An effective few-shot learning approach via location-dependent partial differential equation

Abstract

Recently, learning-based partial differential equation (L-PDE) has achieved success in few-shot learning area, while its feature weighting mechanism and recognition stability require further improvement. To address these issues, we propose a novel model called “location-dependent PDE” (LD-PDE) based on Navier–Stokes equation and rotational invariants in this paper. To our best knowledge, LD-PDE is the first application of the Navier–Stokes equation to achieve image recognition as a high-level vision task. Specifically, we formulate the feature variation with respect to each time step as a linear combination of rotational invariants in LD-PDE. Meanwhile, we design location-dependent mechanism to adaptively weight each invariant in an attention-based approach, which provides hierarchical discrimination in the spatial domain. Once the ultimate feature is learned, we measure the model error with the cross-entropy loss and update the parameters by the coordinate descent algorithm. As a verification, experimental results on face recognition datasets show that LD-PDE method outperforms the state-of-the-art approaches with few training samples. Moreover, compared to L-PDE, LD-PDE achieves a much more stable recognition with low sensitivity to its hyper-parameters.