Linear Lobotomy For Alien Graph Representations : Probing, Ablation and Recovery of Linear Features in Graph Neural Networks

Which graph properties does a graph neural network (GNN) use, and are they the ones a domain expert would name? Instance-level explanations for GNNs are well developed, but tools that answer this model-level question are not. We call a graph-theoretic property that a model encodes and uses, although the literature on the task does not name it, an alien graph representation (AGR), and we make the notion testable by fixing an expert set S2 per task before looking at any result. We then propose linear lobotomy, a pipeline that tests the Linear Representation Hypothesis (LRH) at three levels: linear probing decides whether a property is encoded (Weak), concept erasure with matched random controls decides whether it is used (Strong), and converged retraining of the classifier head decides whether it is exclusively encoded along the erased direction (Exclusive). We compare three erasure operators (LEACE, iterative nullspace projection and a rank-one ablation) and show that the choice of operator, not the property, drives the size of an amnesic drop unless the share of the representation it deletes is reported. Across five datasets, a synthetic motif benchmark, two molecular and social benchmarks and two clinical fMRI connectivity tasks, AGR candidates are the rule at the Weak level, few survive the Strong level, and exclusivity tracks the architecture rather than the property: on the synthetic benchmark a GCN recovers fully from every erasure and a GIN never does. On MUTAG the model relies on branching and size counts rather than the ring counts a chemist would name; on the depression task six spectral, resistance and clique descriptors outside the clinical vocabulary are candidate used AGRs; on the social benchmark, the graph features align with the expert vocabulary.