相关论文: Fano schemes of generic intersections and machine …

We show the existence of a hypersurface that contains a given closed subscheme of a projective space over a finite field and intersects a smooth quasi-projective scheme smoothly, under some condition on the dimension. This generalizes a…

We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…

The Fano effect or Fano resonance with a characteristically asymmetric line shape originates from quantum interference between direct and indirect transition pathways in continuum-bound coupled systems, and is a ubiquitous phenomenon in…

Under a hypothesis on $k$, $d$ and $n$ that is almost the best possible, we prove that for every smooth degree $d$ hypersurface in $P^n$, the $k$-plane sections dominate the moduli space of degree $d$ hypersurface in $P^k$. Using this we…

Counterfactual instances offer human-interpretable insight into the local behaviour of machine learning models. We propose a general framework to generate sparse, in-distribution counterfactual model explanations which match a desired…

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward…

Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…

Generative Adversarial Networks (GANs) can generate near photo realistic images in narrow domains such as human faces. Yet, modeling complex distributions of datasets such as ImageNet and COCO-Stuff remains challenging in unconditional…

We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…

We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

Auto-encoding generative adversarial networks (GANs) combine the standard GAN algorithm, which discriminates between real and model-generated data, with a reconstruction loss given by an auto-encoder. Such models aim to prevent mode…

The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic…

Schema Matching is a method of finding attributes that are either similar to each other linguistically or represent the same information. In this project, we take a hybrid approach at solving this problem by making use of both the provided…

Factorization machine (FM) is a prevalent approach to modeling pairwise (second-order) feature interactions when dealing with high-dimensional sparse data. However, on the one hand, FM fails to capture higher-order feature interactions…

In this paper we address Fano manifolds with positive higher Chern characters. They are expected to enjoy stronger versions of several of the nice properties of Fano manifolds. For instance, they should be covered by higher dimensional…