that SIA naturally emerges from maximum-likelihood optimization on human reasoning traces and is reinforced by standard fine-tuning and reinforcement-learning pipelines. We then derive observable signatures of SIA linking conditional answer entropy dynamics to correctness. We empirically test SIA across multiple reasoning benchmarks (GSM8K, ARC, SVAMP) and a diverse set of open-weight LLMs (Gemma-2, LLaMA-3.2, Qwen-2.5, DeepSeek and Olmo variants), showing that training induces it and that correct traces exhibit characteristic conditional answer entropy patterns.
Executive Summary
This article introduces the Stepwise Informativeness Assumption (SIA) to explain the observed correlation between internal entropy dynamics and external reasoning correctness in Large Language Models (LLMs). SIA posits that autoregressive models reason correctly by accumulating information about the true answer through progressively more answer-informative prefixes during generation. The authors argue SIA emerges from maximum-likelihood optimization on human reasoning traces and is reinforced by common LLM training paradigms. They derive testable signatures of SIA, linking conditional answer entropy dynamics to correctness, and provide empirical validation across diverse LLMs and benchmarks. The work moves beyond empirical observation to offer a theoretical framework for understanding LLM reasoning processes.
Key Points
- ▸ The paper proposes the Stepwise Informativeness Assumption (SIA) as a theoretical explanation for the correlation between internal entropy dynamics and reasoning correctness in LLMs.
- ▸ SIA posits that correct reasoning involves the accumulation of answer-relevant information in expectation through sequential prefixes during generation.
- ▸ SIA is argued to naturally arise from maximum-likelihood optimization on human reasoning traces and is further reinforced by standard LLM fine-tuning and RL pipelines.
- ▸ The authors derive and empirically validate observable signatures of SIA, demonstrating characteristic conditional answer entropy patterns in correct reasoning traces across various LLMs and benchmarks.
Merits
Theoretical Advancement
Moves beyond purely empirical observation by proposing a formal, testable assumption (SIA) to explain a robust phenomenon, offering a deeper theoretical understanding of LLM reasoning.
Broad Empirical Validation
Tests SIA across a diverse set of open-weight LLMs and multiple reasoning benchmarks, strengthening the generalizability of its findings.
Mechanism-Oriented Explanation
Provides an intuitive and mechanistic explanation for the correlation between entropy and correctness, linking it directly to information accumulation during autoregressive generation.
Actionable Insights
The derivation of observable signatures (conditional answer entropy patterns) provides concrete metrics for further research and model analysis.
Demerits
Expectation-Based Assumption
SIA is framed 'in expectation,' which may obscure individual instances of incorrect reasoning where local entropy dynamics deviate from the expected informative trend.
Causality vs. Correlation Nuance
While SIA explains *why* the correlation arises, its causal implications for directly *improving* reasoning through entropy manipulation are not fully explored or guaranteed.
Scope of 'Reasoning'
The benchmarks used primarily focus on arithmetic and logical reasoning tasks; the applicability of SIA to more complex, open-ended, or subjective forms of reasoning remains to be fully investigated.
Expert Commentary
This paper represents a significant advance in moving the study of LLM reasoning from empirical observation to theoretical explanation. The Stepwise Informativeness Assumption (SIA) offers a compelling and intuitively satisfying framework for understanding the robust correlation between entropy dynamics and correctness. Its grounding in maximum-likelihood optimization and reinforcement by standard training paradigms provides strong internal coherence. The derivation of observable signatures and subsequent empirical validation across diverse models and tasks lends considerable credibility. From a legal and academic standpoint, this work is crucial for building trust and explainability in AI systems. By providing a 'why' behind successful reasoning, it offers a foundation for developing more robust diagnostic tools and potentially more trustworthy AI agents, moving us closer to understanding the 'black box' of LLM cognition. Future work should explore SIA's applicability to more complex reasoning tasks and its potential for direct intervention to enhance reasoning quality.
Recommendations
- ✓ Investigate the applicability of SIA to more complex, open-ended, and multi-step reasoning tasks beyond the current benchmarks, including tasks requiring common sense or ethical reasoning.
- ✓ Explore methods for directly incorporating SIA principles into LLM training objectives, potentially by designing loss functions that explicitly penalize deviations from expected stepwise informativeness.
- ✓ Conduct ablation studies to understand the specific contributions of different training components (e.g., pre-training data, fine-tuning, RLHF) to the emergence and reinforcement of SIA.
Sources
Original: arXiv - cs.CL