AI News, The Internet and your brain are more alike than you think

The Internet and your brain are more alike than you think

'The founders of the Internet spent a lot of time considering how to make information flow efficiently,' says Salk Assistant Professor Saket Navlakha, coauthor of the new study that appears online in Neural Computation on February 9, 2017.

To accomplish this, the Internet employs an algorithm called 'additive increase, multiplicative decrease' (AIMD) in which your computer sends a packet of data and then listens for an acknowledgement from the receiver: If the packet is promptly acknowledged, the network is not overloaded and your data can be transmitted through the network at a higher rate.

In this way, users gradually find their 'sweet spot,' and congestion is avoided because users take their foot off the gas, so to speak, as soon as they notice a slowdown.

The neuronal equivalent of multiplicative decrease occurs when the firing of two neurons is reversed (second before first), which weakens their connection, making the first much less likely to trigger the second in the future.

'I was initially surprised that biological neural networks utilized the same algorithms as their engineered counterparts, but, as we learned, the requirements for efficiency, robustness, and simplicity are common to both living organisms and the networks we have built.'

The Internet and your brain are more alike than you think

Salk scientist finds similar rule governing traffic flow in engineered and biological systems LA JOLLA—Although we spend a lot of our time online nowadays—streaming music and video, checking email and social media, or obsessively reading the news—few of us know about the mathematical algorithms that manage how our content is delivered.

Now, a Salk Institute discovery shows that an algorithm used for the Internet is also at work in the human brain, an insight that improves our understanding of engineered and neural networks and potentially even learning disabilities.

To accomplish this, the Internet employs an algorithm called “additive increase, multiplicative decrease” (AIMD) in which your computer sends a packet of data and then listens for an acknowledgement from the receiver: If the packet is promptly acknowledged, the network is not overloaded and your data can be transmitted through the network at a higher rate.

In this way, users gradually find their “sweet spot,” and congestion is avoided because users take their foot off the gas, so to speak, as soon as they notice a slowdown.

“I was initially surprised that biological neural networks utilized the same algorithms as their engineered counterparts, but, as we learned, the requirements for efficiency, robustness, and simplicity are common to both living organisms and the networks we have built.” Understanding how the system works under normal conditions could help neuroscientists better understand what happens when these results are disrupted, for example, in learning disabilities.

Mediacenter

Study finds similar algorithm governing the brain and Internet Although we spend a lot of our time online nowadays–streaming music and video, checking email and social media, or obsessively reading the news–few of us know about the mathematical algorithms that manage how our content is delivered.

Now, a Salk Institute discovery shows that an algorithm used for the Internet is also at work in the human brain, an insight that improves our understanding of engineered and neural networks and potentially even learning disabilities.

(AIMD) in which your computer sends a packet of data and then listens for an acknowledgement from the receiver: If the packet is promptly acknowledged, the network is not overloaded and your data can be transmitted through the network at a higher rate.

As computers throughout the network utilize this strategy, the whole system can continuously adjust to changing conditions, maximizing overall efficiency.

Navlakha, who develops algorithms to understand complex biological networks, wondered if the brain, with its billions of distributed neurons, was managing information similarly.

The neuronal equivalent of multiplicative decrease occurs when the firing of two neurons is reversed (second before first), which weakens their connection, making the first much less likely to trigger the second in the future.

Artificial neural network

Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.[1] Such systems 'learn' to perform tasks by considering examples, generally without being programmed with any task-specific rules.

For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as 'cat' or 'no cat' and using the results to identify cats in other images.

An ANN is based on a collection of connected units or nodes called artificial neurons which loosely model the neurons in a biological brain.

In common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs.

Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.

ANNs have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

With mathematical notation, Rosenblatt described circuitry not in the basic perceptron, such as the exclusive-or circuit that could not be processed by neural networks at the time.[8] In 1959, a biological model proposed by Nobel laureates Hubel and Wiesel was based on their discovery of two types of cells in the primary visual cortex: simple cells and complex cells.[9] The first functional networks with many layers were published by Ivakhnenko and Lapa in 1965, becoming the Group Method of Data Handling.[10][11][12] Neural network research stagnated after machine learning research by Minsky and Papert (1969),[13] who discovered two key issues with the computational machines that processed neural networks.

Much of artificial intelligence had focused on high-level (symbolic) models that are processed by using algorithms, characterized for example by expert systems with knowledge embodied in if-then rules, until in the late 1980s research expanded to low-level (sub-symbolic) machine learning, characterized by knowledge embodied in the parameters of a cognitive model.[citation needed] A

key trigger for renewed interest in neural networks and learning was Werbos's (1975) backpropagation algorithm that effectively solved the exclusive-or problem and more generally accelerated the training of multi-layer networks.

Backpropagation distributed the error term back up through the layers, by modifying the weights at each node.[8] In the mid-1980s, parallel distributed processing became popular under the name connectionism.

Rumelhart and McClelland (1986) described the use of connectionism to simulate neural processes.[14] Support vector machines and other, much simpler methods such as linear classifiers gradually overtook neural networks in machine learning popularity.

However, using neural networks transformed some domains, such as the prediction of protein structures.[15][16] Earlier challenges in training deep neural networks were successfully addressed with methods such as unsupervised pre-training, while available computing power increased through the use of GPUs and distributed computing.

In 1992, max-pooling was introduced to help with least shift invariance and tolerance to deformation to aid in 3D object recognition.[17][18][19] In 2010, Backpropagation training through max-pooling was accelerated by GPUs and shown to perform better than other pooling variants.[20] The vanishing gradient problem affects many-layered feedforward networks that used backpropagation and also recurrent neural networks (RNNs).[21][22] As errors propagate from layer to layer, they shrink exponentially with the number of layers, impeding the tuning of neuron weights that is based on those errors, particularly affecting deep networks.

To overcome this problem, Schmidhuber adopted a multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning and fine-tuned by backpropagation.[23] Behnke (2003) relied only on the sign of the gradient (Rprop)[24] on problems such as image reconstruction and face localization.

(2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine[25] to model each layer.

Once sufficiently many layers have been learned, the deep architecture may be used as a generative model by reproducing the data when sampling down the model (an 'ancestral pass') from the top level feature activations.[26][27] In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.[28] Computational devices were created in CMOS, for both biophysical simulation and neuromorphic computing.

Nanodevices[29] for very large scale principal components analyses and convolution may create a new class of neural computing because they are fundamentally analog rather than digital (even though the first implementations may use digital devices).[30] Ciresan and colleagues (2010)[31] in Schmidhuber's group showed that despite the vanishing gradient problem, GPUs makes back-propagation feasible for many-layered feedforward neural networks.

Between 2009 and 2012, recurrent neural networks and deep feedforward neural networks developed in Schmidhuber's research group won eight international competitions in pattern recognition and machine learning.[32][33] For example, the bi-directional and multi-dimensional long short-term memory (LSTM)[34][35][36][37] of Graves et al.

won three competitions in connected handwriting recognition at the 2009 International Conference on Document Analysis and Recognition (ICDAR), without any prior knowledge about the three languages to be learned.[36][35] Ciresan and colleagues won pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,[38] the ISBI 2012 Segmentation of Neuronal Structures in Electron Microscopy Stacks challenge[39] and others.

Their neural networks were the first pattern recognizers to achieve human-competitive or even superhuman performance[40] on benchmarks such as traffic sign recognition (IJCNN 2012), or the MNIST handwritten digits problem.

Researchers demonstrated (2010) that deep neural networks interfaced to a hidden Markov model with context-dependent states that define the neural network output layer can drastically reduce errors in large-vocabulary speech recognition tasks such as voice search.

GPU-based implementations[41] of this approach won many pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,[38] the ISBI 2012 Segmentation of neuronal structures in EM stacks challenge,[39] the ImageNet Competition[42] and others.

Deep, highly nonlinear neural architectures similar to the neocognitron[43] and the 'standard architecture of vision',[44] inspired by simple and complex cells, were pre-trained by unsupervised methods by Hinton.[45][26] A team from his lab won a 2012 contest sponsored by Merck to design software to help find molecules that might identify new drugs.[46] As of 2011, the state of the art in deep learning feedforward networks alternated convolutional layers and max-pooling layers,[41][47] topped by several fully or sparsely connected layers followed by a final classification layer.

Such supervised deep learning methods were the first to achieve human-competitive performance on certain tasks.[40] ANNs were able to guarantee shift invariance to deal with small and large natural objects in large cluttered scenes, only when invariance extended beyond shift, to all ANN-learned concepts, such as location, type (object class label), scale, lighting and others.

This was realized in Developmental Networks (DNs)[48] whose embodiments are Where-What Networks, WWN-1 (2008)[49] through WWN-7 (2013).[50] An artificial neural network is a network of simple elements called artificial neurons, which receive input, change their internal state (activation) according to that input, and produce output depending on the input and activation.

of predecessor neurons and typically has the form[51] The learning rule is a rule or an algorithm which modifies the parameters of the neural network, in order for a given input to the network to produce a favored output.

