Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views

TL;DR

This paper investigates whether large language models contain a shared internal logical subspace that aligns natural language and symbolic reasoning, and proposes a training-free method to steer reasoning along this subspace, improving logical reasoning accuracy.

Contribution

It introduces a novel approach to identify and utilize a shared logical subspace in LLMs, enhancing reasoning capabilities without additional training.

Findings

Improved reasoning accuracy by up to 11 percentage points.

Demonstrated effective generalization on out-of-domain problems.

Validated approach on four logical reasoning benchmarks.

Abstract

Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.