# The Local Interaction Basis: Identifying Computationally-Relevant and Sparsely Interacting Features in Neural Networks

arXiv: https://arxiv.org/abs/2405.10928 · HTML: https://mlsanity.com/paper/2405.10928/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 17 May 2024.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias](https://mlsanity.com/paper/2004.12265/) (2020)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks](https://mlsanity.com/paper/1602.03616/) (2016)
- [The Hessian Penalty: A Weak Prior for Unsupervised Disentanglement](https://mlsanity.com/paper/2008.10599/) (2020)
- [How far can we go without convolution: Improving fully-connected networks](https://mlsanity.com/paper/1511.02580/) (2015)
- [Explaining Neural Networks by Decoding Layer Activations](https://mlsanity.com/paper/2005.13630/) (2020)

## Built on by (most cited first, 8 of 8)

- [InterpBench: Semi-Synthetic Transformers for Evaluating Mechanistic Interpretability Techniques](https://mlsanity.com/paper/2407.14494/) (2024)
- [Transformers Don't Need LayerNorm at Inference Time: Scaling LayerNorm Removal to GPT-2 XL and the Implications for Mechanistic Interpretability](https://mlsanity.com/paper/2507.02559/) (2025)
- [Feature Identification via the Empirical NTK](https://mlsanity.com/paper/2510.00468/) (2025)
- [Mechanistically Eliciting Latent Behaviors in Language Models](https://mlsanity.com/paper/2606.29604/) (2026)
- [Weight-based Decomposition: A Case for Bilinear MLPs](https://mlsanity.com/paper/2406.03947/) (2024)
- [An Analysis of Residual-Stream Geometry Across Transformer Depth](https://mlsanity.com/paper/2607.18348/) (2026)
- [Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition](https://mlsanity.com/paper/2601.12879/) (2026)
- [RouterInterp: Understanding Superposed Specialisation in Mixture of Experts Routing](https://mlsanity.com/paper/2610.11775/) (2026)

## Abstract (arXiv)

Mechanistic interpretability aims to understand the behavior of neural networks by reverse-engineering their internal computations. However, current methods struggle to find clear interpretations of neural network activations because a decomposition of activations into computational features is missing. Individual neurons or model components do not cleanly correspond to distinct features or functions. We present a novel interpretability method that aims to overcome this limitation by transforming the activations of the network into a new basis - the Local Interaction Basis (LIB). LIB aims to identify computational features by removing irrelevant activations and interactions. Our method drops irrelevant activation directions and aligns the basis with the singular vectors of the Jacobian matrix between adjacent layers. It also scales features based on their importance for downstream computation, producing an interaction graph that shows all computationally-relevant features and interactions in a model. We evaluate the effectiveness of LIB on modular addition and CIFAR-10 models, finding that it identifies more computationally-relevant features that interact more sparsely, compared to principal component analysis. However, LIB does not yield substantial improvements in interpretability or interaction sparsity when applied to language models. We conclude that LIB is a promising theory-driven approach for analyzing neural networks, but in its current form is not applicable to large language models.