Where Decoder Cosine Similarity Fails for SAE Feature Flow Discovery
Authors: Hendrik Droste, Christian Medeiros Adriano, Kathrin Korte, Holger Giese
Abstract
Foundation models are increasingly adapted through fine-tuning, model editing, and alignment procedures while retaining previously acquired capabilities. Understanding the internal computations that support these adaptations is therefore becoming increasingly important for continual model evolution. Sparse autoencoders (SAEs) provide interpretable feature dictionaries for residual-stream activations and sublayer outputs, but it remains unclear how state features and update features interact to produce downstream residual features. In this work, we focus on MLP updates as a first test case. We construct a transition atlas of triples sk+uj→tℓ, where a residual-state feature and an MLP-update feature jointly predict a target residual feature, and validate candidate triples by ablating the decoded update feature. In a 20M-token Pythia-160M L7→L8 run, we find 38,125 strong ablation-effect transitions, but 88.0% have both state-target and update-target decoder cosine similarity below 0.7. As a preliminary cross-model check, a run of 20M-token Gemma-3-4B L21→L22 causally validates only the top 30,000 ranked candidate triples by ablating the decoded update feature, and 53.6% of strong-effect triples have both state-target and update-target decoder cosine similarity below 0.7. The Gemma result is directionally consistent with Pythia, but weaker, since update-target cosine recovers many of the strongest Gemma effects and the run is not a full-atlas causal validation. Ultimately, our results suggest that feature flow atlases can serve as diagnostics of representation-update mechanisms and thereby inform tools for steering model updates. Future work will validate more complex patterns across layers, models, and SAE families.
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 cosine similarity between a large language model's hidden activations before and after Supervised Fine-Tuning (SFT) remains very high. This, at first glance, suggests that SFT leaves the model's activation geometry largely undisturbed. However, projecting both sets of activations through a Sparse Autoencoder (SAE) pretrained on the base model reveals that the underlying sparse latents diverge significantly. We introduce a novel investigative pipeline which utilizes these pretrained SAEs as a high-resolution diagnostic tool to mechanistically investigate the drivers of this representational divergence. Through our analytical pipeline, we discover task-specific and layer-specific distributions of the precise semantic features that are systematically altered during supervised fine-tuning. We additionally identify a layer-wise update profile specific to safety alignment. All code, experimental scripts, and analysis files associated with this work are publicly available at: https://github.com/ruhzi/sae-investigation.
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