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

TL;DR

GeoSteer is a novel framework that enhances the reasoning quality of large language models by steering their internal states along a learned low-dimensional manifold, resulting in more consistent and accurate intermediate reasoning steps.

Contribution

It introduces a manifold-based approach using a VAE and gradient steering to improve the logical coherence of LLM reasoning processes.

Findings

Improved answer accuracy by 0.9 points on GSM8k dataset.

Enhanced reasoning quality by 4.5 points on average.

Demonstrated effective control over LLM intermediate reasoning.

Abstract

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.