This learning process typically amounts to modifying the weights and thresholds of the variables within the network.[51] Neural network models can be viewed as simple mathematical models defining a function

A common use of the phrase 'ANN model' is really the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons or their connectivity).

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(commonly referred to as the activation function[52]) is some predefined function, such as the hyperbolic tangent or sigmoid function or softmax function or rectifier function.

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For applications where the solution is data dependent, the cost must necessarily be a function of the observations, otherwise the model would not relate to the data.

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While it is possible to define an ad hoc cost function, frequently a particular cost (function) is used, either because it has desirable properties (such as convexity) or because it arises naturally from a particular formulation of the problem (e.g., in a probabilistic formulation the posterior probability of the model can be used as an inverse cost).

The basics of continuous backpropagation[10][53][54][55] were derived in the context of control theory by Kelley[56] in 1960 and by Bryson in 1961,[57] using principles of dynamic programming.

In 1962, Dreyfus published a simpler derivation based only on the chain rule.[58] Bryson and Ho described it as a multi-stage dynamic system optimization method in 1969.[59][60] In 1970, Linnainmaa finally published the general method for automatic differentiation (AD) of discrete connected networks of nested differentiable functions.[61][62] This corresponds to the modern version of backpropagation which is efficient even when the networks are sparse.[10][53][63][64] In 1973, Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients.[65] In 1974, Werbos mentioned the possibility of applying this principle to ANNs,[66] and in 1982, he applied Linnainmaa's AD method to neural networks in the way that is widely used today.[53][67] In 1986, Rumelhart, Hinton and Williams noted that this method can generate useful internal representations of incoming data in hidden layers of neural networks.[68] In 1993, Wan was the first[10] to win an international pattern recognition contest through backpropagation.[69] The weight updates of backpropagation can be done via stochastic gradient descent using the following equation: where,

The choice of the cost function depends on factors such as the learning type (supervised, unsupervised, reinforcement, etc.) and the activation function.

For example, when performing supervised learning on a multiclass classification problem, common choices for the activation function and cost function are the softmax function and cross entropy function, respectively.

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The network is trained to minimize L2 error for predicting the mask ranging over the entire training set containing bounding boxes represented as masks.

commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output,

Minimizing this cost using gradient descent for the class of neural networks called multilayer perceptrons (MLP), produces the backpropagation algorithm for training neural networks.

Tasks that fall within the paradigm of supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation).

The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables).

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whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples those quantities would be maximized rather than minimized).

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The aim is to discover a policy for selecting actions that minimizes some measure of a long-term cost, e.g., the expected cumulative cost.

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ANNs are frequently used in reinforcement learning as part of the overall algorithm.[77][78] Dynamic programming was coupled with ANNs (giving neurodynamic programming) by Bertsekas and Tsitsiklis[79] and applied to multi-dimensional nonlinear problems such as those involved in vehicle routing,[80] natural resources management[81][82] or medicine[83] because of the ability of ANNs to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.

In 2004 a recursive least squares algorithm was introduced to train CMAC neural network online.[84] This algorithm can converge in one step and update all weights in one step with any new input data.

Based on QR decomposition, this recursive learning algorithm was simplified to be O(N).[85] Training a neural network model essentially means selecting one model from the set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost.

Backpropagation training algorithms fall into three categories: Evolutionary methods,[87] gene expression programming,[88] simulated annealing,[89] expectation-maximization, non-parametric methods and particle swarm optimization[90] are other methods for training neural networks.

It used a deep feedforward multilayer perceptron with eight layers.[92] It is a supervised learning network that grows layer by layer, where each layer is trained by regression analysis.

convolutional neural network (CNN) is a class of deep, feed-forward networks, composed of one or more convolutional layers with fully connected layers (matching those in typical ANNs) on top.

In particular, max-pooling[18] is often structured via Fukushima's convolutional architecture.[94] This architecture allows CNNs to take advantage of the 2D structure of input data.

CNNs are easier to train than other regular, deep, feed-forward neural networks and have many fewer parameters to estimate.[97] Examples of applications in computer vision include DeepDream[98] and robot navigation.[99] Long short-term memory (LSTM) networks are RNNs that avoid the vanishing gradient problem.[100] LSTM is normally augmented by recurrent gates called forget gates.[101] LSTM networks prevent backpropagated errors from vanishing or exploding.[21] Instead errors can flow backwards through unlimited numbers of virtual layers in space-unfolded LSTM.

