What latent features are encoded in language model (LM) representations? Recent work on training sparse autoencoders (SAEs) to disentangle interpretable features in LM representations has shown significant promise. However, evaluating the quality of these SAEs is difficult because we lack a ground-truth collection of interpretable features which we expect good SAEs to identify. We thus propose to measure progress in interpretable dictionary learning by working in the setting of LMs trained on Chess and Othello transcripts. These settings carry natural collections of interpretable features--for example, "there is a knight on F3"--which we leverage into metrics for SAE quality. To guide progress in interpretable dictionary learning, we introduce a new SAE training technique, $p$-annealing, which demonstrates improved performance on our metric.

Continuing advances in neural interfaces have enabled simultaneous monitoring of spiking activity from hundreds to thousands of neurons. To interpret these large-scale data, several methods have been proposed to infer latent dynamic structure from high-dimensional datasets. One recent line of work uses recurrent neural networks in a sequential autoencoder (SAE) framework to uncover dynamics. SAEs are an appealing option for modeling nonlinear dynamical systems, and enable a precise link between neural activity and behavior on a single-trial basis. However, the very large parameter count and complexity of SAEs relative to other models has caused concern that SAEs may only perform well on very large training sets. We hypothesized that with a method to systematically optimize hyperparameters (HPs), SAEs might perform well even in cases of limited training data.

Recent work has found that sparse autoencoders (SAEs) are an effective technique for unsupervised discovery of interpretable features in language models' (LMs) activations, by finding sparse, linear reconstructions of those activations. We introduce the Gated Sparse Autoencoder (Gated SAE), which achieves a Pareto improvement over training with prevailing methods. In SAEs, the L1 penalty used to encourage sparsity introduces many undesirable biases, such as shrinkage -- systematic underestimation of feature activations. The key insight of Gated SAEs is to separate the functionality of (a) determining which directions to use and (b) estimating the magnitudes of those directions: this enables us to apply the L1 penalty only to the former, limiting the scope of undesirable side effects. Through training SAEs on LMs of up to 7B parameters we find that, in typical hyper-parameter ranges, Gated SAEs solve shrinkage, are similarly interpretable, and require half as many firing features to achieve comparable reconstruction fidelity.

Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge. While CBMs use supervision to align activations with human-labeled concepts, SAEs rely on sparse coding to uncover emergent ones. We show that both paradigms instantiate the same geometric structure: each learns a set of linear directions in activation space whose nonnegative combinations form a concept cone. Supervised and unsupervised methods thus differ not in kind but in how they select this cone. Building on this view, we propose an operational bridge between the two paradigms. CBMs provide human-defined reference geometries, while SAEs can be evaluated by how well their learned cones approximate or contain those of CBMs. This containment framework yields quantitative metrics linking inductive biases -- such as SAE type, sparsity, or expansion ratio -- to emergence of plausible\footnote{We adopt the terminology of \citet{jacovi2020towards}, who distinguish between faithful explanations (accurately reflecting model computations) and plausible explanations (aligning with human intuition and domain knowledge). CBM concepts are plausible by construction -- selected or annotated by humans -- though not necessarily faithful to the true latent factors that organise the data manifold.} concepts. Using these metrics, we uncover a ``sweet spot'' in both sparsity and expansion factor that maximizes both geometric and semantic alignment with CBM concepts. Overall, our work unifies supervised and unsupervised concept discovery through a shared geometric framework, providing principled metrics to measure SAE progress and assess how well discovered concept align with plausible human concepts.

Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparame-ter 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 single 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 L0 must be set correctly to train SAEs with correct features. It is theorized that Large Language Models (LLMs) represent concepts as linear directions in representation space, known as the Linear Representation Hypothesis (LRH) (Elhage et al., 2022; Park et al., 2024). These concepts are nearly orthogonal linear directions, allowing the LLM to represent many more concepts than there are neurons, a phenomenon known as superposition (Elhage et al., 2022). However, superposition poses a challenge for interpretability, as neurons in the LLM are polysemantic, firing on many different concepts. Sparse autoencoders (SAEs) are meant to reverse superposition, and extract interpretable, monose-mantic latent features (Cunningham et al., 2024; Bricken et al., 2023) using sparse dictionary learning (Olshausen & Field, 1997).

