相关论文: Petz map and Python's lunch

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and…

The primary challenge for any autonomous system operating in realistic, rather unconstrained scenarios is to manage the complexity and uncertainty of the real world. While it is unclear how exactly humans and other higher animals master…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

This paper came to existence out of the desire to understand iterations of strictly triangular polynomial maps over finite fields. This resulted in two connected results: First, we give a generalization of $\F_p$-actions on $\F_p^n$ and…

Programming Language Processing (PLP) using machine learning has made vast improvements in the past few years. Increasingly more people are interested in exploring this promising field. However, it is challenging for new researchers and…

Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite…

In a recent paper of Yuan and Zhu (J. Differential Equations 321(2022) 99-129), the nature of dynamics of a generalist predator and prey with stage structure is modeled as a three-dimensional coupled nonlinear differential system. A…

Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are…

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…

The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…

Large language models (LLMs) demonstrate extraordinary abilities in a wide range of natural language processing (NLP) tasks. In this paper, we show that, beyond text understanding capability, LLMs are capable of processing text layouts that…

Pretraining on large, semantically rich datasets is key for developing language models. Surprisingly, recent studies have shown that even synthetic data, generated procedurally through simple semantic-free algorithms, can yield some of the…

We show how the necessary and sufficient conditions for the NFL to apply can be reduced to the single requirement of the set of objective functions under consideration being closed under permutation, and quantify the extent to which a set…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

When does a robot planner need a map? Reactive methods that use only the robot's current sensor data and local information are fast and flexible, but prone to getting stuck in local minima. Is there a middle-ground between fully reactive…

We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse…