Related papers: Generalized Qualification and Qualification Levels…

We introduce the Morse parametric qualification condition for bilevel programming. Generic semi-algebraic functions are Morse parametric in a piecewise sense. Thus, bilevel programs with a Morse parametric lower level constitute a relevant…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

3D shape completion is important to enable machines to perceive the complete geometry of objects from partial observations. To address this problem, view-based methods have been presented. These methods represent shapes as multiple depth…

An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal…

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…

Continual Learning addresses the challenge of learning a number of different tasks sequentially. The goal of maintaining knowledge of earlier tasks without re-accessing them starkly conflicts with standard SGD training for artificial neural…

Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization…

Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…

Many recent datasets contain a variety of different data modalities, for instance, image, question, and answer data in visual question answering (VQA). When training deep net classifiers on those multi-modal datasets, the modalities get…

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…

During the past years there has been an explosion of interest in learning methods based on sparsity regularization. In this paper, we discuss a general class of such methods, in which the regularizer can be expressed as the composition of a…

Support vector classification (SVC) is a classical and well-performed learning method for classification problems. A regularization parameter, which significantly affects the classification performance, has to be chosen and this is usually…

When dealing with general Lipschitzian optimization problems, there are many problem classes where even weak constraint qualifications fail at local minimizers. In contrast to a constraint qualification, a problem qualification does not…

We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies both, introduces new challenges. This paper introduces new…

Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept…

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…