Related papers: QuasiNet: a neural network with trainable product …

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…

As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

In recent years, machine learning techniques based on neural networks for mobile computing become increasingly popular. Classical multi-layer neural networks require matrix multiplications at each stage. Multiplication operation is not an…

Physics-informed neural networks (PINNs) have emerged as promising methods for solving partial differential equations (PDEs) by embedding physical laws within neural architectures. However, these classical approaches often require a large…

We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based…

Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…

While quantum architectures are still under development, when available, they will only be able to process quantum data when machine learning algorithms can only process numerical data. Therefore, in the issues of classification or…

Despite the recent successes of deep neural networks, the corresponding training problem remains highly non-convex and difficult to optimize. Classes of models have been proposed that introduce greater structure to the objective function at…

The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

Deep learning is a subset of a broader family of machine learning methods based on learning data representations. These models are inspired by human biological nervous systems, even if there are various differences pertaining to the…

Although deep learning has shown its powerful performance in many applications, the mathematical principles behind neural networks are still mysterious. In this paper, we consider the problem of learning a one-hidden-layer neural network…

Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane.…

Model compression, such as pruning and quantization, has been widely applied to optimize neural networks on resource-limited classical devices. Recently, there are growing interest in variational quantum circuits (VQC), that is, a type of…

The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization,…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains…

Humans learn continually throughout their lifespan by accumulating diverse knowledge and fine-tuning it for future tasks. When presented with a similar goal, neural networks suffer from catastrophic forgetting if data distributions across…

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…