Related papers: Generalised elastic nets

We propose a general framework for deriving generalization bounds for parallel positively homogeneous neural networks--a class of neural networks whose input-output map decomposes as the sum of positively homogeneous maps. Examples of such…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural…

Machine learning is evolving towards high-order models that necessitate pre-training on extensive datasets, a process associated with significant overheads. Traditional models, despite having pre-trained weights, are becoming obsolete due…

We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…

In Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…

Objectives: Functional connectivity triggered by naturalistic stimulus (e.g., movies) and machine learning techniques provide a great insight in exploring the brain functions such as fluid intelligence. However, functional connectivity are…

Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…

We introduce a general theoretical framework, designed for the study of gradient optimisation of deep neural networks, that encompasses ubiquitous architecture choices including batch normalisation, weight normalisation and skip…

The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients.…

Learning the dynamics of a physical system wherein an autonomous agent operates is an important task. Often these systems present apparent geometric structures. For instance, the trajectories of a robotic manipulator can be broken down into…

An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy. We characterize when a…

Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including…

Generative adversarial networks (GANs) have been shown to produce realistic samples from high-dimensional distributions, but training them is considered hard. A possible explanation for training instabilities is the inherent imbalance…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Neural networks are promising tools for high-throughput and accurate transmission electron microscopy (TEM) analysis of nanomaterials, but are known to generalize poorly on data that is "out-of-distribution" from their training data. Given…

Despite the popularity and success of deep learning, there is limited understanding of when, how, and why neural networks generalize to unseen examples. Since learning can be seen as extracting information from data, we formally study…

Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…