Disentangling Polysemantic Neurons with a Null-Calibrated Polysemanticity Index and Causal Patch Interventions

Abstract: Neural networks often contain polysemantic neurons that respond to multiple, sometimes unrelated, features, complicating mechanistic interpretability. We introduce the Polysemanticity Index (PSI), a null-calibrated metric that quantifies when a neuron's top activations decompose into semantically distinct clusters. PSI multiplies three independently calibrated components: geometric cluster quality (S), alignment to labeled categories (Q), and open-vocabulary semantic distinctness via CLIP (D). On a pretrained ResNet-50 evaluated with Tiny-ImageNet images, PSI identifies neurons whose activation sets split into coherent, nameable prototypes, and reveals strong depth trends: later layers exhibit substantially higher PSI than earlier layers. We validate our approach with robustness checks (varying hyperparameters, random seeds, and cross-encoder text heads), breadth analyses (comparing class-only vs. open-vocabulary concepts), and causal patch-swap interventions. In particular, aligned patch replacements increase target-neuron activation significantly more than non-aligned, random, shuffled-position, or ablate-elsewhere controls. PSI thus offers a principled and practical lever for discovering, quantifying, and studying polysemantic units in neural networks.