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arxiv: 2606.20624 · v1 · pith:HHJ3RGZZnew · submitted 2026-05-26 · 💻 cs.AI · cs.CL· cs.LG· stat.ML

In LLM Reasoning, there is Irrationality on top of Value Misalignment

Kejiang Qian , Fengxiang He This is my paper

Pith reviewed 2026-06-29 17:34 UTC · model grok-4.3

classification 💻 cs.AI cs.CLcs.LGstat.ML
keywords rational value riskLLM reasoningvalue alignmentutility maximizationinference-time strategyestimation errorsteepest direction
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The pith

LLMs can fail to maximize aligned values in reasoning even after successful post-training alignment due to rational value risk.

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

The paper claims that value alignment achieved during training does not ensure LLMs will select reasoning paths that actually maximize the aligned utility at inference time. It defines rational value risk as the gap between the utility of a model's deployed reasoning strategy and the utility of its rational counterpart, where the counterpart consists of responses that maximize expected utility along the steepest direction. This risk is decomposed into estimation error from finite candidate sets, finite prompt sets, and imperfect verifiers. Experiments across Llama, Qwen, Tulu, GPT, and DeepSeek families on feedback, math, and coding benchmarks show the risk is widespread, reduced but not removed by alignment, sensitive to reasoning strategy, and improved by longer chains with diminishing returns.

Core claim

The paper formalizes rational value risk as the utility discrepancy between a model's deployed reasoning strategy and its rational counterpart, defined to be the responses that maximise expected utility in the steepest direction; the estimation error of this risk decomposes into three components arising from finite candidates, finite prompts, and imperfect verifiers.

What carries the argument

Rational value risk, the utility discrepancy between deployed reasoning and the steepest-utility rational counterpart.

If this is right

  • Rational value risk remains widespread even in aligned models from multiple families and sizes.
  • Value alignment during training reduces but does not eliminate rational value risk.
  • The magnitude of the risk depends strongly on the inference-time reasoning strategy employed.
  • Extending reasoning length improves rationality, yet gains diminish after a point.

Where Pith is reading between the lines

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

  • Post-training alignment may need to be supplemented by inference-time mechanisms that explicitly search for steepest-utility responses.
  • The three error components suggest targeted improvements in candidate generation, prompt design, or verifier accuracy could shrink the risk.
  • Tasks requiring precise value maximization, such as safety-critical decisions, may remain unreliable until rational value risk is directly addressed.
  • The same gap between alignment and rational deployment could appear in non-LLM agent systems that optimize under uncertainty.

Load-bearing premise

The rational counterpart can be identified as responses that maximise expected utility in the steepest direction, and the three-component decomposition fully captures all sources of the risk.

What would settle it

A controlled experiment in which a model's deployed reasoning strategy is shown to achieve equal or higher expected utility than the identified steepest-direction responses on the same task would falsify the presence of rational value risk.

Figures

Figures reproduced from arXiv: 2606.20624 by Fengxiang He, Kejiang Qian.

Figure 1
Figure 1. Figure 1: Effects of sampling temperature τ = {0.0, 0.7, 1.0} on rational value risk of Tülu-3-8B-RLVR (Tülu-3- 8B), Qwen2.5-7B-Instruct (Qwen2.5-7B), and Llama-3.1-8B-Instruct (Llama-3.1-8B) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effects of self-consistency budget n = {2, 4, 8, 16, 32} on rational value risk of Tülu-3-8B￾RLVR (Tülu-3-8B), Qwen2.5-7B-Instruct (Qwen2.5- 7B), and Llama-3.1-8B-Instruct (Llama-3.1-8B). value risk remains after DPO. After RLVR, Tülu￾3-8B-RLVR still has rational value risk of 0.309 on MATH and 0.450 on HumanEval. The improve￾ment from DPO to RLVR is also limited on several benchmarks. For example, rationa… view at source ↗
Figure 3
Figure 3. Figure 3: Rational value risk of of Tülu-3-8B-RLVR [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Significant progress has been made in aligning LLMs with target value functions. We argue that, even when an LLM has been well aligned in (post-)training, it may still fail to maximise the aligned value in reasoning. We mathematically formalise this gap as rational value risk: the utility discrepancy between a model's deployed reasoning strategy and its rational counterpart, which is defined to be the responses that maximise expected utility in the steepest direction. The estimation error of rational value risk is further decomposed into three components from finite candidates, finite prompts, and imperfect verifiers. Extensive experiments are conducted, covering models Llama-3.1, Qwen-2.5, T{\"}ulu-3 families (7B-72B), GPT-5.2, GPT-5.5, and DeepSeek-V4, and benchmarks UltraFeedback, AlpacaEval, GSM8K, MATH, HumanEval, and MathArena. The results validate that (1) rational value risk is widespread; (2) value alignment can reduce, but cannot eliminate, it; (3) the risk is highly sensitive to inference-time reasoning strategy; and (4) longer reasoning improves rationality with diminishing returns. The code is at https://github.com/EVIEHub/LLM-Rationality.

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

2 major / 1 minor

Summary. The paper claims that even after value alignment in post-training, LLMs may still fail to maximize the aligned value during reasoning. This gap is formalized as rational value risk: the utility discrepancy between a model's deployed reasoning strategy and its rational counterpart (defined as the responses that maximize expected utility in the steepest direction). The estimation error of this risk is decomposed into three components arising from finite candidates, finite prompts, and imperfect verifiers. Experiments across Llama-3.1, Qwen-2.5, Tulu-3 (7B-72B), GPT-5.2/5.5, and DeepSeek-V4 on benchmarks including UltraFeedback, AlpacaEval, GSM8K, MATH, HumanEval, and MathArena show that rational value risk is widespread, reduced but not eliminated by alignment, highly sensitive to inference-time strategies, and decreases with longer reasoning (with diminishing returns).

Significance. If the formalization holds without circularity, the work usefully separates value alignment from rational maximization in reasoning, with practical implications for inference-time methods. The broad empirical scope across model families, sizes, and tasks provides concrete evidence that the phenomenon is not isolated; the public code release supports reproducibility.

major comments (2)
  1. [Abstract / Formalization] Abstract and formalization (likely §3): the rational counterpart is defined as responses that 'maximise expected utility in the steepest direction.' In discrete token/output spaces this requires an explicit metric, embedding, or operator (e.g., a policy gradient or continuous relaxation) to define 'direction' and 'steepest'; none is supplied in the visible description. Without such an operator independent of the deployed strategy, the discrepancy measure risks being partly tautological with the alignment process itself.
  2. [Error decomposition] Abstract and § on error decomposition: the three-component decomposition (finite candidates, finite prompts, imperfect verifiers) inherits the same ambiguity in the definition of the rational benchmark. If the benchmark itself is under-specified, the attribution of estimation error to these sources cannot be cleanly separated from the definitional issue.
minor comments (1)
  1. [Experiments] The abstract states that 'the results validate' the four claims but does not report how the steepest-direction strategy was computed or cross-checked against the paper's own data; adding a short methods paragraph or appendix table would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the formalization and error decomposition. We address each major point below and will incorporate clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract / Formalization] Abstract and formalization (likely §3): the rational counterpart is defined as responses that 'maximise expected utility in the steepest direction.' In discrete token/output spaces this requires an explicit metric, embedding, or operator (e.g., a policy gradient or continuous relaxation) to define 'direction' and 'steepest'; none is supplied in the visible description. Without such an operator independent of the deployed strategy, the discrepancy measure risks being partly tautological with the alignment process itself.

    Authors: We agree that the current high-level phrasing of 'maximise expected utility in the steepest direction' requires an explicit operator to be well-defined in discrete output spaces. The manuscript does not supply this operator in the provided description. In revision we will add a precise definition (e.g., via a continuous relaxation of the token embedding space or a directional derivative with respect to the aligned value function) that is independent of any deployed reasoning strategy. This will also make explicit that the rational benchmark is computed solely from the aligned value function and is therefore not tautological with post-training alignment. revision: yes

  2. Referee: [Error decomposition] Abstract and § on error decomposition: the three-component decomposition (finite candidates, finite prompts, imperfect verifiers) inherits the same ambiguity in the definition of the rational benchmark. If the benchmark itself is under-specified, the attribution of estimation error to these sources cannot be cleanly separated from the definitional issue.

    Authors: We concur that the error decomposition presupposes a well-specified rational benchmark. Once the operator for the steepest direction is formalized as described above, each of the three error sources can be attributed relative to that benchmark. The revised manuscript will include an expanded derivation showing how the finite-candidate, finite-prompt, and verifier-error terms are isolated from the now-explicit rational reference. revision: yes

Circularity Check

0 steps flagged

No significant circularity; definition is explicit and claims rest on independent experiments

full rationale

The paper explicitly defines rational value risk as the utility discrepancy to a separately defined rational counterpart (responses maximising expected utility in the steepest direction). The three-component decomposition applies only to estimation error of this quantity, not to the quantity itself. Validation rests on empirical results across multiple model families and benchmarks (Llama-3.1, Qwen-2.5, etc.; UltraFeedback, GSM8K, etc.), which are external to the definition. No equations reduce the central claim to a fit or self-citation by construction, and no load-bearing self-citation or ansatz smuggling is present in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.1-grok · 5767 in / 1070 out tokens · 35409 ms · 2026-06-29T17:34:32.233628+00:00 · methodology

discussion (0)

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Reference graph

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