That is, LSTM can learn 'very deep learning' tasks[10] that require memories of events that happened thousands or even millions of discrete time steps ago.

Stacks of LSTM RNNs[103] trained by Connectionist Temporal Classification (CTC)[104] can find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences.

In 2003, LSTM started to become competitive with traditional speech recognizers.[105] In 2007, the combination with CTC achieved first good results on speech data.[106] In 2009, a CTC-trained LSTM was the first RNN to win pattern recognition contests, when it won several competitions in connected handwriting recognition.[10][36] In 2014, Baidu used CTC-trained RNNs to break the Switchboard Hub5'00 speech recognition benchmark, without traditional speech processing methods.[107] LSTM also improved large-vocabulary speech recognition,[108][109] text-to-speech synthesis,[110] for Google Android,[53][111] and photo-real talking heads.[112] In 2015, Google's speech recognition experienced a 49% improvement through CTC-trained LSTM.[113] LSTM became popular in Natural Language Processing.

Unlike previous models based on HMMs and similar concepts, LSTM can learn to recognise context-sensitive languages.[114] LSTM improved machine translation,[115][116] language modeling[117] and multilingual language processing.[118] LSTM combined with CNNs improved automatic image captioning.[119] Deep Reservoir Computing and Deep Echo State Networks (deepESNs)[120][121] provide a framework for efficiently trained models for hierarchical processing of temporal data, while enabling the investigation of the inherent role of RNN layered composition.[clarification needed] A

This allows for both improved modeling and faster convergence of the fine-tuning phase.[123] Large memory storage and retrieval neural networks (LAMSTAR)[124][125] are fast deep learning neural networks of many layers that can use many filters simultaneously.

Its speed is provided by Hebbian link-weights[126] that integrate the various and usually different filters (preprocessing functions) into its many layers and to dynamically rank the significance of the various layers and functions relative to a given learning task.

This grossly imitates biological learning which integrates various preprocessors (cochlea, retina, etc.) and cortexes (auditory, visual, etc.) and their various regions.

Its deep learning capability is further enhanced by using inhibition, correlation and its ability to cope with incomplete data, or 'lost' neurons or layers even amidst a task.

The link-weights allow dynamic determination of innovation and redundancy, and facilitate the ranking of layers, of filters or of individual neurons relative to a task.

LAMSTAR has been applied to many domains, including medical[127][128][129] and financial predictions,[130] adaptive filtering of noisy speech in unknown noise,[131] still-image recognition,[132] video image recognition,[133] software security[134] and adaptive control of non-linear systems.[135] LAMSTAR had a much faster learning speed and somewhat lower error rate than a CNN based on ReLU-function filters and max pooling, in 20 comparative studies.[136] These applications demonstrate delving into aspects of the data that are hidden from shallow learning networks and the human senses, such as in the cases of predicting onset of sleep apnea events,[128] of an electrocardiogram of a fetus as recorded from skin-surface electrodes placed on the mother's abdomen early in pregnancy,[129] of financial prediction[124] or in blind filtering of noisy speech.[131] LAMSTAR was proposed in 1996 (A U.S. Patent 5,920,852 A) and was further developed Graupe and Kordylewski from 1997–2002.[137][138][139] A modified version, known as LAMSTAR 2, was developed by Schneider and Graupe in 2008.[140][141] The auto encoder idea is motivated by the concept of a good representation.

The whole process of auto encoding is to compare this reconstructed input to the original and try to minimize the error to make the reconstructed value as close as possible to the original.

This idea was introduced in 2010 by Vincent et al.[142] with a specific approach to good representation, a good representation is one that can be obtained robustly from a corrupted input and that will be useful for recovering the corresponding clean input.

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might be either the cross-entropy loss with an affine-sigmoid decoder, or the squared error loss with an affine decoder.[142] In order to make a deep architecture, auto encoders stack.[143] Once the encoding function

of the first denoising auto encoder is learned and used to uncorrupt the input (corrupted input), the second level can be trained.[142] Once the stacked auto encoder is trained, its output can be used as the input to a supervised learning algorithm such as support vector machine classifier or a multi-class logistic regression.[142] A

deep stacking network (DSN)[144] (deep convex network) is based on a hierarchy of blocks of simplified neural network modules.

