From Token Lists to Graph Motifs: Weisfeiler-Lehman Analysis of Sparse Autoencoder Features
Authors: Ruben Fernandez-Boullon, Pablo Magariños-Docampo, Javier Perez-Robles
Organizations: University of Vigo
Abstract
Sparse autoencoders (SAEs) have become central to mechanistic interpretability, decomposing transformer activations into monosemantic features. Yet existing analyses characterise features almost exclusively through top-activating token lists or decoder weight vectors, leaving the higher-order co-occurrence structure shared across features largely unexamined. We introduce a graph-structured representation in which each SAE feature is modelled as a token co-occurrence graph: nodes are the tokens most frequent near strong activations, and edges connect pairs that co-occur within local context windows. A custom WL-style, frequency-binned graph kernel then provides a similarity measure over this structural space. Applied as a proof of concept to features from a large SAE trained on GPT-2 Small and probed with a synthetic mixed-domain corpus, our clustering recovers heuristic motif families (punctuation-heavy patterns, language and script clusters, and code-like templates) that are not recovered by clustering on decoder cosine similarity. A token-histogram baseline achieves higher overall purity, so the contribution of the graph view is complementary rather than dominant: it surfaces structural relationships that token-frequency and decoder-weight views alone do not capture. Cluster assignments are stable across graph-construction hyperparameters and random seeds.
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.
Sparse autoencoders (SAEs) extract millions of interpretable features from a language model, but flat feature inventories aren't very useful on their own. Domain concepts get mixed with generic and weakly grounded features, while related ideas are scattered across many units, and there's no way to understand relationships between features. We address this by first constructing a strict domain-specific concept universe from a large SAE inventory using contrastive activations and a multi-stage filtering process. Next, we build two aligned graph views on the filtered set: a co-occurrence graph for corpus-level conceptual structure, organized at multiple levels of granularity, and a transcoder-based mechanism graph that links source-layer and target-layer features through sparse latent pathways. Automated edge labeling then turns these graph views into readable knowledge graphs rather than unlabeled layouts. In a case study on a biology textbook, these graphs recover coherent chapter and subchapter-level structure, reveal concepts that bridge neighboring topics, and transform messy sentence-level activity containing thousands of features into compact, readable views that illustrate the model's local activity. Taken together, this reframes a flat SAE inventory as an internal knowledge graph that converts feature-level interpretability into a global map of model knowledge and enables audits of reasoning faithfulness.
Sparse autoencoders (SAEs) have become a central tool for interpreting language models. However, two key SAE analyses that remain difficult to scale are (1) matching semantically similar features across multi-layers and (2) compressing large feature circuits into interpretable supernodes. Although these have been treated as separate problems, we show that both are instances of a more fundamental challenge, which we frame as the estimation of semantic distances between SAE features that lie on different activation manifolds. We introduce a distributional framework for this problem, in which each feature is represented not by a single decoder vector like in the literature, but by an activation-weighted distribution over the hidden states that express it. By projecting these distributions into a shared reference space and comparing them with Wasserstein distance, our method provides a unified semantic metric for cross-layer feature comparison. We prove that our representation is invariant to activation rescaling, stable under perturbations, and recovers true matches under finite-sample margin conditions. Empirically, our method outperforms decoder-vector and LLM-based baselines and captures subtle functional distinctions between related features. Notably, our method compresses large feature circuits into interpretable supernodes automatically.