Related papers: Topological derivative approach for deep neural ne…

We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial…

Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

Neuroevolution is one of the methodologies that can be used for learning optimal architecture during training. It uses evolutionary algorithms to generate the topology of artificial neural networks and its parameters. The main benefits are…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

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…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric…

This paper develops a randomized approach for incrementally building deep neural networks, where a supervisory mechanism is proposed to constrain the random assignment of the weights and biases, and all the hidden layers have direct links…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits…

Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework…

This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…