The standard sparse-autoencoder (SAE) interpretability protocol labels each feature from its top-activating contexts and validates by single-feature steering. We propose the pairwise matrix protocol, co-varying steering coefficient with joint condition, and report three findings the standard one-corner protocol misses on Qwen3-1.7B-Instruct, replicated on Gemma-2-2B-it. First, a feature labelled "AI self-disclaimer" from its top contexts produces an inverted U-shape under a coefficient sweep: at c=+500 the model substitutes a fluent contemplative-philosopher voice for the disclaimer. Two further features anchor the criterion (one monotonic, one pure breakdown). Second, three near-orthogonal cluster-specific features that individually steer a philosophy-of-mind register, jointly suppressed at c=-500, damage grounded composition on recipes and engine explanations as well as introspective prompts; single-feature suppression at the same magnitude leaves controls intact. Third, a matched-geometry comparison of single-feature, joint, and random-direction perturbations (norm ~1.55, cosine ~0.64) yields three distinct output regimes: single-feature substitutes strategy filler, random direction substitutes diverse content, joint suppression alone produces placeholder text. Coherence loss is direction-pattern-dependent, not magnitude-dependent. All three findings reproduce on Gemma with model-specific damage signatures; the matched-geometry control is CI-separated by ~10x. The pipeline also locates a top causally responsible feature in Llama-3.1-8B-Instruct.
Sparse autoencoder (SAE) features are used to interpret and steer large language models, yet whether a feature's causal role is stable across SAE families remains untested. Single-token features that activate on one vocabulary item provide the diagnostic case where ground truth permits direct comparison. We analyze 3.9M features across six models and three SAE families using zero-ablation at full layer depth. Single-token features cluster 4.7x tighter in decoder space and concentrate in early layers (Layer 0 in GPT2-Small; L0-L4 in Gemma). Ablating them yields Benjamini-Hochberg-significant logit reductions in 178 of 208 full-layer conditions, with depth controlling whether damage cascades downstream or shapes the output directly. Cross-family causal differences exceed within-family scale effects: on the same base model, GemmaScope and BatchTopK features remain causally anchored, while LlamaScope features are locally redundant. The target token's rank recovers to within 2x baseline 96-98% of the time after the same ablation, and a controlled activation-function comparison reverses sign within the same model, leaving training recipe as the residual candidate. Cross-family interpretability claims are therefore sensitive to training methodology, not just activation function or scale.
The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.
Phu Gia Hoang, Anwoy Chatterjee, Tanmoy Chakraborty +2
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.