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Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Denoising Diffusion Probabilistic Models (DDPM) process images as a whole. Since adjacent pixels are highly likely to belong to the same object, we propose the Heat Diffusion Model (HDM) to further preserve image details and generate more…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

Despite the popularity of deep learning, structure learning for deep models remains a relatively under-explored area. In contrast, structure learning has been studied extensively for probabilistic graphical models (PGMs). In particular, an…

Dataset distillation compresses large training sets into compact synthetic datasets while preserving downstream performance. As modern systems increasingly operate on paired vision-language inputs, multimodal distillation must preserve…

The availability of affordable 3D full body reconstruction systems has given rise to free-viewpoint video (FVV) of human shapes. Most existing solutions produce temporally uncorrelated point clouds or meshes with unknown point/vertex…

Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…

Increasing data rate in wireless networks can be accomplished through a two-pronged approach, which are 1) increasing the network flow rate through parallel independent routes and 2) increasing the user's link rate through beamforming…

The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However,…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…

Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…

Machine learning deployments in real-world wireless communication tasks face significant generalization challenges due to location and environment-specific signal structure, high diversity in data across different deployments, and limited…

In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Most existing metric learning methods focus on learning a similarity or distance measure relying on similar and dissimilar relations between sample pairs. However, pairs of samples cannot be simply identified as similar or dissimilar in…

Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…

Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting…

A new geometrically exact micro-structured model is constructed using a generalisation of the notion of Riemann-Cartan manifolds and fibre bundle theory of rank 3. This model is based around the concept of two different length scales: a…