It was introduced in 2011 by Deng and Dong.[145] It formulates the learning as a convex optimization problem with a closed-form solution, emphasizing the mechanism's similarity to stacked generalization.[146] Each DSN block is a simple module that is easy to train by itself in a supervised fashion without backpropagation for the entire blocks.[147] Each block consists of a simplified multi-layer perceptron (MLP) with a single hidden layer.

It offers two important improvements: it uses higher-order information from covariance statistics, and it transforms the non-convex problem of a lower-layer to a convex sub-problem of an upper-layer.[148] TDSNs use covariance statistics in a bilinear mapping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order tensor.

While parallelization and scalability are not considered seriously in conventional DNNs,[149][150][151] all learning for DSNs and TDSNs is done in batch mode, to allow parallelization.[145][144] Parallelization allows scaling the design to larger (deeper) architectures and data sets.

The need for deep learning with real-valued inputs, as in Gaussian restricted Boltzmann machines, led to the spike-and-slab RBM (ssRBM), which models continuous-valued inputs with strictly binary latent variables.[152] Similar to basic RBMs and its variants, a spike-and-slab RBM is a bipartite graph, while like GRBMs, the visible units (input) are real-valued.

A spike is a discrete probability mass at zero, while a slab is a density over continuous domain;[153] their mixture forms a prior.[154] An extension of ssRBM called µ-ssRBM provides extra modeling capacity using additional terms in the energy function.

Features can be learned using deep architectures such as DBNs,[26] DBMs,[155] deep auto encoders,[156] convolutional variants,[157][158] ssRBMs,[153] deep coding networks,[159] DBNs with sparse feature learning,[160] RNNs,[161] conditional DBNs,[162] de-noising auto encoders.[163] This provides a better representation, allowing faster learning and more accurate classification with high-dimensional data.

However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input (a distributed representation) and must be adjusted together (high degree of freedom).

It is a full generative model, generalized from abstract concepts flowing through the layers of the model, which is able to synthesize new examples in novel classes that look 'reasonably' natural.

All the levels are learned jointly by maximizing a joint log-probability score.[169] In a DBM with three hidden layers, the probability of a visible input ν is: where

deep predictive coding network (DPCN) is a predictive coding scheme that uses top-down information to empirically adjust the priors needed for a bottom-up inference procedure by means of a deep, locally connected, generative model.

DPCNs predict the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from previous states.[170] DPCNs can be extended to form a convolutional network.[170] Integrating external memory with ANNs dates to early research in distributed representations[171] and Kohonen's self-organizing maps.

For example, in sparse distributed memory or hierarchical temporal memory, the patterns encoded by neural networks are used as addresses for content-addressable memory, with 'neurons' essentially serving as address encoders and decoders.

Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting and associative recall from input and output examples.

They out-performed Neural turing machines, long short-term memory systems and memory networks on sequence-processing tasks.[180][181][182][183][184] Approaches that represent previous experiences directly and use a similar experience to form a local model are often called nearest neighbour or k-nearest neighbors methods.[185] Deep learning is useful in semantic hashing[186] where a deep graphical model the word-count vectors[187] obtained from a large set of documents.[clarification needed] Documents are mapped to memory addresses in such a way that semantically similar documents are located at nearby addresses.

Unlike sparse distributed memory that operates on 1000-bit addresses, semantic hashing works on 32 or 64-bit addresses found in a conventional computer architecture.

These models have been applied in the context of question answering (QA) where the long-term memory effectively acts as a (dynamic) knowledge base and the output is a textual response.[190] Deep neural networks can be potentially improved by deepening and parameter reduction, while maintaining trainability.

While training extremely deep (e.g., 1 million layers) neural networks might not be practical, CPU-like architectures such as pointer networks[191] and neural random-access machines[192] overcome this limitation by using external random-access memory and other components that typically belong to a computer architecture such as registers, ALU and pointers.

The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently – unlike models like LSTM, whose number of parameters grows quadratically with memory size.

In that work, an LSTM RNN or CNN was used as an encoder to summarize a source sentence, and the summary was decoded using a conditional RNN language model to produce the translation.[196] These systems share building blocks: gated RNNs and CNNs and trained attention mechanisms.

For the sake of dimensionality reduction of the updated representation in each layer, a supervised strategy selects the best informative features among features extracted by KPCA.

more straightforward way to use kernel machines for deep learning was developed for spoken language understanding.[199] The main idea is to use a kernel machine to approximate a shallow neural net with an infinite number of hidden units, then use stacking to splice the output of the kernel machine and the raw input in building the next, higher level of the kernel machine.

