Related papers: Designing Universal Causal Deep Learning Models: T…

This paper addresses the growing need to process non-Euclidean data, by introducing a geometric deep learning (GDL) framework for building universal feedforward-type models compatible with differentiable manifold geometries. We show that…

Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…

Geometric analyses of large language model (LLM) representations reveal structured variation across depth but remain fundamentally correlational with respect to token prediction formation. Meanwhile, causal interventions expose…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…

Protein engineering is experiencing a paradigmatic shift through the integration of geometric deep learning into computational design workflows. While traditional strategies, such as rational design and directed evolution, have enabled…

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…

This paper introduces a novel optimization framework that fundamentally integrates the Minimum Description Length (MDL) principle into the training dynamics of deep neural networks. Moving beyond its conventional role as a model selection…

The increased availability of data and computing resources has enabled researchers to successfully adopt machine learning (ML) techniques and make significant contributions in several engineering areas. ML and in particular deep learning…

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling…

Deep Learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in…

Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces $\mathcal{X}$ and $\mathcal{Y}$ using elementary functions between Euclidean…

Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve…