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

arXiv: https://arxiv.org/abs/2508.16950 · HTML: https://mlsanity.com/paper/2508.16950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks](https://mlsanity.com/paper/1602.03616/) (2016)
- [PURE: Turning Polysemantic Neurons Into Pure Features by Identifying Relevant Circuits](https://mlsanity.com/paper/2404.06453/) (2024)

## Built on by (most cited first, 1 of 1)

- [How Many Thoughts Can a Vector Hold? The Capacity of Reasoning by Superposition](https://mlsanity.com/paper/2609.13747/) (2026)

## Abstract (arXiv)

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.