Sparse Autoencoders for Mechanistic Interpretability in NLP: A Critical Survey of Recoverability, Interpretability, and Utility

Sparse autoencoders (SAEs) are a central tool in mechanistic interpretability. However, existing SAEs are primarily trained per layer. The modeling subspace is therefore fixed by layer identity, independent of which token-layer states actually drive each prediction. We argue that this constraint contributes to several limitations observed in layer-wise SAEs, including low feature utilization, high dictionary redundancy, and features that lack direct behavioral grounding. In this paper, we propose ScopeSAE, which selects the modeling subspace per token by attributing each prediction to its most influential token-layer state via normalized gradient-based attribution, and learns features over the resulting prediction-relevant subspace. Empirically, ScopeSAE yields an effect we term reconstruction-better-than-original. Written-back reconstructions of the SAE produce lower next-token cross-entropy than the original activations, an outcome that, to our knowledge, has not previously been reported for SAEs. Through interventional analyses and a KL fine-tuning counter-experiment, we show that this effect is attributable to ScopeSAE's prediction-relevant subspace itself rather than to architectural changes. ScopeSAE further improves effective feature count, interpretability, utilization, and dictionary redundancy over existing layer-based baselines, suggesting that choosing the SAE modeling subspace by predictive relevance leads to more useful and behaviorally meaningful 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.

Sparse autoencoders (SAEs) are a core interpretability tool for large language models, and progress on SAE architectures depends on benchmarks that reliably distinguish better SAEs from worse ones. We audit the SAE quality metrics in SAEBench, the de-facto standard SAE evaluation suite, through three complementary lenses: reseed noise on a fixed SAE, ground-truth correlation on synthetic SAEs, and discriminability across training trajectories. We find that two of these metrics, Targeted Probe Perturbation (TPP) and Spurious Correlation Removal (SCR), fail multiple lenses at their canonical settings and should not be used to evaluate SAEs. The other metrics show higher reseed noise and lower discriminability than the field assumes. The sae-probes variant of $k$-sparse probing is the most reliable metric we tested, but even sae-probes struggles to separate variants of the same SAE architecture. Our results show the field needs better SAE benchmarks.