Related papers: On some global implicit function theorems for set-…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding…
The concept of the value-gradient is introduced and developed in the context of reinforcement learning. It is shown that by learning the value-gradients exploration or stochastic behaviour is no longer needed to find locally optimal…
Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that…
In this paper we present the notion of globally integrable quantum system that we introduced in [BL22]: we motivate it using the spectral theory of pseudodifferential operators and then we give some results on linear and nonlinear…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
Recently wide application in engineering-economic problems was received with problems of vector optimization. Development of methods of the decision of these problems it is executed in works A. Messac and others. Complexity of the offered…
An important factor in the practical implementation of optimization models is the acceptance by the intended users. This is influenced among other factors by the interpretability of the solution process. Decision rules that meet this…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
As increasingly popular metrics of worker and institutional quality, estimated value-added (VA) measures are now widely used as dependent or explanatory variables in regressions. For example, VA is used as an explanatory variable when…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
In the setting of real vector spaces, we establish a general set-valued Ekeland variational principle (briefly, denoted by EVP), where the objective function is a set-valued map taking values in a real vector space quasi-ordered by a convex…
This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…