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arxiv: 2604.06192 · v1 · submitted 2026-03-11 · 💻 cs.CL · cs.AI· cs.IT· cs.LG· math.IT

Recognition: no theorem link

The Stepwise Informativeness Assumption: Why are Entropy Dynamics and Reasoning Correlated in LLMs?

Mar Gonz\`alez I Catal\`a , Haitz S\'aez de Oc\'ariz Borde , George D. Monta\~nez , Pietro Li\`o
Authors on Pith no claims yet

Pith reviewed 2026-05-15 13:01 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.ITcs.LGmath.IT
keywords Stepwise Informativeness Assumptionentropy dynamicsLLM reasoningautoregressive modelsinformation accumulationconditional entropyreasoning tracescorrectness correlation
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The pith

The correlation between entropy dynamics and reasoning correctness in LLMs arises because autoregressive models accumulate information about the true answer in their generation prefixes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Recent empirical work has found robust correlations between internal entropy dynamics in LLMs and the correctness of their reasoning outputs. This paper explains the correlation by arguing that autoregressive models produce correct answers when their reasoning prefixes accumulate information relevant to the true answer. The authors introduce the Stepwise Informativeness Assumption to formalize this process, demonstrating that it naturally results from training on human reasoning traces. Experiments across multiple models and benchmarks like GSM8K support the assumption by showing distinct entropy patterns in correct versus incorrect traces.

Core claim

The paper claims that autoregressive models reason correctly when they accumulate information about the true answer via answer-informative prefixes. This intuition is formalized in the Stepwise Informativeness Assumption, which states that reasoning prefixes accumulate answer-relevant information in expectation as generation progresses. SIA emerges from maximum-likelihood optimization on human reasoning traces and is reinforced by fine-tuning and reinforcement-learning pipelines. Deriving observable signatures, the authors link conditional answer entropy dynamics to correctness and validate this empirically on benchmarks including GSM8K, ARC, and SVAMP using various open-weight LLMs.

What carries the argument

The Stepwise Informativeness Assumption (SIA), under which reasoning prefixes accumulate answer-relevant information in expectation as generation progresses, linking entropy reduction to answer correctness.

If this is right

  • Correct reasoning traces display characteristic patterns of decreasing conditional answer entropy.
  • SIA is induced naturally by maximum-likelihood training on human reasoning traces.
  • Fine-tuning and reinforcement learning pipelines further reinforce SIA.
  • Entropy-based signals serve as reliable indicators of reasoning correctness across models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If SIA is true, methods that enhance stepwise information accumulation could improve LLM reasoning performance.
  • The assumption may apply to other autoregressive tasks where sequence generation builds toward a target outcome.
  • New interpretability tools could monitor prefix informativeness to detect likely correct reasoning in real time.

Load-bearing premise

Reasoning prefixes accumulate answer-relevant information in expectation as generation progresses.

What would settle it

An observation that would falsify the claim is the absence of distinct conditional answer entropy reduction patterns in correct reasoning traces compared to incorrect ones across the tested benchmarks and models.

Figures

Figures reproduced from arXiv: 2604.06192 by George D. Monta\~nez, Haitz S\'aez de Oc\'ariz Borde, Mar Gonz\`alez I Catal\`a, Pietro Li\`o.

Figure 2
Figure 2. Figure 2: Separability. AUC for using conditional answer en￾tropy to distinguish correct from incorrect traces vs. relative pre￾fix length s across aligned models in GSM8k dataset [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Saturation. Mean conditional answer entropy trajecto￾ries across non-aligned and aligned models in GSM8k dataset. reveals when and how answer-relevant information is ac￾quired. Importantly, all signatures vanish or weaken when this structure is absent (see Appendix B.1). 5.3. Ablations Finally, we test whether observed dynamics reflect step￾wise structure rather than superficial artifacts. Shuffle-prefix a… view at source ↗
Figure 1
Figure 1. Figure 1: Early information accumulation. Normalized cumu￾lative gain G(s) vs. relative prefix length s, split by correctness in llama-3.2-3B-it (aligned model) in GSM8k dataset. Early separability of correct vs. incorrect traces. Fig￾ure 2 reports the AUC for using conditional entropy at pre￾fix length s to distinguish correct from incorrect traces. For SIA-internalized models, separability is already strong well b… view at source ↗
Figure 4
Figure 4. Figure 4: Early information accumulation in non-aligned models. Normalized cumulative gain G(s) vs. relative prefix length s, split by correctness in llama-3.2-3B (non-aligned model) in GSM8k dataset. Entropy is not a correctness signal in this regime. Failure of early separability [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Separability in non-aligned models. AUC for using conditional answer entropy to distinguish correct from incorrect traces vs. relative prefix length s across non-aligned models in GSM8k dataset. Entropy is not an early diagnostic signal in this regime. Together, these results confirm that the empirical signatures described in Section 5.2 are not generic properties of autore￾gressive models, but arise speci… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper claims that the robust correlation between internal entropy dynamics and external reasoning correctness in LLMs arises because autoregressive models accumulate answer-relevant information via answer-informative prefixes during correct reasoning. It formalizes this as the Stepwise Informativeness Assumption (SIA), argues that SIA emerges from maximum-likelihood optimization on human reasoning traces (and is reinforced by fine-tuning/RL), derives observable signatures linking conditional answer entropy patterns to correctness, and empirically validates the signatures on GSM8K, ARC, and SVAMP across Gemma-2, LLaMA-3.2, Qwen-2.5, DeepSeek, and Olmo models.

Significance. If the central derivation can be tightened, the result would supply a mechanistic account for why entropy signals track correctness, unifying disparate empirical findings on LLM reasoning dynamics and providing a training-objective-based explanation for the utility of entropy as a diagnostic. The multi-benchmark, multi-model empirical component strengthens the case for generality if controls are sufficient.

major comments (1)
  1. [Section 3] Section 3: The argument that SIA follows directly from MLE on reasoning traces treats the expectation over prefixes as given and does not demonstrate that the MLE predictive distribution necessarily produces the observed monotonic drop in conditional answer entropy exclusively on correct traces. If the correlation is instead driven by higher probability mass on ground-truth sequences irrespective of prefix informativeness, SIA is epiphenomenal rather than explanatory.
minor comments (2)
  1. [Abstract] The abstract states that SIA is reinforced by 'standard fine-tuning and reinforcement-learning pipelines,' but the main text should specify which exact objectives or datasets were examined to support this claim.
  2. [Empirical evaluation] Empirical sections: Clarify the exact controls used when comparing entropy dynamics across the diverse set of models to rule out architecture-specific confounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The major comment identifies a genuine gap in the tightness of the derivation in Section 3, and we will revise the paper to address it directly.

read point-by-point responses

  1. Referee: Section 3: The argument that SIA follows directly from MLE on reasoning traces treats the expectation over prefixes as given and does not demonstrate that the MLE predictive distribution necessarily produces the observed monotonic drop in conditional answer entropy exclusively on correct traces. If the correlation is instead driven by higher probability mass on ground-truth sequences irrespective of prefix informativeness, SIA is epiphenomenal rather than explanatory.

    Authors: We agree that the current argument in Section 3 motivates SIA from MLE but does not rigorously derive the specific entropy dynamics as a necessary consequence. The manuscript notes that MLE on human traces encourages stepwise information accumulation but leaves the link to monotonic conditional entropy reduction implicit. In revision we will add a formal proposition and short proof sketch showing that the MLE objective induces lower conditional answer entropy on prefixes that align with the training distribution (correct traces) while incorrect traces lack this property. This will distinguish SIA from a simple higher probability mass on ground-truth sequences and make the explanatory role explicit. We will also add a brief discussion of why the alternative (epiphenomenal) account is inconsistent with the observed cross-model and cross-benchmark patterns. revision: yes

Circularity Check

1 steps flagged

SIA derivation from MLE reduces to definitional link between training objective and entropy drop on correct traces

specific steps
  1. self definitional [Section 3]
    "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."

    SIA is defined as reasoning prefixes accumulating answer-relevant information in expectation. MLE on human traces (correct reasoning sequences) trains the model to minimize loss exactly on those sequences, which by definition produces lower conditional entropy on the ground-truth answer tokens for correct generations. The claimed derivation of entropy dynamics from SIA is therefore equivalent to the training objective itself.

full rationale

The paper claims SIA emerges naturally from MLE on human reasoning traces and then derives entropy-correctness signatures from it. However, SIA is defined precisely as prefixes accumulating answer-relevant information (i.e., lowering conditional entropy on the true answer), while MLE on correct traces optimizes exactly for higher probability on those sequences. This makes the central explanatory link hold by construction rather than independent derivation. Empirical checks on benchmarks are present but do not break the definitional dependence. No load-bearing self-citations or uniqueness theorems are invoked in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the newly introduced SIA, which is motivated by but not strictly derived from maximum-likelihood training; no additional free parameters or invented entities are stated in the abstract.

axioms (1)
  • ad hoc to paper Stepwise Informativeness Assumption: reasoning prefixes accumulate answer-relevant information in expectation as generation progresses.
    This is the load-bearing assumption introduced to explain the entropy-correctness correlation.

pith-pipeline@v0.9.0 · 5543 in / 1095 out tokens · 57345 ms · 2026-05-15T13:01:09.663013+00:00 · methodology

discussion (0)

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