Patterning: The Dual of Interpretability

TL;DR

This paper introduces patterning, a method to determine training data modifications needed to achieve specific internal model behaviors, demonstrated on language models and synthetic tasks.

Contribution

It presents a novel approach to invert the interpretability framework, allowing targeted data interventions to shape neural network internal structures.

Findings

Re-weighting data along susceptibility directions influences internal structure formation.

Patterning can select among multiple algorithms in a synthetic task.

The method effectively steers models toward desired internal configurations.

Abstract

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.