Measuring Monosemanticity in Sparse Autoencoders via Latent Activation Coherence

Within Explainable Artificial Intelligence, mechanistic interpretability uses Sparse Autoencoders (SAEs) to extract more interpretable features from neural representations. However, assessing their monosemanticity, and thus explanation quality, remains challenging. Existing metrics require external concept labels or depend on pretrained embedding models, making them sensitive to encoder's geometry. We introduce the Tversky Monosemanticity Score (TMS), a label-free metric that operationalizes monosemanticity as activation-set coherence of binarized SAE latents, and does not require external embedding encoders. We evaluate TMS on SAEs trained on features from pretrained vision and vision-language models (DINOv3, CLIP, BLIP2), two common SAE regimes (TopK, BatchTopK), multiple sparsity levels, and expansion factors. Our results show that TMS is less affected by encoder anisotropy than its embedding-based alternative, while remaining aligned with established monosemanticity indicators. TMS also reveals distinct SAE training dynamics across base models. Moreover, under encoder anisotropy, TMS provides a stronger indication of probe-based concept deletion effectiveness, while being competitive otherwise.

Beyond the Hard Budget: Sparsity Regularizers for More Interpretable Top-k Sparse Autoencoders

Sparse autoencoders (SAEs) have become a leading tool for interpreting the representations of vision foundation models, decomposing their polysemantic activations into a larger set of sparse, more monosemantic features. The Top-$k$ SAE, a now-standard variant, enforces sparsity architecturally through its activation function, retaining only the $k$ most active latents per input. Because it was designed precisely to avoid the $\ell_1$ penalty used by earlier SAEs and its known drawbacks, it has not been combined with an explicit sparsity regularizer, despite retaining limitations of its own, such as a budget $k$ that is fixed regardless of input complexity and a tendency to overfit to the training value of $k$. We introduce two sparsity regularizers compatible with the Top-$k$ architecture, both acting on the activations before the Top-$k$ selection: an $\ell_1$ penalty on the unselected (off-support) units, and a scale-invariant $\ell_1/\ell_2$-ratio penalty that concentrates the code onto fewer effective units. Both penalties are applied only to the batch-active units, those selected by the Top-$k$ operator at least once within the batch. Across two datasets, three vision foundation models, and a range of $k$, both regularizers consistently improve monosemanticity at no cost to reconstruction quality. The $\ell_1/\ell_2$ penalty further concentrates information into fewer latents, making reconstruction more robust to the inference-time choice of $k$ and improving small-budget linear probing. Our central finding is that hard architectural sparsity and soft sparsity regularization are complementary rather than mutually exclusive.