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arXiv · 2504.00194

Identifying Sparsely Active Circuits Through Local Loss Landscape Decomposition

Brianna Chrisman·Lucius Bushnaq·Lee Sharkey
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Abstract

Much of mechanistic interpretability has focused on understanding the activation spaces of large neural networks. However, activation space-based approaches reveal little about the underlying circuitry used to compute features. To better understand the circuits employed by models, we introduce a new decomposition method called Local Loss Landscape Decomposition (L3D). L3D identifies a set of low-rank subnetworks: directions in parameter space of which a subset can reconstruct the gradient of the loss between any sample's output and a reference output vector. We design a series of progressively more challenging toy models with well-defined subnetworks and show that L3D can nearly perfectly recover the associated subnetworks. Additionally, we investigate the extent to which perturbing the model in the direction of a given subnetwork affects only the relevant subset of samples. Finally, we apply L3D to a real-world transformer model and a convolutional neural network, demonstrating its potential to identify interpretable and relevant circuits in parameter space.

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Brianna Chrisman, Lucius Bushnaq, Lee Sharkey. 2025-03-31. Identifying Sparsely Active Circuits Through Local Loss Landscape Decomposition. https://arxiv.org/abs/2504.00194

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