The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network.[200] Using ANNs requires an understanding of their characteristics.

ANN capabilities fall within the following broad categories:[citation needed] Because of their ability to reproduce and model nonlinear processes, ANNs have found many applications in a wide range of disciplines.

Application areas include system identification and control (vehicle control, trajectory prediction,[201] process control, natural resource management), quantum chemistry,[202] game-playing and decision making (backgammon, chess, poker), pattern recognition (radar systems, face identification, signal classification,[203] object recognition and more), sequence recognition (gesture, speech, handwritten and printed text recognition), medical diagnosis, finance[204] (e.g.

automated trading systems), data mining, visualization, machine translation, social network filtering[205] and e-mail spam filtering.

ANNs have been used to diagnose cancers, including lung cancer,[206] prostate cancer, colorectal cancer[207] and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.[208][209] ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters.[210][211] ANNs have also been used for building black-box models in geoscience: hydrology,[212][213] ocean modelling and coastal engineering,[214][215] and geomorphology,[216] are just few examples of this kind.

They range from models of the short-term behavior of individual neurons,[217] models of how the dynamics of neural circuitry arise from interactions between individual neurons and finally to models of how behavior can arise from abstract neural modules that represent complete subsystems.

These include models of the long-term, and short-term plasticity, of neural systems and their relations to learning and memory from the individual neuron to the system level.

specific recurrent architecture with rational valued weights (as opposed to full precision real number-valued weights) has the full power of a universal Turing machine,[218] using a finite number of neurons and standard linear connections.

Further, the use of irrational values for weights results in a machine with super-Turing power.[219] Models' 'capacity' property roughly corresponds to their ability to model any given function.

It is related to the amount of information that can be stored in the network and to the notion of complexity.[citation needed] Models may not consistently converge on a single solution, firstly because many local minima may exist, depending on the cost function and the model.

However, for CMAC neural network, a recursive least squares algorithm was introduced to train it, and this algorithm can be guaranteed to converge in one step.[84] Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training.

but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.

Supervised neural networks that use a mean squared error (MSE) cost function can use formal statistical methods to determine the confidence of the trained model.

A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.

By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based neural network) for categorical target variables, the outputs can be interpreted as posterior probabilities.

common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation.[citation needed] Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example and by grouping examples in so-called mini-batches.

For example, by introducing a recursive least squares algorithm for CMAC neural network, the training process only takes one step to converge.[84] No neural network has solved computationally difficult problems such as the n-Queens problem, the travelling salesman problem, or the problem of factoring large integers.

Back propagation is a critical part of most artificial neural networks, although no such mechanism exists in biological neural networks.[220] How information is coded by real neurons is not known.

Sensor neurons fire action potentials more frequently with sensor activation and muscle cells pull more strongly when their associated motor neurons receive action potentials more frequently.[221] Other than the case of relaying information from a sensor neuron to a motor neuron, almost nothing of the principles of how information is handled by biological neural networks is known.

Alexander Dewdney commented that, as a result, artificial neural networks have a 'something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are.

Weng[224] argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.

Large and effective neural networks require considerable computing resources.[225] While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may compel a neural network designer to fill many millions of database rows for its connections – which can consume vast amounts of memory and storage.

Schmidhuber notes that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before.[226] The use of parallel GPUs can reduce training times from months to days.[225] Neuromorphic engineering addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry.

Another chip optimized for neural network processing is called a Tensor Processing Unit, or TPU.[227] Arguments against Dewdney's position are that neural networks have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft[228] to detecting credit card fraud to mastering the game of Go.

Technology writer Roger Bridgman commented: Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be 'an opaque, unreadable table...valueless as a scientific resource'.

In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers.

An unreadable table that a useful machine could read would still be well worth having.[229] Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network.

Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful.

For example, local vs non-local learning and shallow vs deep architecture.[230] Advocates of hybrid models (combining neural networks and symbolic approaches), claim that such a mixture can better capture the mechanisms of the human mind.[231][232] Artificial neural networks have many variations.

Deep Learning

He told Page, who had read an early draft, that he wanted to start a company to develop his ideas about how to build a truly intelligent computer: one that could understand language and then make inferences and decisions on its own.

The basic idea—that software can simulate the neocortex’s large array of neurons in an artificial “neural network”—is decades old, and it has led to as many disappointments as breakthroughs.

