相关论文: Petz map and Python's lunch

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…

We consider a generic representation problem of internal coordinates (bond lengths, valence angles, and dihedral angles) and their transformation to 3-dimensional Cartesian coordinates of a biomolecule. We show that the…

This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…

Supercomputers getting ever larger and energy-efficient is at odds with the reliability of the used hardware. Thus, the time intervals between component failures are decreasing. Contrarily, the latencies for individual operations of…

The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to generalize well. While minimizers' flatness consistently…

In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit…

We present an application of hierarchical Bayesian estimation to robot map building. The revisiting problem occurs when a robot has to decide whether it is seeing a previously-built portion of a map, or is exploring new territory. This is a…

Jupyter Notebooks are an enormously popular tool for creating and narrating computational research projects. They also have enormous potential for creating reproducible scientific research artifacts. Capturing the complete state of a…

Modern microarchitectures are some of the world's most complex man-made systems. As a consequence, it is increasingly difficult to predict, explain, let alone optimize the performance of software running on such microarchitectures. As a…

A Lorenz map is a Poincar\'e map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a…

We introduce a formal statistical definition for the problem of backdoor detection in machine learning systems and use it to analyze the feasibility of such problems, providing evidence for the utility and applicability of our definition.…

We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around…

Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested…

We show the existence of open sets of bifurcations near Latt{\`e}s maps of sufficiently high degree. In particular, every Latt{\`e}s map has an iterate which is in the closure of the interior of the bifurcation locus. To show this, we…

Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…

In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…

Methods inspired by Artificial Intelligence (AI) are starting to fundamentally change computational science and engineering through breakthrough performances on challenging problems. However, reliability and trustworthiness of such…

Preceptron model updating with back propagation has become the routine of deep learning. Continuous feed forward procedure is required in order for backward propagate to function properly. Doubting the underlying physical interpretation on…

An approach that combines Self-Organizing maps, hierarchical clustering and network components is presented, aimed at comparing protein conformational ensembles obtained from multiple Molecular Dynamic simulations. As a first result the…

Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…