Large Language Models Encode Semantics in Low-Dimensional Linear Subspaces

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. However, it remains unclear to what extent LLMs internally organize representations related to semantic understanding. To explore this, we conduct a large-scale empirical study of hidden representations in 11 autoregressive models across 6 scientific topics. We find that high-level semantic information consistently resides in low-dimensional subspaces that form linearly separable representations across domains. This separability becomes more pronounced in deeper layers and under prompts that elicit structured reasoning or alignment behavior$\unicode{x2013}$even when surface content remains unchanged. These findings support geometry-aware tools that operate directly in latent space to detect and mitigate harmful or adversarial content. As a proof of concept, we train an MLP probe on final-layer hidden states to act as a lightweight latent-space guardrail. This approach substantially improves refusal rates on malicious queries and prompt injections that bypass both the model's built-in safety alignment and external token-level filters.