Last June, a Google deep-learning system that had been shown 10 million images from YouTube videos proved almost twice as good as any previous image recognition effort at identifying objects such as cats.

In October, Microsoft chief research officer Rick Rashid wowed attendees at a lecture in China with a demonstration of speech software that transcribed his spoken words into English text with an error rate of 7 percent, translated them into Chinese-language text, and then simulated his own voice uttering them in Mandarin.

Hinton, who will split his time between the university and Google, says he plans to “take ideas out of this field and apply them to real problems” such as image recognition, search, and natural-language understanding, he says.

Extending deep learning into applications beyond speech and image recognition will require more conceptual and software breakthroughs, not to mention many more advances in processing power.

Neural networks, developed in the 1950s not long after the dawn of AI research, looked promising because they attempted to simulate the way the brain worked, though in greatly simplified form.

These weights determine how each simulated neuron responds—with a mathematical output between 0 and 1—to a digitized feature such as an edge or a shade of blue in an image, or a particular energy level at one frequency in a phoneme, the individual unit of sound in spoken syllables.

Programmers would train a neural network to detect an object or phoneme by blitzing the network with digitized versions of images containing those objects or sound waves containing those phonemes.

The eventual goal of this training was to get the network to consistently recognize the patterns in speech or sets of images that we humans know as, say, the phoneme “d” or the image of a dog.

This is much the same way a child learns what a dog is by noticing the details of head shape, behavior, and the like in furry, barking animals that other people call dogs.

Once that layer accurately recognizes those features, they’re fed to the next layer, which trains itself to recognize more complex features, like a corner or a combination of speech sounds.

Because the multiple layers of neurons allow for more precise training on the many variants of a sound, the system can recognize scraps of sound more reliably, especially in noisy environments such as subway platforms.

Hawkins, author of On Intelligence, a 2004 book on how the brain works and how it might provide a guide to building intelligent machines, says deep learning fails to account for the concept of time.

Brains process streams of sensory data, he says, and human learning depends on our ability to recall sequences of patterns: when you watch a video of a cat doing something funny, it’s the motion that matters, not a series of still images like those Google used in its experiment.

In high school, he wrote software that enabled a computer to create original music in various classical styles, which he demonstrated in a 1965 appearance on the TV show I’ve Got a Secret.

Since then, his inventions have included several firsts—a print-to-speech reading machine, software that could scan and digitize printed text in any font, music synthesizers that could re-create the sound of orchestral instruments, and a speech recognition system with a large vocabulary.

This isn’t his immediate goal at Google, but it matches that of Google cofounder Sergey Brin, who said in the company’s early days that he wanted to build the equivalent of the sentient computer HAL in 2001: A Space Odyssey—except one that wouldn’t kill people.

“My mandate is to give computers enough understanding of natural language to do useful things—do a better job of search, do a better job of answering questions,” he says.

queries as quirky as “a long, tiresome speech delivered by a frothy pie topping.” (Watson’s correct answer: “What is a meringue harangue?”) Kurzweil isn’t focused solely on deep learning, though he says his approach to speech recognition is based on similar theories about how the brain works.

“That’s not a project I think I’ll ever finish.” Though Kurzweil’s vision is still years from reality, deep learning is likely to spur other applications beyond speech and image recognition in the nearer term.

Microsoft’s Peter Lee says there’s promising early research on potential uses of deep learning in machine vision—technologies that use imaging for applications such as industrial inspection and robot guidance.

10 misconceptions about Neural Networks

In quantitative finance neural networks are often used for time-series forecasting, constructing proprietary indicators, algorithmic trading, securities classification and credit risk modelling.

One reason why I believe current generation neural networks are not capable of sentience (a different concept to intelligence) is because I believe that biological neurons are much more complex than artificial neurons.

In the context of quantitative finance I think it is important to remember that because whilst it may sound cool to say that something is 'inspired by the brain', this statement may result unrealistic expectations or fear.

The difference between a multiple linear regression and a perceptron is that a perceptron feeds the signal generated by a multiple linear regression into an activation function which may or may not be non-linear.

The input layer receives input patterns and the output layer could contain a list of classifications or output signals to which those input patterns may map.

Given a pattern, p, the objective of this network would be to minimize the error of the output signal, o_p, relative to some known target value for some given training pattern, t_p.

For example, if the neuron was supposed to map p to -1 but it mapped it to 1 then the error, as measured by sum-squared distance, of the neuron would be 4, (-1 - 1)^2. 

think that one of the problems facing the use of deep neural networks for trading (in addition to the obvious risk of overfitting) is that the inputs into the neural network are almost always heavily pre-processed meaning that there may be few features to actually extract because the inputs are already to some extent features.

