Sparse Autoencoders Map Brain-LLM Alignment onto Cortical Semantic Topography

A central goal of cognitive neuroscience is to characterize the features that are represented by human language cortex. Artificial language models (LMs) have emerged as a powerful tool to address this challenge, but studies relating biological and artificial representations are often criticized as relating one black box to another. The present work introduces Augmented Sparse Encoding Models, an encoding framework that replaces dense LM hidden states with hierarchically-organized sparse autoencoder (SAE) features, while explicitly including surprisal as a predictor. Using this approach, we (i) produce interpretations of neural responses and (ii) test whether model-brain alignment reflects primary or idiosyncratic variation in LM representations. Using a high-field 7T fMRI dataset of eight participants listening to 200 linguistically diverse sentences, we first validate our modeling framework by recovering previous interpretations of voxel populations tuned to processing difficulty and meaning abstractness. We then interpret a previously-uncharacterized (but reliable) voxel population and find that it is tuned to people-related content. Next, we show that the fronto-temporal human language network is predicted by a common set of features across its constituent regions, but find that frontal regions are relatively well-explained by surprisal alone, even in the absence of LM-based features. Finally, we show that brain responses during language processing are not merely predictable from an arbitrary set of LM features. Rather, brain responses are best explained by the features that tend to capture the most general information encoded in LM representations, suggesting a nontrivial correspondence between brain and LM language representation.

Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparameter is L0: how many SAE features should fire per token on average. Existing work compares SAE algorithms using sparsity-reconstruction tradeoff plots, implying L0 is a free parameter with no inherently correct value aside from its effect on reconstruction. In this work we study the effect of L0 on SAEs, and show that if L0 is not set correctly, the SAE fails to disentangle the underlying features of the LLM. If L0 is too low, the SAE will mix correlated features to improve reconstruction. If L0 is too high, the SAE finds degenerate solutions that also mix features. Further, we present a proxy metric that can help guide the search for the correct L0 for an SAE on a given training distribution. We show that our method finds the correct L0 in toy models and coincides with peak sparse probing performance in LLM SAEs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that practitioners must set L0 correctly to train SAEs with monosemantic features.

Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension $d_i \ge 2$ to error $\varepsilon$ with single-direction decoders forces a number of atoms that is exponential in $d_i$. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove that there exists a continuous path from the true $d_i$-dimensional basis to a strictly lower risk of the $\ell_1$-regularized SAE objective, whose descent directions drive any trained dictionary into that exponential regime. A single coherent feature is therefore fragmented across many near-collinear latents, producing spurious multiplicity and obscuring the intrinsic geometry. Motivated by this, we introduce Subspace-Aware Sparse Autoencoders (SASA), which replace single-vector decoders with learned decoder subspaces, enforce block sparsity via Top-$s$ group gating, and adapt each group's effective rank with a nuclear-norm regularizer. We then show that once the block size satisfies $r \ge d_i$, a single group not only can represent the entire feature slice but is the global minimizer of the SASA objective. This consolidation yields a sample complexity polynomial in $d_i$ rather than exponential -- a decisive advantage given that every training activation costs an LLM forward pass. Empirically, on GPT-2 and Mistral-7B, SASA reduces feature splitting and absorption, improves monosemanticity and interpretability, and matches or exceeds standard SAEs while training on roughly half the token budget.