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Recurrent neural networks (RNNs) are a class of artificial neural network commonly used for sequential data processing. Unlike feedforward neural networks , which process data in a single pass, RNNs process data across multiple time steps, making them well-adapted for modelling and processing text, speech, and time series .
A Hopfield network (or associative memory) is a form of recurrent neural network, or a spin glass system, that can serve as a content-addressable memory.The Hopfield network, named for John Hopfield, consists of a single layer of neurons, where each neuron is connected to every other neuron except itself.
In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction–diffusion system inspired by Alan Turing’s model of morphogenesis.
The simplest kind of feedforward neural network (FNN) is a linear network, which consists of a single layer of output nodes with linear activation functions; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated at each node.
Hopfield networks [6] [7] are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron is defined by a time-dependent variable , which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how ...
Long short-term memory (LSTM) [1] is a type of recurrent neural network (RNN) aimed at mitigating the vanishing gradient problem [2] commonly encountered by traditional RNNs. Its relative insensitivity to gap length is its advantage over other RNNs, hidden Markov models , and other sequence learning methods.
In this layer, the network detects edges, textures, and patterns. The outputs from this layer are then fed into a fully-connected layer for further processing. See also: CNN model. The Pooling layer [5] is used to reduce the size of data input. The Recurrent layer is used for text processing with a memory function. Similar to the Convolutional ...
[15] constructed single hidden layer networks with bounded width that are still universal approximators for univariate functions. However, this does not apply for multivariable functions. [16] obtained precise quantitative information on the depth and width required to approximate a target function by deep and wide ReLU neural networks.