Through a Steerable Lens: Magnifying Neural Network Interpretability via Phase-Based Extrapolation

Understanding the internal representations and decision mechanisms of deep neural networks remains a critical open challenge. While existing interpretability methods often identify influential input regions, they may not elucidate how a model distinguishes between classes or what specific changes would transition an input from one category to another. To address these limitations, we propose a novel framework that visualizes the implicit path between classes by treating the network gradient as a form of infinitesimal motion. Drawing inspiration from phase-based motion magnification, we first decompose images using invertible transforms-specifically the Complex Steerable Pyramid-then compute class-conditional gradients in the transformed space. Rather than iteratively integrating the gradient to trace a full path, we amplify the one-step gradient to the input and perform a linear extrapolation to expose how the model moves from source to target class. By operating in the steerable pyramid domain, these amplified gradients produce semantically meaningful, spatially coherent morphs that highlight the classifier's most sensitive directions, giving insight into the geometry of its decision boundaries. Experiments on both synthetic and real-world datasets demonstrate that our phase-focused extrapolation yields perceptually aligned, semantically meaningful transformations, offering a novel, interpretable lens into neural classifiers' internal representations.