Robust Network Learning via Inverse Scale Variational Sparsification

While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on enhancing robustness against specific noise types, limiting their adaptability to others. Previous studies have addressed general robustness by adopting a spectral perspective, which tends to blur crucial features like texture and object contours. Our proposed solution, however, introduces an inverse scale variational sparsification framework within a time-continuous inverse scale space formulation. This framework progressively learns finer-scale features by discerning variational differences between pixels, ultimately preserving only large-scale features in the smoothed image. Unlike frequency-based methods, our approach not only removes noise by smoothing small-scale features where corruptions often occur but also retains high-contrast details such as textures and object contours. Moreover, our framework offers simplicity and efficiency in implementation. By integrating this algorithm into neural network training, we guide the model to prioritize learning large-scale features. We show the efficacy of our approach through enhanced robustness against various noise types.

Incremental Gauss--Newton Methods with Superlinear Convergence Rates

This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms existing methods that only achieve linear convergence rate. In particular, we formulate our problem by the nonlinear least squares with finite-sum structure, and our method incrementally iterates with the information of one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods.