Related papers: Fano schemes of generic intersections and machine …

In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

Multiple data types naturally co-occur when describing real-world phenomena and learning from them is a long-standing goal in machine learning research. However, existing self-supervised generative models approximating an ELBO are not able…

Field localization boosts nonlinear optical processes at the hot spots of metal nanostructures. Fano resonances can further enhance these "local" processes taking place at the hot spots. However, in conventional nonlinear materials, the…

We investigate a new structure for machine learning classifiers applied to problems in high-energy physics by expanding the inputs to include not only measured features but also physics parameters. The physics parameters represent a…

Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional…

An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…

We show that the set of families of smooth well-formed Fano weighted complete intersections admits a natural partition with respect to the variance $\mathrm{var}(X) = \mathrm{coind}(X) - \mathrm{codim}(X)$. Moreover, we obtain the…

Fake face detection is a significant challenge for intelligent systems as generative models become more powerful every single day. As the quality of fake faces increases, the trained models become more and more inefficient to detect the…

Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…

Marginal MAP problems are notoriously difficult tasks for graphical models. We derive a general variational framework for solving marginal MAP problems, in which we apply analogues of the Bethe, tree-reweighted, and mean field…

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…

We study rational curves on general Fano hypersurfaces in projective space, mostly by degenerating the hypersurface along with its ambient projective space to reducible varieties. We prove results on existence of low-degree rational curves…

This paper studies the singularities of jet schemes of homogeneous hypersurfaces of general type. We obtain the condition of the degree and the dimension for the singularities of the jet schemes to be of dense $F$-regular type. This…

In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…

We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin's Conjecture for smooth Fano threefolds, including the classification of subvarieties with…

Ensuring validation for highly automated driving poses significant obstacles to the widespread adoption of highly automated vehicles. Scenario-based testing offers a potential solution by reducing the homologation effort required for these…

We study parallelisms on Veronese spaces associated with affine spaces, determine hyperplanes in Veronese spaces associated with projective spaces, and analyse the geometry of parallelisms determined by these hyperplanes.

In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…