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.

翻译：大型语言模型在复杂多步逻辑推理中仍面临挑战。现有方法要么纯粹以自然语言形式优化推理链，要么将符号求解器作为外部模块附加。本研究则探讨大语言模型是否包含一个共享的内部逻辑子空间，该子空间能同时对齐推理过程的自然语言视图与符号语言视图。我们假设该逻辑子空间捕获了模型中共有且独立于表层形式的逻辑推理能力。为验证这一假设，我们对自然语言推理链与符号语言推理链的配对残差激活进行典型相关分析，学习具有最大跨视图相关性的低维子空间。此外，我们设计了一种无需训练的方法，沿该逻辑子空间引导模型的推理链，从而综合利用两个视图的互补推理信号。在四个逻辑推理基准上的实验表明，本方法可将准确率提升最多11个百分点，并具有良好的跨领域泛化能力。