Related papers: Cauchy-Schwarz Regularizers
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…
We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…
Neural implicit fields have recently emerged as a useful representation for 3D shapes. These fields are commonly represented as neural networks which map latent descriptors and 3D coordinates to implicit function values. The latent…
In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. It is challenging in this setting to train expressive, non-linear…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and…
Deep Reinforcement Learning (Deep RL) has been receiving increasingly more attention thanks to its encouraging performance on a variety of control tasks. Yet, conventional regularization techniques in training neural networks (e.g., $L_2$…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…
Continual learning algorithms which keep the parameters of new tasks close to that of previous tasks, are popular in preventing catastrophic forgetting in sequential task learning settings. However, 1) the performance for the new continual…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau…
The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…