# Measuring and curing reasoning rigidity: from decorative chain-of-thought to genuine faithfulness

arXiv: https://arxiv.org/abs/2603.22816 · HTML: https://mlsanity.com/paper/2603.22816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 21 of 21)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [Making Reasoning Matter: Measuring and Improving Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2402.13950/) (2024)
- [Measuring Chain of Thought Faithfulness by Unlearning Reasoning Steps](https://mlsanity.com/paper/2502.14829/) (2025)
- [Counterfactual Simulation Training for Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2602.20710/) (2026)
- [Can Aha Moments Be Fake? Towards Quantifying Decorative and True Thinking in Chain-of-Thought](https://mlsanity.com/paper/2510.24941/) (2025)
- [RFEval: Benchmarking Reasoning Faithfulness under Counterfactual Reasoning Intervention in Large Reasoning Models](https://mlsanity.com/paper/2602.17053/) (2026)
- [Reasoning or Retrieval? A Study of Answer Attribution on Large Reasoning Models](https://mlsanity.com/paper/2509.24156/) (2025)
- [Mechanistic Evidence for Faithfulness Decay in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.11201/) (2026)
- [Causal Consistency Regularization: Training Verifiably Sensitive Reasoning in Large Language Models](https://mlsanity.com/paper/2509.01544/) (2025)
- [Lie to Me: How Faithful Is Chain-of-Thought Reasoning in Reasoning Models?](https://mlsanity.com/paper/2603.22582/) (2026)

## Built on by (most cited first, 1 of 1)

- [Clinical Reasoning Graphs: Structured Evaluation of LLM Diagnostic Reasoning Reveals Competence Without Consistency](https://mlsanity.com/paper/2606.29876/) (2026)

## Abstract (arXiv)

Language models increasingly show their work by writing step-by-step reasoning before answering. But are these steps genuinely used, or is the answer rigid - fixed before reasoning begins? We introduce the Step-Level Reasoning Capacity (SLRC) metric and prove it is a consistent causal estimator (Theorem 1). We propose LC-CoSR, a training method with Lyapunov stability guarantees that directly reduces rigidity. Evaluating 16 frontier models (o4-mini, GPT-5.4, Claude Opus, Grok-4, DeepSeek-R1, Gemini 2.5 Pro, and others) across six domains at N=133-500, we find reasoning falls into three modes. OpenAI's o4-mini shows 74-88% step necessity on five of six tasks (73.8-88.3%) - the highest SLRC in our study. The critical differentiator is RL-based reasoning training, not thinking tokens: Grok-4's reasoning mode shows lower faithfulness than its non-reasoning mode (1.4% vs 7.2% necessity). We discover a faithfulness paradox - high-SLRC models are more susceptible to sycophancy - and propose the Reasoning Integrity Score (RIS = SLRC x (1-Sycophancy)), which significantly predicts error detection (rho=0.66, p=0.026). LC-CoSR achieves 2.6x less negative reward than FARL and CSR baselines without external model dependencies.