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Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…
Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute…
Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden features. Their practical performance,…
The ability to model relational information using machine learning has driven advancements across various domains, from medicine to social science. While graph representation learning has become mainstream over the past decade, representing…
Learning the representation of data with hierarchical structures in the hyperbolic space attracts increasing attention in recent years. Due to the constant negative curvature, the hyperbolic space resembles tree metrics and captures the…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…
We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…
Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…
Statistical learning under distribution shift is challenging when neither prior knowledge nor fully accessible data from the target distribution is available. Distributionally robust learning (DRL) aims to control the worst-case statistical…
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as…
As machine learning models are deployed ever more broadly, it becomes increasingly important that they are not only able to perform well on their training distribution, but also yield accurate predictions when confronted with distribution…
Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…
The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…