Related papers: Erzeugunsgrad, VC-Dimension and Neural Networks wi…

Continuous-variable (CV) quantum computing has shown great potential for building neural network models. These neural networks can have different levels of quantum-classical hybridization depending on the complexity of the problem. Previous…

This paper introduces a promising alternative method for training Generative Adversarial Networks (GANs) on large-scale datasets with clear theoretical guarantees. GANs are typically learned through a minimax game between a generator and a…

Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…

The architecture and the parameters of neural networks are often optimized independently, which requires costly retraining of the parameters whenever the architecture is modified. In this work we instead focus on growing the architecture…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

It is argued that several papers where SU(3) Clebsch-Gordan coefficients were calculated in order to describe properties of hadronic systems are, up to a phase convention, particular cases of analytic formulae derived by Hecht in 1965 in…

Numerous theories of learning propose to prevent the gradient from exponential growth with depth or time, to stabilize and improve training. Typically, these analyses are conducted on feed-forward fully-connected neural networks or simple…

The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…

We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving…

We propose a neuropsychological approach to the explainability of artificial neural networks, which involves using concepts from human cognitive psychology as relevant heuristic references for developing synthetic explanatory frameworks…

Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…

Measuring the quality of a generated sequence against a set of references is a central problem in many learning frameworks, be it to compute a score, to assign a reward, or to perform discrimination. Despite great advances in model…

We generalize the notion of Erd\H{o}s-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtain various lower and upper bounds. These bounds are…

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…

The VC-dimension, introduced by Vapnik and Chervonenkis in 1968 in the context of learning theory, has in recent years provided a rich source of problems in combinatorial geometry. Given $E\subseteq \mathbb{F}_q^d$ or $E\subseteq…

We propose a principle for exploring context in machine learning models. Starting with a simple assumption that each observation may or may not depend on its context, a conditional probability distribution is decomposed into two parts:…

Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While Large Language Models (LLMs) offer inferential…

Given a domain $X$ and a collection $\mathcal{H}$ of functions $h:X\to \{0,1\}$, the Vapnik-Chervonenkis (VC) dimension of $\mathcal{H}$ measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical…

A brain can detect outlier just by using only normal samples. Similarly, one-class classification (OCC) also uses only normal samples to train the model and trained model can be used for outlier detection. In this paper, a multi-layer…

To characterize the function space explored by neural networks (NNs) is an important aspect of learning theory. In this work, noticing that a multi-layer NN generates implicitly a hierarchy of reproducing kernel Hilbert spaces (RKHSs) -…