# Making Sense Of Distributed Representations With Activation Spectroscopy

arXiv: https://arxiv.org/abs/2501.15435 · HTML: https://mlsanity.com/paper/2501.15435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 26 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)

## Abstract (arXiv)

In the study of neural network interpretability, there is growing evidence to suggest that relevant features are encoded across many neurons in a distributed fashion. Making sense of these distributed representations without knowledge of the network's encoding strategy is a combinatorial task that is not guaranteed to be tractable. This work explores one feasible path to both detecting and tracing the joint influence of neurons in a distributed representation. We term this approach Activation Spectroscopy (ActSpec), owing to its analysis of the pseudo-Boolean Fourier spectrum defined over the activation patterns of a network layer. The sub-network defined between a given layer and an output logit is cast as a special class of pseudo-Boolean function. The contributions of each subset of neurons in the specified layer can be quantified through the function's Fourier coefficients. We propose a combinatorial optimization procedure to search for Fourier coefficients that are simultaneously high-valued, and non-redundant. This procedure can be viewed as an extension of the Goldreich-Levin algorithm which incorporates additional problem-specific constraints. The resulting coefficients specify a collection of subsets, which are used to test the degree to which a representation is distributed. We verify our approach in a number of synthetic settings and compare against existing interpretability benchmarks. We conclude with a number of experimental evaluations on an MNIST classifier, and a transformer-based network for sentiment analysis.