Related papers: Fano schemes of generic intersections and machine …

Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

This paper explores the Fano variety of lines in hypersurfaces, particularly focusing on those with mild singularities. Our first result explores the irreducibility of the variety $\Sigma$ of lines passing through a singular point $y$ on a…

Classical emulation of a ubiquitous quantum mechanical phenomenon of double-continuum Fano (DCF) interference using metasurfaces is experimentally realized by engineering the near-field interaction between two bright and one dark plasmonic…

Approach-level models were developed to accommodate the diversity of approaches within the same intersection. A random effect term, which indicates the intersection-specific effect, was incorporated into each crash type model to deal with…

Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several known et new results concerning the anti-canonically polar…

We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…

In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…

Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing…

We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…

In this paper, we study the algebraic hyperbolicity of very general surfaces in general Fano threefolds with Picard number one. We completely classify the algebraically hyperbolicity of those surfaces, except for surfaces in weighted…

We consider the problem to determine which blow-ups along subvarieties in products of two projective spaces are log Fano. By describing the nef cones of such blow-ups with special centers, we give a partial classification result. For each…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…

Fano varieties are 'atomic pieces' of algebraic varieties, the shapes that can be defined by polynomial equations. We describe the role of computation and database methods in the construction and classification of Fano varieties, with an…

Using ideas from the theory of tropical curves and degeneration, we prove that any Fano hypersurface (and more generally Fano complete intersections) is swept by at most quadratic rational curves.

Graph neural networks are increasingly becoming the framework of choice for graph-based machine learning. In this paper, we propose a new graph neural network architecture that substitutes classical message passing with an analysis of the…

We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension $n$ as a well formed complete intersection and it is not an intersection with a linear cone therein, then the…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Learning under distribution shifts is a challenging task. One principled approach is to exploit the invariance principle via the structural causal models. However, the invariance principle is violated when the response is intervened, making…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…