# GeoSteer: Faithful Chain-of-Thought Steering via Latent Manifold Gradients

arXiv: https://arxiv.org/abs/2601.10229 · HTML: https://mlsanity.com/paper/2601.10229/

## Key facts

- Cited by 4 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 24 of its 35 references that are in the map.
- First posted on arXiv 15 Jan 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, 24 of 24)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Shared Global and Local Geometry of Language Model Embeddings](https://mlsanity.com/paper/2503.21073/) (2025)
- [Large Language Models Encode Semantics and Alignment in Linearly Separable Representations](https://mlsanity.com/paper/2507.09709/) (2025)
- [Feature Extraction and Steering for Enhanced Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2505.15634/) (2025)
- [Steering LLMs for Formal Theorem Proving](https://mlsanity.com/paper/2502.15507/) (2025)

## Built on by (most cited first, 4 of 4)

- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability](https://mlsanity.com/paper/2603.10384/) (2026)
- [LLM Reasoning Is Latent, Not the Chain of Thought](https://mlsanity.com/paper/2604.15726/) (2026)
- [GeoFaith: A Spatio-Temporal Dual View of Faithful Chain-of-Thought](https://mlsanity.com/paper/2605.26893/) (2026)

## Abstract (arXiv)

Recent advances in Large Language Models (LLMs) have demonstrated remarkable progress in their reasoning capabilities, such as Chain-of-Thought (CoT). Most approaches rely on CoT rationales. Previous studies have shown that LLMs often generate logically inconsistent reasoning steps even when their final answers are correct. These inconsistencies reduce the reliability of the reasoning process. We propose GeoSteer, a manifold-based framework that improves the quality of intermediate reasoning. The method consists of: (1) constructing a CoT dataset with step-level scores, (2) training a Variational Autoencoder (VAE) model and a quality estimation model to learn a low-dimensional manifold of high-quality CoT trajectories, and (3) steering hidden states of target LLMs toward higher-quality regions in the latent space. This last step enables steering of the hidden states by following gradients along the learned manifold. It facilitates geometrically coherent steering. Evaluation experiments were conducted on the GSM8k dataset using the Qwen3 series. We evaluated performance using two metrics: answer accuracy and overall reasoning quality. GeoSteer improved the accuracy by 0.9 points and enhanced the reasoning quality by 4.5 points on average, compared with those of original LLMs. These results indicate that GeoSteer improves an effective and controllable mechanism for improving the quality of intermediate reasoning in LLMs.