Related papers: Orthogonal Weight Normalization: Solution to Optim…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear elliptic partial differential equations. The proposed scheme…
The Orthogonal-Time-Frequency-Space (OTFS) signaling is known to be resilient to doubly-dispersive channels, which impacts high mobility scenarios. On the other hand, the Orthogonal-Frequency-Division-Multiplexing (OFDM) waveforms enjoy the…
This paper introduces a novel neural network for efficiently solving Structured Inverse Eigenvalue Problems (SIEPs). The main contributions lie in two aspects: firstly, a unified framework is proposed that can handle various SIEPs…
Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…
The ability of intelligent agents to learn and remember multiple tasks sequentially is crucial to achieving artificial general intelligence. Many continual learning (CL) methods have been proposed to overcome catastrophic forgetting which…
A parameterized orthogonality-constrained neural network is proposed for the first time to solve the parameterized generalized inverse eigenvalue problem (PGIEP) on product manifolds, offering a new perspective to address PGIEP. The key…
Deep Neural Networks (DNNs) have achieved extraordinary performance in various application domains. To support diverse DNN models, efficient implementations of DNN inference on edge-computing platforms, e.g., ASICs, FPGAs, and embedded…
We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…
Loss of plasticity, trainability loss, and primacy bias have been identified as issues arising when training deep neural networks on sequences of tasks -- all referring to the increased difficulty in training on new tasks. We propose to use…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However,…
Permutation symmetries of deep networks make basic operations like model merging and similarity estimation challenging. In many cases, aligning the weights of the networks, i.e., finding optimal permutations between their weights, is…
Deep neural networks (DNNs) have been increasingly explored for receiver design because they can handle complex environments without relying on explicit channel models. Nevertheless, because communication channels change rapidly, their…
Deep neural networks are a promising approach towards multi-task learning because of their capability to leverage knowledge across domains and learn general purpose representations. Nevertheless, they can fail to live up to these promises…
This work addresses weight optimization problem for fully-connected feed-forward neural networks. Unlike existing approaches that are based on back-propagation (BP) and chain rule gradient-based optimization (which implies iterative…
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…
In this work, we present some applications of random matrix theory for the training of deep neural networks. Recently, random matrix theory (RMT) has been applied to the overfitting problem in deep learning. Specifically, it has been shown…
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…
A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…