Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views
Feihao Fang, My T. Thai, Yuanyuan Lei
TLDR
This paper introduces a method to improve LLM logical reasoning by discovering and steering a shared internal logical subspace that aligns natural language and symbolic views.
Key contributions
- Proposes a "shared logical subspace" within LLMs that aligns natural language and symbolic reasoning.
- Employs Canonical Correlation Analysis (CCA) on activations to discover this cross-view logical subspace.
- Introduces a training-free method to steer LLM reasoning along this subspace, combining both views.
- Improves logical reasoning accuracy by up to 11% and shows strong generalization on new problems.
Why it matters
LLMs often struggle with complex multi-step logical reasoning tasks. This paper presents a novel, training-free method that significantly enhances LLM logical reasoning by leveraging an internal shared subspace. It achieves notable accuracy improvements and better generalization on unseen problems.
Original 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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.