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Recursive neural network

A recursive neural network (RNN) is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order.

RNNs have been successful, for instance, in learning sequence and tree structures in natural language processing, mainly phrase and sentence continuous representations based on word embedding.

RNNs have first been introduced to learn distributed representations of structure, such as logical terms.[1] Models and general frameworks have been developed in further works since the 90s.[2][3]

This architecture, with a few improvements, has been used for successfully parsing natural scenes and for syntactic parsing of natural language sentences.[4] RecCC is a constructive neural network approach to deal with tree domains[2] with pioneering applications to chemistry[5] and extension to directed acyclic graphs.[6] A

framework for unsupervised RNN has been introduced in 2004.[7][8] Recursive neural tensor networks use one, tensor-based composition function for all nodes in the tree.[9] Typically, stochastic gradient descent (SGD) is used to train the network.

Universal approximation capability of RNN over trees has been proved in literature.[10][11] Recurrent neural networks are recursive artificial neural networks with a certain structure: that of a linear chain.

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.

Recurrent neural network

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

This makes them applicable to tasks such as unsegmented, connected handwriting recognition[1] or speech recognition.[2][3] Recurrent neural networks are used somewhat indiscriminately about two broad classes of networks with a similar general structure, where one is finite impulse and the other is infinite impulse.

Both classes of networks exhibit temporal dynamic behavior.[4] 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.

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] Long short-term memory (LSTM) networks were invented by Hochreiter and Schmidhuber in 1997 and set accuracy records in multiple applications domains.[6] Around 2007, LSTM started to revolutionize speech recognition, outperforming traditional models in certain speech applications.[7] In 2009, a Connectionist Temporal Classification (CTC)-trained LSTM network was the first RNN to win pattern recognition contests when it won several competitions in connected handwriting recognition.[8][9] 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] LSTM also improved large-vocabulary speech recognition[2][3] and text-to-speech synthesis[11] and was used in Google Android.[8][12] In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49%[citation needed] through CTC-trained LSTM, which was used by Google voice search.[13] LSTM broke records for improved machine translation,[14] Language Modeling[15] and Multilingual Language Processing.[16] LSTM combined with convolutional neural networks (CNNs) improved automatic image captioning.[17] RNNs come in many variants.

BAM network has two layers, either of which can be driven as an input to recall an association and produce an output on the other layer.[25] 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 system effectively minimises the description length or the negative logarithm of the probability of the data.[32] 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.

It is possible to distill the RNN hierarchy into two RNNs: the 'conscious' chunker (higher level) and the 'subconscious' automatizer (lower level).[31] 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.

They are used in the full form and several simplified variants.[42][43] Their performance on polyphonic music modeling and speech signal modeling was found to be similar to that of long short-term memory.[44] They have fewer parameters than LSTM, as they lack an output gate.[45] Bi-directional RNNs use a finite sequence to predict or label each element of the sequence based on the element's past and future contexts.

the rate of change of activation is given by: Where: CTRNNs have been applied to evolutionary robotics where they have been used to address vision,[48] co-operation,[49] and minimal cognitive behaviour.[50] 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.

The biological approval of such a type of hierarchy was discussed in the memory-prediction theory of brain function by Hawkins in his book On Intelligence.[citation needed] Neural Turing machines (NTMs) are a method of extending recurrent neural networks by coupling them to external memory resources which they can interact with by attentional processes.

The combined system is analogous to a Turing machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent.[55] Differentiable neural computers (DNCs) are an extension of Neural Turing machines, allowing for usage of fuzzy amounts of each memory address and a record of chronology.

Biological neural networks appear to be local with respect to both time and space.[61][62] 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] An online hybrid between BPTT and RTRL with intermediate complexity exists,[64][65] along with variants for continuous time.[66] 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.[33][67] LSTM combined with a BPTT/RTRL hybrid learning method attempts to overcome these problems.[6] The on-line algorithm called causal recursive backpropagation (CRBP), implements and combines BPTT and RTRL paradigms for locally recurrent networks.[68] It works with the most general locally recurrent networks.

One approach to the computation of gradient information in RNNs with arbitrary architectures is based on signal-flow graphs diagrammatic derivation.[69] It uses the BPTT batch algorithm, based on Lee's theorem for network sensitivity calculations.[70] It was proposed by Wan and Beaufays, while its fast online version was proposed by Campolucci, Uncini and Piazza.[70] Training the weights in a neural network can be modeled as a non-linear global optimization problem.

The most common global optimization method for training RNNs is genetic algorithms, especially in unstructured networks.[71][72][73] 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.

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.

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