Sparse autoencoders (SAEs) are a mechanistic interpretability technique that have been used to provide insight into learned concepts within large protein language models. Here, we employ TopK and Ordered SAEs to investigate an autoregressive antibody language model, p-IgGen, and steer its generation. We show that TopK SAEs can reveal biologically meaningful latent features, but high feature concept correlation does not guarantee causal control over generation. In contrast, Ordered SAEs impose an hierarchical structure that reliably identifies steerable features, but at the expense of more complex and less interpretable activation patterns. These findings advance the mechanistic interpretability of domain-specific protein language models and suggest that, while TopK SAEs are sufficient for mapping latent features to concepts, Ordered SAEs are preferable when precise generative steering is required.

Sparse autoencoders (SAEs) have been widely used for interpretability of neural networks, but their learned features often vary across seeds and hyperparame-ter settings. We introduce Ordered Sparse Autoencoders (OSAE), which extend Matryoshka SAEs by (1) establishing a strict ordering of latent features and (2) deterministically using every feature dimension, avoiding the sampling-based approximations of prior nested SAE methods. Theoretically, we show that OSAEs resolve permutation non-identifiability in settings of sparse dictionary learning where solutions are unique (up to natural symmetries). Empirically on Gemma2-2B and Pythia-70M, we show that OSAEs can help improve consistency compared to Matryoshka baselines.

Sparse Autoencoders (SAEs) have recently gained attention as a means to improve the interpretability and steerability of Large Language Models (LLMs), both of which are essential for AI safety. In this work, we extend the application of SAEs to Vision-Language Models (VLMs), such as CLIP, and introduce a comprehensive framework for evaluating monosemanticity at the neuron-level in visual representations. To ensure that our evaluation aligns with human perception, we propose a benchmark derived from a large-scale user study. Our experimental results reveal that SAEs trained on VLMs significantly enhance the monosemanticity of individual neurons, with sparsity and wide latents being the most influential factors. Further, we demonstrate that applying SAE interventions on CLIP's vision encoder directly steers multimodal LLM outputs (e.g., LLaVA), without any modifications to the underlying language model. These findings emphasize the practicality and efficacy of SAEs as an unsupervised tool for enhancing both interpretability and control of VLMs. Code and benchmark data are available at https://github.com/ExplainableML/sae-for-vlm.

Large language models (LLMs) have achieved remarkable progress, yet their internal mechanisms remain largely opaque, posing a significant challenge to their safe and reliable deployment. Sparse autoencoders (SAEs) have emerged as a promising tool for decomposing LLM representations into more interpretable features, but explaining the features captured by SAEs remains a challenging task. In this work, we propose SAGE (SAE AGentic Explainer), an agent-based framework that recasts feature interpretation from a passive, single-pass generation task into an active, explanation-driven process. SAGE implements a rigorous methodology by systematically formulating multiple explanations for each feature, designing targeted experiments to test them, and iteratively refining explanations based on empirical activation feedback. Experiments on features from SAEs of diverse language models demonstrate that SAGE produces explanations with significantly higher generative and predictive accuracy compared to state-of-the-art baselines.an agent-based framework that recasts feature interpretation from a passive, single-pass generation task into an active, explanationdriven process. SAGE implements a rigorous methodology by systematically formulating multiple explanations for each feature, designing targeted experiments to test them, and iteratively refining explanations based on empirical activation feedback. Experiments on features from SAEs of diverse language models demonstrate that SAGE produces explanations with significantly higher generative and predictive accuracy compared to state-of-the-art baselines.

Large language models (LLMs) have been widely deployed across numerous fields. Reinforcement Learning from Human Feedback (RLHF) leverages reward models (RMs) as proxies for human preferences to align LLM behaviors with human values, making the accuracy, reliability, and interpretability of RMs critical for effective alignment. However, traditional RMs lack interpretability, offer limited insight into the reasoning behind reward assignments, and are inflexible toward user preference shifts. While recent multidimensional RMs aim for improved interpretability, they often fail to provide feature-level attribution and require costly annotations. To overcome these limitations, we introduce the Sparse Autoencoder-enhanced Reward Model (SARM), a novel architecture that integrates a pretrained Sparse Autoencoder (SAE) into a reward model. SARM maps the hidden activations of LLM-based RM into an interpretable, sparse, and monosemantic feature space, from which a scalar head aggregates feature activations to produce transparent and conceptually meaningful reward scores. Empirical evaluations demonstrate that SARM facilitates direct feature-level attribution of reward assignments, allows dynamic adjustment to preference shifts, and achieves superior alignment performance compared to conventional reward models. Our code is available at https://github.com/schrieffer-z/sarm.