Related papers: Density of compressible types and some consequence…

Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue…

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…

The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra B to each formula. We show some basic results regarding the effect of the properties of B on the behavior of…

Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…

We introduce "representative generation," extending the theoretical framework for generation proposed by Kleinberg et al. (2024) and formalized by Li et al. (2024), to additionally address diversity and bias concerns in generative models.…

In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework…

We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and…

Generative networks implicitly approximate complex densities from their sampling with impressive accuracy. However, because of the enormous scale of modern datasets, this training process is often computationally expensive. We cast…

With time, machine learning models have increased in their scope, functionality and size. Consequently, the increased functionality and size of such models requires high-end hardware to both train and provide inference after the fact. This…

Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…

We prove a definable version of Matou\v{s}ek's $(p,q)$-theorem in NIP theories. This answers a question of Chernikov and Simon. We also prove a uniform version. The proof builds on a proof of Boxall and Kestner who proved this theorem in…

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…

Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are…

We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…

Diffusion models have become a powerful family of deep generative models, with record-breaking performance in many applications. This paper first gives an overview and derivation of the basic theory of diffusion models, then reviews the…

We leverage probabilistic models of neural representations to investigate how residual networks fit classes. To this end, we estimate class-conditional density models for representations learned by deep ResNets. We then use these models to…

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…