Patterning: The Dual of Interpretability

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization, determine what training data produces it. Our approach is based on susceptibilities, which measure how posterior expectation values of observables respond to infinitesimal shifts in the data distribution. Inverting this linear response relationship yields the data intervention that steers the model toward a target internal configuration. We demonstrate patterning in a small language model, showing that re-weighting training data along principal susceptibility directions can accelerate or delay the formation of structure, such as the induction circuit. In a synthetic parentheses balancing task where multiple algorithms achieve perfect training accuracy, we show that patterning can select which algorithm the model learns by targeting the local learning coefficient of each solution. These results establish that the same mathematical framework used to read internal structure can be inverted to write it.

Interpretability aims to understand how and what neural networks learn from their training data, and does so analogously to human neuroscience, by studying behaviors and reverse-engineering internal structure. We introduce patterning, which inverts this process. That is, given some desired behavior or structure, what would have to be in the training data for the neural network to learn it? We answer this question by studying the responses of a neural network to small perturbations, and test our interventions in two small networks.