# Logical subspace in LLMs

arXiv: https://arxiv.org/abs/2609.32907 · HTML: https://mlsanity.com/paper/2609.32907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Emergent Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2212.09196/) (2022)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning](https://mlsanity.com/paper/2405.12241/) (2024)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models](https://mlsanity.com/paper/2502.20332/) (2025)
- [When can transformers reason with abstract symbols?](https://mlsanity.com/paper/2310.09753/) (2023)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Interpreting Encoding and Decoding Models](https://mlsanity.com/paper/1812.00278/) (2018)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [Causal Head Gating: A Framework for Interpreting Roles of Attention Heads in Transformers](https://mlsanity.com/paper/2505.13737/) (2025)
- [Modular Cognitive Architecture Emerges in Large Language Models](https://mlsanity.com/paper/2608.13567/) (2026)
- [Beyond Language: Format-Agnostic Reasoning Subspaces in Large Language Models](https://mlsanity.com/paper/2605.09496/) (2026)

## Abstract (arXiv)

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.