Related papers: Dynamic Toolbox for ETRINV
This work presents a fully integrated tree-based combined exploration-planning algorithm: Exploration-RRT (ERRT). The algorithm is focused on providing real-time solutions for local exploration in a fully unknown and unstructured…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
In the previous work [2] (i.e., arXiv:2105.03385), we considered continuous solutions of an iterative equation involving the multiplication of iterates. In this paper, we continue to investigate this equation for differentiable solutions.…
Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…
A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…
Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
As a popular and easy-to-implement machine learning method for solving differential equations, the physics-informed neural network (PINN) sometimes may fail and find poor solutions which bias against the exact ones. In this paper, we…
The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific…
The debts' clearing problem is about clearing all the debts in a group of n entities (persons, companies etc.) using a minimal number of money transaction operations. The problem is known to be NP-hard in the strong sense. As for many…
AI-based Intelligent Tutoring Systems (ITS) have significant potential to transform teaching and learning. As efforts continue to design, develop, and integrate ITS into educational contexts, mixed results about their effectiveness have…
Machine learned models often must abide by certain requirements (e.g., fairness or legal). This has spurred interested in developing approaches that can provably verify whether a model satisfies certain properties. This paper introduces a…
The intensive integration of power converters is changing the way that power systems operate, leading to the emergence of new types of dynamic phenomena and instabilities. At the same time, converters act as an interface between traditional…
Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…