# Making LLMs Say What They Think: Measuring and Improving CoT-Interpretability Alignment

arXiv: https://arxiv.org/abs/2609.38972 · HTML: https://mlsanity.com/paper/2609.38972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 15 of 15)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Eight Things to Know about Large Language Models](https://mlsanity.com/paper/2304.00612/) (2023)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [Counterfactual Simulation Training for Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2602.20710/) (2026)
- [Is Chain-of-Thought Really Not Explainability? Chain-of-Thought Can Be Faithful without Hint Verbalization](https://mlsanity.com/paper/2512.23032/) (2025)
- [Latent Reasoning with Supervised Thinking States](https://mlsanity.com/paper/2602.08332/) (2026)
- [Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfalls](https://mlsanity.com/paper/2510.00184/) (2025)

## Abstract (arXiv)

Chain-of-thought (CoT) traces often serve as a proxy for how Large Language Models (LLMs) arrive at their answers. However, growing evidence shows that models' CoT often fails to reflect their internal computations and can be changed without affecting their final answers. In this work, we measure and improve the alignment between the reasoning described in an LLM's CoT and what it computes internally. We propose CoT-Interpretability Alignment (CIA), a metric that measures the agreement between a model's CoT traces and its internal reasoning strategies as detected by interpretability tools. We evaluate CIA on three tasks (two-hop question answering, hint intervention, and integer multiplication) across three LLMs, finding that LLMs exhibit limited alignment across all tasks (44.8-75.9%). We then experiment with improving CIA via post-training, setting both the task accuracy and parametric faithfulness signals as a reward. Experiments show that we can substantially improve CoT parametric faithfulness while maintaining or improving the task accuracy. We provide rich analysis, such as their generalization patterns. Our work provides both a framework for auditing CoT parametric faithfulness and a pathway toward making models' explicit reasoning more trustworthy. Code and data are available at https://github.com/yihuaihong/CIA-minimal-repro.