# Investigating the Interplay between Contextual and Parametric Chain-of-Thought Faithfulness under Optimization

arXiv: https://arxiv.org/abs/2605.24960 · HTML: https://mlsanity.com/paper/2605.24960/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 24 May 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, 12 of 12)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [Are DeepSeek R1 And Other Reasoning Models More Faithful?](https://mlsanity.com/paper/2501.08156/) (2025)
- [Is Chain-of-Thought Really Not Explainability? Chain-of-Thought Can Be Faithful without Hint Verbalization](https://mlsanity.com/paper/2512.23032/) (2025)
- [Model Merging in the Era of Large Language Models: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2603.09938/) (2026)
- [Aligning What LLMs Do and Say: Towards Self-Consistent Explanations](https://mlsanity.com/paper/2506.07523/) (2025)
- [Measuring Faithfulness Depends on How You Measure: Classifier Sensitivity in LLM Chain-of-Thought Evaluation](https://mlsanity.com/paper/2603.20172/) (2026)

## Built on by (most cited first, 2 of 2)

- [Limitations of Automated Simulatability: LLM Simulators Can Bypass Explanations](https://mlsanity.com/paper/2609.08585/) (2026)
- [From Concept Alignment to Causal Grounding: An Intervention Test of Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2609.23065/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) faithfulness, i.e., whether CoTs genuinely reflect large language models' (LLM) underlying behavior, is typically evaluated with metrics under two disjoint paradigms: contextual faithfulness, measured by perturbing the input or CoT trace, and parametric faithfulness, assessed by intervening on a model's parametric knowledge. Yet prior work compares them only descriptively. We fill this gap by proposing FaithMATE, a unified preference-alignment interface for optimizing models towards either faithfulness paradigm. It enables us to investigate the interplay between the two paradigms, examining whether and to what extent faithfulness gains generalize within and across paradigms. Across three models, two datasets, and six faithfulness metrics, we find that the two paradigms are positively coupled, yet asymmetric: optimizing towards parametric faithfulness yields consistent gains across both paradigms, whereas the contextual counterpart delivers more variable gains. Within the contextual paradigm, faithfulness gains on one metric do not consistently transfer to others, implying that existing contextual metrics capture disjoint facets of faithfulness and exposing inherent trade-offs. These findings imply that CoT faithfulness is not a monolithic objective and therefore requires multifaceted optimization and evaluation.