# AI News, Difference between revisions of "Artificial Neural Networks/Recurrent Networks"

- On Thursday, October 4, 2018
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## Difference between revisions of "Artificial Neural Networks/Recurrent Networks"

In a recurrent network, the weight matrix for each layer l contains input weights from all other neurons in the network, not just neurons from the previous layer.

Recurrent networks, in contrast to feed-forward networks, do have feedback elements that enable signals from one layer to be fed back to a previous layer.

A set of additional context units are added to the input layer that receive input from the hidden layer neurons.

- On Wednesday, October 10, 2018
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## Artificial Neural Networks/Recurrent Networks

In a recurrent network, the weight matrix for each layer l contains input weights from all other neurons in the network, not just neurons from the previous layer.

Recurrent networks, in contrast to feed-forward networks, do have feedback elements that enable signals from one layer to be fed back to a previous layer.

context layer feeds the hidden layer at iteration N with a value computed from the output of the hidden layer at iteration N-1, providing a short memory effect.

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## Recurrent neural network

A recurrent neural network (RNN) is a class of artificial neural network where connections between nodes form a directed graph along a sequence.

The term 'recurrent neural network' is used indiscriminately to refer to two broad classes of networks with a similar general structure, where one is finite impulse and the other is infinite impulse.

A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.

Both finite impulse and infinite impulse recurrent networks can have additional stored state, and the storage can be under direct control by the neural network.

Such controlled states are referred to as gated state or gated memory, and are part of long short-term memorys (LSTMs) and gated recurrent units.

In 1993, a neural history compressor system solved a 'Very Deep Learning' task that required more than 1000 subsequent layers in an RNN unfolded in time.[5]

In 2014, the Chinese search giant Baidu used CTC-trained RNNs to break the Switchboard Hub5'00 speech recognition benchmark without using any traditional speech processing methods.[10]

Basic RNNs are a network of neuron-like nodes organized into successive 'layers', each node in a given layer is connected with a directed (one-way) connection to every other node in the next successive layer.[citation needed]

Nodes are either input nodes (receiving data from outside the network), output nodes (yielding results), or hidden nodes (that modify the data en route from input to output).

For supervised learning in discrete time settings, sequences of real-valued input vectors arrive at the input nodes, one vector at a time.

At any given time step, each non-input unit computes its current activation (result) as a nonlinear function of the weighted sum of the activations of all units that connect to it.

For example, if the input sequence is a speech signal corresponding to a spoken digit, the final target output at the end of the sequence may be a label classifying the digit.

Instead a fitness function or reward function is occasionally used to evaluate the RNN's performance, which influences its input stream through output units connected to actuators that affect the environment.

An Elman network is a three-layer network (arranged horizontally as x, y, and z in the illustration) with the addition of a set of 'context units' (u in the illustration).

The fixed back-connections save a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied).

Thus the network can maintain a sort of state, allowing it to perform such tasks as sequence-prediction that are beyond the power of a standard multilayer perceptron.

Each neuron in one layer only receives its own past state as context information (instead of full connectivity to all other neurons in this layer) and thus neurons are independent of each other's history.

Given a lot of learnable predictability in the incoming data sequence, the highest level RNN can use supervised learning to easily classify even deep sequences with long intervals between important events.

Once the chunker has learned to predict and compress inputs that are unpredictable by the automatizer, then the automatizer can be forced in the next learning phase to predict or imitate through additional units the hidden units of the more slowly changing chunker.

LSTM works even given long delays between significant events and can handle signals that mix low and high frequency components.

to find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences.

continuous time recurrent neural network (CTRNN) uses a system of ordinary differential equations to model the effects on a neuron of the incoming spike train.

Note that, by the Shannon sampling theorem, discrete time recurrent neural networks can be viewed as continuous-time recurrent neural networks where the differential equations have transformed into equivalent difference equations.

multiple timescales recurrent neural network (MTRNN) is a neural-based computational model that can simulate the functional hierarchy of the brain through self-organization that depends on spatial connection between neurons and on distinct types of neuron activities, each with distinct time properties.[53][54]

With such varied neuronal activities, continuous sequences of any set of behaviors are segmented into reusable primitives, which in turn are flexibly integrated into diverse sequential behaviors.

In neural networks, it can be used to minimize the error term by changing each weight in proportion to the derivative of the error with respect to that weight, provided the non-linear activation functions are differentiable.

In this context, local in space means that a unit's weight vector can be updated using only information stored in the connected units and the unit itself such that update complexity of a single unit is linear in the dimensionality of the weight vector.

Local in time means that the updates take place continually (on-line) and depend only on the most recent time step rather than on multiple time steps within a given time horizon as in BPTT.

For recursively computing the partial derivatives, RTRL has a time-complexity of O(number of hidden x number of weights) per time step for computing the Jacobian matrices, while BPTT only takes O(number of weights) per time step, at the cost of storing all forward activations within the given time horizon.[63]

major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size of the time lag between important events.[34][67]

This fact improves stability of the algorithm, providing a unifying view on gradient calculation techniques for recurrent networks with local feedback.

A target function can be formed to evaluate the fitness or error of a particular weight vector as follows: First, the weights in the network are set according to the weight vector.

Initially, the genetic algorithm is encoded with the neural network weights in a predefined manner where one gene in the chromosome represents one weight link.The whole network is represented as a single chromosome.

Other global (and/or evolutionary) optimization techniques may be used to seek a good set of weights, such as simulated annealing or particle swarm optimization.

Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step.

In particular, RNNs can appear as nonlinear versions of finite impulse response and infinite impulse response filters and also as a nonlinear autoregressive exogenous model (NARX).[74]

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## Types of artificial neural networks

Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown.

Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat).

Most artificial neural networks bear only some resemblance to their more complex biological counterparts, but are very effective at their intended tasks (e.g.

Neural networks can be hardware- (neurons are represented by physical components) or software-based (computer models), and can use a variety of topologies and learning algorithms.

An autoencoder, autoassociator or Diabolo network[5]:19 is similar to the multilayer perceptron (MLP) – with an input layer, an output layer and one or more hidden layers connecting them.

Then, using PDF of each class, the class probability of a new input is estimated and Bayes’ rule is employed to allocate it to the class with the highest posterior probability.[10]

time delay neural network (TDNN) is a feedforward architecture for sequential data that recognizes features independent of sequence position.

In order to achieve time-shift invariance, delays are added to the input so that multiple data points (points in time) are analyzed together.

In a convolutional neural network (CNN, or ConvNet or shift invariant or space invariant.[14][15]) the unit connectivity pattern is inspired by the organization of the visual cortex.

Regulatory feedback networks started as a model to explain brain phenomena found during recognition including network-wide bursting and difficulty with similarity found universally in sensory recognition.[20]

In regression problems the output layer is a linear combination of hidden layer values representing mean predicted output.

In classification problems the output layer is typically a sigmoid function of a linear combination of hidden layer values, representing a posterior probability.

In classification problems the fixed non-linearity introduced by the sigmoid output function is most efficiently dealt with using iteratively re-weighted least squares.

A common solution is to associate each data point with its own centre, although this can expand the linear system to be solved in the final layer and requires shrinkage techniques to avoid overfitting.

All three approaches use a non-linear kernel function to project the input data into a space where the learning problem can be solved using a linear model.

Alternatively, if 9-NN classification is used and the closest 9 points are considered, then the effect of the surrounding 8 positive points may outweigh the closest 9 (negative) point.

The Euclidean distance is computed from the new point to the center of each neuron, and a radial basis function (RBF) (also called a kernel function) is applied to the distance to compute the weight (influence) for each neuron.

It determines when to stop adding neurons to the network by monitoring the estimated leave-one-out (LOO) error and terminating when the LOO error begins to increase because of overfitting.

For supervised learning in discrete time settings, training sequences of real-valued input vectors become sequences of activations of the input nodes, one input vector at a time.

At each time step, each non-input unit computes its current activation as a nonlinear function of the weighted sum of the activations of all units from which it receives connections.

For example, if the input sequence is a speech signal corresponding to a spoken digit, the final target output at the end of the sequence may be a label classifying the digit.

To minimize total error, gradient descent can be used to change each weight in proportion to its derivative with respect to the error, provided the non-linear activation functions are differentiable.

A major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size of the time lag between important events.[32][33]

Instead a fitness function or reward function or utility function is occasionally used to evaluate performance, which influences its input stream through output units connected to actuators that affect the environment.

At each time step, the input is propagated in a standard feedforward fashion, and then a backpropagation-like learning rule is applied (not performing gradient descent).

The fixed back connections leave a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied).

This realization gave birth to the concept of modular neural networks, in which several small networks cooperate or compete to solve problems.

Because neural networks suffer from local minima, starting with the same architecture and training but using randomly different initial weights often gives vastly different results.[citation needed]

The CoM is similar to the general machine learning bagging method, except that the necessary variety of machines in the committee is obtained by training from different starting weights rather than training on different randomly selected subsets of the training data.

The associative neural network (ASNN) is an extension of committee of machines that combines multiple feedforward neural networks and the k-nearest neighbor technique.

If new data become available, the network instantly improves its predictive ability and provides data approximation (self-learns) without retraining.

Another important feature of ASNN is the possibility to interpret neural network results by analysis of correlations between data cases in the space of models.[44]

SNN and the temporal correlations of neural assemblies in such networks—have been used to model figure/ground separation and region linking in the visual system.

It uses multiple types of units, (originally two, called simple and complex cells), as a cascading model for use in pattern recognition tasks.[49][50][51]

Dynamic neural networks address nonlinear multivariate behaviour and include (learning of) time-dependent behaviour, such as transient phenomena and delay effects.

The Cascade-Correlation architecture has several advantages: It learns quickly, determines its own size and topology, retains the structures it has built even if the training set changes and requires no backpropagation.

While typical artificial neural networks often contain only sigmoid functions (and sometimes Gaussian functions), CPPNs can include both types of functions and many others.

Furthermore, unlike typical artificial neural networks, CPPNs are applied across the entire space of possible inputs so that they can represent a complete image.

Since they are compositions of functions, CPPNs in effect encode images at infinite resolution and can be sampled for a particular display at whatever resolution is optimal.

It is done by creating a specific memory structure, which assigns each new pattern to an orthogonal plane using adjacently connected hierarchical arrays.[57]

HTM is a method for discovering and inferring the high-level causes of observed input patterns and sequences, thus building an increasingly complex model of the world.

HTM combines and extends approaches used in Bayesian networks, spatial and temporal clustering algorithms, while using a tree-shaped hierarchy of nodes that is common in neural networks.

- On Friday, September 20, 2019

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