Related papers: A feed-forward neural network as a nonlinear dynam…
In this work, we solve inverse problems of nonlinear Schr\"{o}dinger equations that can be formulated as a learning process of a special convolutional neural network. Instead of attempting to approximate functions in the inverse problems,…
We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input…
Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can…
We show that the forward and backward propagation can be formulated as a solution of lower and upper triangular systems of equations. For standard feedforward (FNNs) and recurrent neural networks (RNNs) the triangular systems are always…
We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…
Gatys et al. recently demonstrated that deep networks can generate beautiful textures and stylized images from a single texture example. However, their methods requires a slow and memory-consuming optimization process. We propose here an…
Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions…
Graph based semi-supervised learning (GSSL) has intuitive representation and can be improved by exploiting the matrix calculation. However, it has to perform iterative optimization to achieve a preset objective, which usually leads to low…
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical…
Binary Neural Networks (BNNs) have garnered significant attention due to their immense potential for deployment on edge devices. However, the non-differentiability of the quantization function poses a challenge for the optimization of BNNs,…
Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…
The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…
The increasing complexity of neural networks and the energy consumption associated with training and inference create a need for alternative neuromorphic approaches, e.g. using optics. Current proposals and implementations rely on physical…
Sparse random networks contain structures that can be considered as diluted feed-forward networks. Modeling of cortical circuits has shown that feed-forward structures, if strongly pronounced compared to the embedding random network, enable…
Fast feedforward networks (FFFs) are a class of neural networks that exploit the observation that different regions of the input space activate distinct subsets of neurons in wide networks. FFFs partition the input space into separate…
Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL…
This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…
There has been an increasing interest in learning dynamics simulators for model-based control. Compared with off-the-shelf physics engines, a learnable simulator can quickly adapt to unseen objects, scenes, and tasks. However, existing…
In this work, we perform a detailed review about the theoretical modeling of the optical propagation of ultra-short pulses in different scenarios of nonlinear optics. In particular, we focus our efforts on optical fibers and uniform media,…
Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep…