Logical subspace in LLMs
TL;DR
The minimal viable subspace (MVS) method, which searches for the lowest-rank activation subspace at a layer that preserves task performance when everything outside that subspace is ablated, suggests a functionally localizable core machinery for logic akin to that in the human brain.
Abstract
Recent work has identified a human brain network specialized for abstract formal reasoning (Kean et al., 2025). Does the same hold true in language models? To answer this question, we introduce the minimal viable subspace (MVS) method, which searches for the lowest-rank activation subspace at a layer that preserves task performance when everything outside that subspace is ablated. Using MVS, we demonstrate low-rank subspaces supporting logical inference on Gemma and Qwen models. Furthermore, these subspaces exhibit a clear dissociation from model capacities on other tasks, such that retaining these late logic subspaces preserves inference while impairing factual knowledge, working memory, cognitive control, and arithmetic. Conversely, ablating them reduces logical inference accuracy to chance while largely sparing these other capacities. Our results suggest a functionally localizable core machinery for logic akin to that in the human brain.
