Related papers: Capacity of the covariance perceptron
Neural network training is typically viewed as gradient descent on a loss surface. We propose a fundamentally different perspective: learning is a structure-preserving transformation (a functor L) between the space of network parameters…
Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its…
Combinatorial generalization - the ability to understand and produce novel combinations of already familiar elements - is considered to be a core capacity of the human mind and a major challenge to neural network models. A significant body…
Feed-forward convolutional neural networks (CNNs) are currently state-of-the-art for object classification tasks such as ImageNet. Further, they are quantitatively accurate models of temporally-averaged responses of neurons in the primate…
A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum…
We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…
Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…
Neural networks can be compressed to reduce memory and computational requirements, or to increase accuracy by facilitating the use of a larger base architecture. In this paper we focus on pruning individual neurons, which can simultaneously…
Recent learning-to-plan methods have shown promising results on planning directly from observation space. Yet, their ability to plan for long-horizon tasks is limited by the accuracy of the prediction model. On the other hand, classical…
Neural networks have shown to be a practical way of building a very complex mapping between a pre-specified input space and output space. For example, a convolutional neural network (CNN) mapping an image into one of a thousand object…
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…
The capacity of a classical-quantum channel (or in other words the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a…
Capsule networks are a recently developed class of neural networks that potentially address some of the deficiencies with traditional convolutional neural networks. By replacing the standard scalar activations with vectors, and by…
We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained…
An effective neural network algorithm of the perceptron type is proposed. The algorithm allows us to identify strongly distorted input vector reliably. It is shown that its reliability and processing speed are orders of magnitude higher…
Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix.…
Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…