Related papers: Local Propagation in Constraint-based Neural Netwo…

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

The backpropagation algorithm is often debated for its biological plausibility. However, various learning methods for neural architecture have been proposed in search of more biologically plausible learning. Most of them have tried to solve…

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood…

Constraint Programming (CP) and Local Search (LS) are different paradigms for dealing with combinatorial search and optimization problems. Their complementary features motivated researchers to create hybrid CP/LS solutions, maintaining both…

This paper presents a locally decoupled network parameter learning with local propagation. Three elements are taken into account: (i) sets of nonlinear transforms that describe the representations at all nodes, (ii) a local objective at…

Motivated by broad applications in various fields of engineering, we study a network resource allocation problem where the goal is to optimally allocate a fixed quantity of resources over a network of nodes. We consider large scale networks…

Graph Neural Networks (GNNs) have achieved remarkable performance on graph-based tasks. The key idea for GNNs is to obtain informative representation through aggregating information from local neighborhoods. However, it remains an open…

Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…

In the article we present a general theory of augmented Lagrangian functions for cone constrained optimization problems that allows one to study almost all known augmented Lagrangians for cone constrained programs within a unified…

Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the…

Conventional computer vision models rely on very deep, feedforward networks processing whole images and trained offline with extensive labeled data. In contrast, biological vision relies on comparatively shallow, recurrent networks that…

Predictive coding (PC) is a general theory of cortical function. The local, gradient-based learning rules found in one kind of PC model have recently been shown to closely approximate backpropagation. This finding suggests that this…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…

Temporal models based on recurrent neural networks have proven to be quite powerful in a wide variety of applications. However, training these models often relies on back-propagation through time, which entails unfolding the network over…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…