An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form highly enmeshed clusters via spectral graph clustering. We thus train models to be more modular using a "clusterability loss" function that encourages the formation of non-interacting clusters. Using automated interpretability techniques, we show that our method can help train models that are more modular and learn different, disjoint, and smaller circuits. We investigate CNNs trained on MNIST and CIFAR, small transformers trained on modular addition, and language models. Our approach provides a promising direction for training neural networks that learn simpler functions and are easier to interpret.

An approach to improve network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We find pretrained models to be highly unclusterable and thus train models to be more modular using an ``enmeshment loss'' function that encourages the formation of non-interacting clusters. Using automated interpretability measures, we show that our method finds clusters that learn different, disjoint, and smaller circuits for CIFAR-10 labels. Our approach provides a promising direction for making neural networks easier to interpret.