Logical reasoning serve as a central capability in LLMs and includes three main forms: deductive, inductive, and abductive reasoning. In this work, we study the knowledge representations of these reasoning types in LLMs and analyze the correlations among them. Our analysis shows that each form of logical reasoning can be captured as a reasoning-specific knowledge vector in a linear representation space, yet these vectors are largely independent of each other. Motivated by cognitive science theory that these subforms of logical reasoning interact closely in the human brain, as well as our observation that the reasoning process for one type can benefit from the reasoning chain produced by another, we further propose to refine the knowledge representations of each reasoning type in LLMs to encourage complementarity between them. To this end, we design a complementary subspace-constrained refinement framework, which introduces a complementary loss that enables each reasoning vector to leverage auxiliary knowledge from the others, and a subspace constraint loss that prevents erasure of their unique characteristics. Through steering experiments along reasoning vectors, we find that refined vectors incorporating complementary knowledge yield consistent performance gains. We also conduct a mechanism-interpretability analysis of each reasoning vector, revealing insights into the shared and specific features of different reasoning in LLMs.
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.
While LLMs demonstrate impressive reasoning capabilities, they remain fragile in multi-step logical deduction, where a single transition error can propagate through the entire reasoning chain, leading to unstable performance. In this work, we identify logical connectives as primary points of this structural fragility. Through empirical analysis, we show that connective tokens function as high entropy forking points, at which models frequently struggle to determine the correct logical direction. Motivated by this observation, we hypothesize that intervening in logical connective selection can guide LLMs toward more correct logical direction, thereby improving the overall reasoning chain. To validate this hypothesis, we propose a multi-layered framework that intervenes specifically at these logic-critical junctions in the reasoning process. Our framework includes (1) Gradient-based Logical Steering to guide LLMs internal representations towards valid reasoning subspaces, (2) Localized Branching to resolve ambiguity via targeted look-ahead search, and (3) Targeted Transition Preference Optimization, a surgical reinforcement learning objective that selectively optimizes single-token preferences at logical pivots. Crucially, by concentrating intervention solely on logic-critical transitions, our framework achieves a favorable accuracy--efficiency trade-off compared to global inference time scaling methods like beam search and self-consistency.
The correspondence between large language models (LLMs) and the neural mechanisms underlying human higher-order cognition remains insufficiently characterized. Given that language and reasoning in the human brain appear dissociable, an open question is whether LLMs align with neural signals from reasoning-related regions and whether such signals can improve them. Here, focusing on deductive reasoning, we show that LLM internal representations are not only partially aligned with task-fMRI activity but can also be directly enhanced by these signals. Using a neural-predictivity metric, we find that LLMs explain a substantial fraction of the explainable variance in reasoning-related regions at the aggregate level, whereas predictivity within specific reasoning types is lower, indicating both alignment and divergence. Building on this, we propose a brain-guided framework: we steer model representations along directions induced by the joint structure of model and brain representations, applying intervention at inference and fine-tuning during training. We demonstrate that task-evoked brain signals can directly enhance LLM reasoning, yielding gains orthogonal to language-only supervision across 10 LLMs (1.5B-72B), with transfer across reasoning types and up to 13% absolute accuracy gain. Our results advance LLM-brain correspondences from correlation to guidance, establishing a brain-signal-driven pathway toward more robust and cognitively aligned AI.