Related papers: The Interconnection Tensor Rank and the Neural Net…

The classical perceptron is a simple neural network that performs a binary classification by a linear mapping between static inputs and outputs and application of a threshold. For small inputs, neural networks in a stationary state also…

An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is…

Weight-sharing plays a significant role in the success of many deep neural networks, by increasing memory efficiency and incorporating useful inductive priors about the problem into the network. But understanding how weight-sharing can be…

We have calculated the key characteristics of associative (content-addressable) spatial-temporal memories based on neuromorphic networks with restricted connectivity - "CrossNets". Such networks may be naturally implemented in…

The storage capacity of a binary classification model is the maximum number of random input-output pairs per parameter that the model can learn. It is one of the indicators of the expressive power of machine learning models and is important…

The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper…

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

In recent studies [1][13][12] Recurrent Neural Networks were used for generative processes and their surprising performance can be explained by their ability to create good predictions. In addition, data compression is also based on…

It is widely appreciated that well-balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, such balance could be achieved by many possible configurations of excitatory and inhibitory…

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use…

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

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…

This study clarifies the proper criteria to assess the modeling capacity of a general tensor model. The work analyze the problem based on the study of tensor ranks, which is not a well-defined quantity for higher order tensors. To process,…

Reservoir computing is a promising neuromorphic paradigm, and its quantum implementation using spin networks has shown some advantage when entanglement is present. Here, we consider a distributed scenario in which two distinct input time…

The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…

The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…

Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…

Neural architecture search has recently attracted lots of research efforts as it promises to automate the manual design of neural networks. However, it requires a large amount of computing resources and in order to alleviate this, a…