Residualized Temporal Sparse Autoencoders for Interpreting Diffusion Models

Sparse autoencoders (SAEs) have recently been proposed as interpretable tools for concept-level manipulation, under the assumption that isolated features can serve as controllable intervention points. In this work, we systematically evaluate this assumption in the context of object erasure and steering in diffusion models. We show that while SAEs reliably detect and localize semantic concepts within diffusion model activations, direct intervention in their latent space frequently induces out-of-distribution activations, resulting in severe visual artifacts. To disentangle detection from intervention, we use SAE activations purely as semantic detectors to identify image regions containing the target object, and replace those patch embeddings with the ones that do not contain it. This detection-based replacement preserves the diffusion model's activation statistics and produces significantly cleaner erasure results than latent steering. Our findings reveal a fundamental gap between concept detection and concept intervention in diffusion models: monosemantic or sparse features are not inherently suitable as control knobs for steering. These results position SAEs as powerful interpretability tools for analyzing generative models, but highlight important limitations when used for direct manipulation, such as unlearning.

Sparse autoencoders (SAEs) decompose language model activations into sparse features, yet these models traditionally encode each token independently, failing to expose information that persists across a sequence. We first show that temporal persistence can naturally emerge in standard SAE features: after a feature activates, the hidden state remains aligned with its direction, and past activations help reconstruct later hidden states. How long this lasts varies widely across features. We therefore introduce Persistent Sparse Autoencoders (Persistent SAEs), an extension of standard SAEs that learns a persistence coefficient for each feature, allowing the model to learn feature-specific timescales from reconstruction alone. Our experiments show that Persistent SAEs retain competitive reconstruction quality while learning a spectrum of timescales: short-timescale (fast) features stay locally interpretable, whereas long-timescale (slow) features accumulate information that identifies the current context. Moreover, we show in a prompt-injection monitoring case study that slow features preserve injection-related signals and remain causally effective over long contexts. These results suggest that Persistent SAEs offer new opportunities for interpreting and monitoring language models via persistent sparse features.

Sparse autoencoders (SAEs) are typically trained to reconstruct the \textbf{entire} residual stream through a sparse dictionary, implicitly assuming that all activation content is amenable to sparse, monosemantic decomposition. We question this assumption and hypothesize that activations contain a low-rank, dense component that is computationally important to the model yet inherently unsuitable for sparse representation, which serves as a major source of the persistent dense latents widely observed in trained SAEs. To test this, we add a small rank-$r$ linear bottleneck in parallel with standard SAEs (BatchTopK and Matryoshka), allowing dense structure to be absorbed before sparse reconstruction. On Gemma-2-2B layer 12, a rank-24 bottleneck reduces dense latent count by up to 84% while improving sparse probing and targeted probe perturbation on both architectures at matched sparsity. The absorbed component is (i) \textbf{structurally identifiable} as the top principal components and outlier dimensions; (ii) \textbf{causally necessary}, with removing it raising next-token cross-entropy by 7.5$\times$, far exceeding the 2.8$\times$ from removing the geometrically near-identical top-24 PCA directions; and (iii) \textbf{redundantly encoded by sparse dictionaries}, with ablating 787 maximally aligned sparse features raising cross-entropy by only 2.9$\times$ and ablating 2,048 topic-aligned features leaving MMLU topic classification virtually unchanged, whereas removing the scaffold drops it from 98.7% to chance. Together, our findings identify a compact, semantically informative and causally important component of residual stream activations (which we term a \textbf{computational scaffold}) that standard sparse dictionaries represent inefficiently, suggesting that the scope of sparsity-based interpretability methods warrants careful re-examination.