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Oversmoothing has been claimed as a primary bottleneck for multi-layered graph neural networks (GNNs). Multiple analyses have examined how and why oversmoothing occurs. However, none of the prior work addressed how optimization is performed…

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…

We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…

We extend the results of our 2020 paper in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. There, we associated to each of an infinite family of triangle Fuchsian groups a one-parameter family of continued fraction…

We present a generative model that is defined on finite sets of exchangeable, potentially high dimensional, data. As the architecture is an extension of RealNVPs, it inherits all its favorable properties, such as being invertible and…

Approximations in computing model likelihoods with continuous normalizing flows (CNFs) hinder the use of these models for importance sampling of Boltzmann distributions, where exact likelihoods are required. In this work, we present Verlet…

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when…

We define a projective Fraiss\'e family whose limit approximates the universal Knaster continuum. The family is such that the group $\textrm{Aut}(\mathbb{K})$ of automorphisms of the Fraiss\'e limit is a dense subgroup of the group,…

Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the…

This thesis presents novel contributions in two primary areas: advancing the efficiency of generative models, particularly normalizing flows, and applying generative models to solve real-world computer vision challenges. The first part…

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared…

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix…

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…

We prove an exponential separation in sample complexity between Euclidean and hyperbolic representations for learning on hierarchical data under standard Lipschitz regularization. For depth-$R$ hierarchies with branching factor $m$, we…

We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equation and Brownian motion, there is a Feynman-Kac type…

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…

Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…