Related papers: Certifying the Potential Energy Landscape
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte…
We perform and extend real-time numerical simulation of a low-dimensional scalar field theory or a quantum mechanical system using stochastic quantization. After a brief review of the quantization method and the complex Langevin dynamics,…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the…
The problem of recovering the parameters of a mixture of spike signals convolved with different PSFs is considered. Herein, the spike support is assumed to be known, while the PSFs lie on a manifold. A non-linear least squares estimator of…
This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the…
This work presents a new algorithm for empirical risk minimization. The algorithm bridges the gap between first- and second-order methods by computing a search direction that uses a second-order-type update in one subspace, coupled with a…
State-specific approximations can provide an accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of…
Q-learning is widely used algorithm in reinforcement learning community. Under the lookup table setting, its convergence is well established. However, its behavior is known to be unstable with the linear function approximation case. This…
Many complex cyber-physical systems can be modeled as heterogeneous components interacting with each other in real-time. We assume that the correctness of each component can be specified as a requirement satisfied by the output signals…
When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently…
Local certification consists in assigning labels (called \emph{certificates}) to the nodes of a network to certify a property of the network or the correctness of a data structure distributed on the network. The verification of this…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical…