Related papers: Universality Theorems for Generative Models
Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…
An open secret in contemporary machine learning is that many models work beautifully on standard benchmarks but fail to generalize outside the lab. This has been attributed to biased training data, which provide poor coverage over real…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
Time series data are everywhere -- from finance to healthcare -- and each domain brings its own unique complexities and structures. While advanced models like Transformers and graph neural networks (GNNs) have gained popularity in time…
In this paper, a universal approximation theorem (UAT) for shallow neural networks whose inputs belong to a topological vector space (TVS) and whose outputs take values in a Hausdorff locally convex TVS is established. The networks are…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen or trained set of parameters. However, a more practical…
Generative neural networks are able to mimic intricate probability distributions such as those of handwritten text, natural images, etc. Since their inception several models were proposed. The most successful of these were based on…
A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…
Feedforward neural networks have wide applicability in various disciplines of science due to their universal approximation property. Some authors have shown that single hidden layer feedforward neural networks (SLFNs) with fixed weights…
Despite recent advances, the remaining bottlenecks in deep generative models are necessity of extensive training and difficulties with generalization from small number of training examples. We develop a new generative model called…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…
One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal property. Though the past few decades have seen tremendous advances in theories of neural networks, a single…
Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and to identify principles with which to understand them. Within this discipline, one…
Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or…
We train deep generative models on datasets of reflexive polytopes. This enables us to compare how well the models have picked up on various global properties of generated samples. Our datasets are complete in the sense that every single…