Related papers: On a new notion of regularizer

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…

In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…

Even though every mathematician knows intuitively what it means to "simplify" a mathematical expression, there is still no universally accepted rigorous mathematical definition of "simplify". In this paper, we shall give a simple and…

We define some notions of the decentralization of a deterministic input-output machine. This opens the possibility for introducing game-theoretic elements -- such as strategic players -- inside the machine, as part of its design.

In this paper, an attempt is made to systematically discuss the development of simulation systems for manufacturing system design. General requirements on manufacturing simulators are formulated and a framework to address the requirements…

The substitution of a system with another one may occur in several situations like system adaptation, system failure management, system resilience, system reconfiguration, etc. It consists in replacing a running system by another one when…

This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…

A rule to assign a physical meaning to Lagrange multipliers is discussed. Examples from mechanics, statistical mechanics and quantum mechanics are given.

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…

In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to…

Transformers have had a significant impact on natural language processing and have recently demonstrated their potential in computer vision. They have shown promising results over convolution neural networks in fundamental computer vision…

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use…

We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS…

Regularization is a well-established technique in machine learning (ML) to achieve an optimal bias-variance trade-off which in turn reduces model complexity and enhances explainability. To this end, some hyper-parameters must be tuned,…

Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…

While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…

The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…

This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…

We characterize normalization by evaluation as the composition of a self-interpreter with a self-reducer using a special representation scheme, in the sense of Mogensen (1992). We do so by deriving in a systematic way an untyped…