Non-linear Interventions on Large Language Models

Abstract: Intervention is one of the most representative and widely used methods for understanding the internal representations of LLMs. However, existing intervention methods are confined to linear interventions grounded in the Linear Representation Hypothesis, leaving features encoded along non-linear manifolds beyond their reach. In this work, we introduce a general formulation of intervention that extends naturally to non-linearly represented features, together with a learning procedure that further enables intervention on implicit features lacking a direct output signature. We validate our framework on refusal bypass steering, where it steers the model more precisely than linear baselines by intervening on a non-linear feature governing refusal.