Learning Fourier shapes to probe the geometric world of deep neural networks
This work addresses the under-explored area of geometric perception in DNNs, offering a versatile framework for interpretability and adversarial challenges in machine perception.
The paper tackled the problem of probing the geometric understanding of deep neural networks (DNNs) by developing a framework to generate optimized shapes that act as semantic carriers, interpretability tools, and adversarial examples, achieving high-confidence classifications and precise isolation of salient regions.
While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized shapes can act as potent semantic carriers, generating high-confidence classifications from inputs defined purely by their geometry; second, that they are high-fidelity interpretability tools that precisely isolate a model's salient regions; and third, that they constitute a new, generalizable adversarial paradigm capable of deceiving downstream visual tasks. This is achieved through an end-to-end differentiable framework that unifies a powerful Fourier series to parameterize arbitrary shapes, a winding number-based mapping to translate them into the pixel grid required by DNNs, and signal energy constraints that enhance optimization efficiency while ensuring physically plausible shapes. Our work provides a versatile framework for probing the geometric world of DNNs and opens new frontiers for challenging and understanding machine perception.