Related papers: Diffusion-Guided Renormalization of Neural Systems…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

Recent advances in Graph Neural Networks (GNNs) have revolutionized graph-structured data modeling, yet traditional GNNs struggle with complex heterogeneous structures prevalent in real-world scenarios. Despite progress in handling…

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

Structural node embeddings, vectors capturing local connectivity information for each node in a graph, have many applications in data mining and machine learning, e.g., network alignment and node classification, clustering and anomaly…

We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…

Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward…

Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network's output distribution to move closer to the symbolic…

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…

We propose a cross-order Laplacian renormalization group (X-LRG) scheme for arbitrary higher-order networks. The renormalization group is a pillar of the theory of scaling, scale-invariance, and universality in physics. An RG scheme based…

At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…

Imaging through diffusive media is a challenging problem, where the existing solutions heavily rely on digital computers to reconstruct distorted images. We provide a detailed analysis of a computer-free, all-optical imaging method for…

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…

Image denoising is a fundamental and challenging task in the field of computer vision. Most supervised denoising methods learn to reconstruct clean images from noisy inputs, which have intrinsic spectral bias and tend to produce…

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…

We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…

Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…

Deep neural networks can obtain impressive performance on various tasks under the assumption that their training domain is identical to their target domain. Performance can drop dramatically when this assumption does not hold. One…