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Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…

We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…

Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…

The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical…

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures.…

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…

Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…

Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…

We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…

We use machine learning (ML) to infer stress and plastic flow rules using data from repre- sentative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response…

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds…

This paper approaches the unsupervised learning problem by gradient descent in the space of probability density functions. A main result shows that along the gradient flow induced by a distribution-dependent ordinary differential equation…

Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

The traffic assignment problem is essential for traffic flow analysis, traditionally solved using mathematical programs under the Equilibrium principle. These methods become computationally prohibitive for large-scale networks due to…

Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics education, solving these equations traditionally relies on iterative numerical methods…