# On Recovering Higher-order Interactions from Protein Language Models

arXiv: https://arxiv.org/abs/2405.06645 · HTML: https://mlsanity.com/paper/2405.06645/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Efficiently Computing Sparse Fourier Transforms of q-ary Functions](https://mlsanity.com/paper/2301.06200/) (2023)

## Built on by (most cited first, 10 of 10)

- [ProxySPEX: Inference-Efficient Interpretability via Sparse Feature Interactions in LLMs](https://mlsanity.com/paper/2505.17495/) (2025)
- [SPEX: Scaling Feature Interaction Explanations for LLMs](https://mlsanity.com/paper/2502.13870/) (2025)
- [SHAP zero Explains Biological Sequence Models with Near-zero Marginal Cost for Future Queries](https://mlsanity.com/paper/2410.19236/) (2024)
- [Sparse Autoencoders for Low-N Protein Function Prediction and Design](https://mlsanity.com/paper/2508.18567/) (2025)
- [Protein Circuit Tracing via Cross-layer Transcoders](https://mlsanity.com/paper/2602.12026/) (2026)
- [Beyond Tokens: Probing Higher-Order Epistasis in Learned Protein Representations](https://mlsanity.com/paper/2608.24953/) (2026)
- [Efficient Algorithm for Sparse Fourier Transform of Generalized q-ary Functions](https://mlsanity.com/paper/2501.12365/) (2025)
- [Circuit Tracing in Autoregressive Protein Language Models](https://mlsanity.com/paper/2606.16044/) (2026)
- [Learning Task-Specific Antibody Representations via Function-Aware Masking](https://mlsanity.com/paper/2609.00518/) (2026)
- [ORBIT-FMIB: Tracking Order-Resolved Epistatic Information Through ESM-2](https://mlsanity.com/paper/2610.00672/) (2026)

## Abstract (arXiv)

Protein language models leverage evolutionary information to perform state-of-the-art 3D structure and zero-shot variant prediction. Yet, extracting and explaining all the mutational interactions that govern model predictions remains difficult as it requires querying the entire amino acid space for n sites using 20n sequences, which is computationally expensive even for moderate values of n (e.g., n~10). Although approaches to lower the sample complexity exist, they often limit the interpretability of the model to just single and pairwise interactions. Recently, computationally scalable algorithms relying on the assumption of sparsity in the Fourier domain have emerged to learn interactions from experimental data. However, extracting interactions from language models poses unique challenges: it's unclear if sparsity is always present or if it is the only metric needed to assess the utility of Fourier algorithms. Herein, we develop a framework to do a systematic Fourier analysis of the protein language model ESM2 applied on three proteins-green fluorescent protein (GFP), tumor protein P53 (TP53), and G domain B1 (GB1)-across various sites for 228 experiments. We demonstrate that ESM2 is dominated by three regions in the sparsity-ruggedness plane, two of which are better suited for sparse Fourier transforms. Validations on two sample proteins demonstrate recovery of all interactions with R2=0.72 in the more sparse region and R2=0.66 in the more dense region, using only 7 million out of 2010~1013 ESM2 samples, reducing the computational time by a staggering factor of 15,000. All codes and data are available on our GitHub repository https://github.com/amirgroup-codes/InteractionRecovery.