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

Recent advances in Large Language Models (LLMs) have improved multi-step reasoning. Most approaches rely on Chain-of-Thought (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 step-level reasoning. We propose GeoSteer, a manifold-based framework that improves the quality of intermediate reasoning. The method consists of: (1) constructing a CoT dataset with segment-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 update in a latent space behaves like a natural-gradient adjustment in the original hidden-state space. It ensures geometrically coherent steering. We evaluate GeoSteer on the GSM8k dataset using the Qwen3 series. We measure via answer accuracy and overall reasoning performance. GeoSteer improved the exact match accuracy by up to 2.6 points. It also enhanced the pairwise win rate by 5.3 points. These results indicate that GeoSteer provides an effective and controllable mechanism for improving the quality of intermediate reasoning in LLMs.