# GeoFaith: A Spatio-Temporal Dual View of Faithful Chain-of-Thought

arXiv: https://arxiv.org/abs/2605.26893 · HTML: https://mlsanity.com/paper/2605.26893/

## 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 32 of its 55 references that are in the map.
- First posted on arXiv 26 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, 30 of 32)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [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)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Robotic Control via Embodied Chain-of-Thought Reasoning](https://mlsanity.com/paper/2407.08693/) (2024)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Chain-of-Thought Reasoning In The Wild Is Not Always Faithful](https://mlsanity.com/paper/2503.08679/) (2025)
- [LogiQA: A Challenge Dataset for Machine Reading Comprehension with Logical Reasoning](https://mlsanity.com/paper/2007.08124/) (2020)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [FaithCoT-Bench: Benchmarking Instance-Level Faithfulness of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.04040/) (2025)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [KnowRL: Exploring Knowledgeable Reinforcement Learning for Factuality](https://mlsanity.com/paper/2506.19807/) (2025)
- [Entropy-Regularized Token-Level Policy Optimization for Language Agent Reinforcement](https://mlsanity.com/paper/2402.06700/) (2024)
- [RFEval: Benchmarking Reasoning Faithfulness under Counterfactual Reasoning Intervention in Large Reasoning Models](https://mlsanity.com/paper/2602.17053/) (2026)
- [Decoder ensembling for learned latent geometries](https://mlsanity.com/paper/2408.07507/) (2024)
- [LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision](https://mlsanity.com/paper/2512.18196/) (2025)
- [Evaluating GRPO and DPO for Faithful Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2512.22631/) (2025)
- [Reasoning emerges from constrained inference manifolds in large language models](https://mlsanity.com/paper/2605.08142/) (2026)
- [Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability](https://mlsanity.com/paper/2603.10384/) (2026)
- [GeoSteer: Faithful Chain-of-Thought Steering via Latent Manifold Gradients](https://mlsanity.com/paper/2601.10229/) (2026)
- [FaithLens: Detecting and Explaining Faithfulness Hallucination](https://mlsanity.com/paper/2512.20182/) (2025)

## Abstract (arXiv)

Chain-of-Thought (CoT) reasoning has advanced large language models (LLMs), but outcome-based supervision leads to pervasive post-hoc rationalization, producing plausible yet unfaithful reasoning chains. Most prior faithfulness assessment methods are either unscalable, expensive, or unreliable. We propose GeoFaith, a spatio-temporal framework that leverages latent geometric structure and entropy dynamics to diagnose and enforce faithful reasoning. We develop a scalable bootstrapping pipeline expanding step-level annotations from 1k to 20k samples across four domains, train an 8B faithfulness detector outperforming GPT-5 on standard benchmarks, and design a faithfulness-aware reinforcement learning framework jointly optimizing outcome correctness, process faithfulness, and trajectory consistency. Experiments show the proposed method achieves superior performance on both faithfulness detection and downstream reasoning, producing shorter, more interpretable chains without sacrificing accuracy. Our code will be made available publicly.