Sum squared error (SSE), \epsilon = \sum^{P_T}_{p=1} \big ( t_p - o_p \big )^2 Given that the objective of the network is to minimize \epsilon we can use an optimization algorithm to adjust the weights in the neural network.

The most common learning algorithm for neural networks is the gradient descent algorithm although other and potentially better optimization algorithms can be used. Gradient descent works by calculating the partial derivative of the error with respect to the weights for each layer in the neural network and then moving in the opposite direction to the gradient (because we want to minimize the error of the neural network).

Expressed mathematically the update rule for the weights in the neural network (\textbf{v}) is given by, v_i(t) = v_i(t - 1) + \delta v_i(t) where \delta v_i(t) = \eta(-\frac{\partial \epsilon}{\partial v_i}) where \frac{\partial \epsilon}{\partial v_i} = -2(t_p - o_p) \frac{\partial f}{\partial net_p}z_{i,p} where \eta is the learning rate which controls how quickly or slowly the neural network converges.

It is worth nothing that the calculation of the partial derivative of f with respect to the net input signal for a pattern p represents a problem for any discontinuous activation functions;

That having been said I do agree that some practitioners like to treat neural networks as a 'black box' which can be thrown at any problem without first taking the time to understand the nature of the problem and whether or not neural networks are an appropriate choice.

Many modern day advances in the field of machine learning do not come from rethinking the way that perceptrons and optimization algorithms work but rather from being creative regarding how these components fit together.

Below I discuss some very interesting and creative neural network architectures which have been developed over time,  Recurrent Neural Networks - some or all connections flow backwards meaning that feed back loops exist in the network.

Deep neural networks have become extremely popular in more recent years due to their unparalleled success in image and voice recognition problems. The number of deep neural network architectures is growing quite quickly but some of the most popular architectures include deep belief networks, convolutional neural networks, deep restricted Boltzmann machines, stacked auto-encoders, and many more.

Radial basis networks - although not a different type of architecture in the sense of perceptrons and connections, radial basis functions make use of radial basis functions as their activation functions, these are real valued functions whose output depends on the distance from a particular point.

The most commonly used radial basis functions is the Gaussian distribution. Because radial basis functions can take on much more complex forms, they were originally used for performing function interpolation.

As such, quantitative analysts interested in using neural networks should probably test multiple neural network architectures and consider combining their outputs together in an ensemble to maximize their investment performance.

The reasons why these questions are important is because if the neural network is too large (too small) the neural network could potentially overfit (underfit) the data meaning that the network would not generalize well out of sample.

There are two popular approaches used in industry namely early stopping and regularization and then there is my personal favourite approach, global search, Early stopping involves splitting your training set into the main training set and a validation set.

This is the equivalent of adding a prior which essentially makes the neural network believe that the function it is approximating is smooth, \epsilon = \beta \sum^{P_T}_{p=1} \big ( t_p - o_p \big )^2 + \alpha \sum^n_{j=1} v_j^2 where n is the number of weights in the neural network.

This condition is typically either when the error of the network reaches an acceptable level of accuracy on the training set, when the error of the network on the validation set begins to deteriorate, or when the specified computational budget has been exhausted. The most common learning algorithm for neural networks is the backpropagation algorithm which uses stochastic gradient descent which was discussed earlier on in this article.

Adjusting all the weights at once can result in a significant movement of the neural network in weight space, the gradient descent algorithm is quite slow, and is susceptible to local minima.

Here is how they can be used to train neural networks: Neural network vector representation - by encoding the neural network as a vector of weights, each representing the weight of a connection in the neural network, we can train neural networks using most meta-heuristic search algorithms.

The fitness function is calculated as the sum-squared error of the reconstructed neural network after completing one feedforward pass of the training data set.

These three operators are, In addition to these population-based metaheuristic search algorithms, other algorithms have been used to train of neural networks including backpropagation with added momentum, differential evolution, Levenberg Marquardt, simulated annealing, and many more.

Neural networks can use one of three learning strategies namely a supervised learning strategy, an unsupervised learning strategy, or a reinforcement learning strategy. Supervised learning require at least two data sets, a training set which consists of inputs with the expected output, and a testing set which consists of inputs without the expected output.

Reinforcement learning are based on the simple premise of rewarding neural networks for good behaviours and punishing them for bad behaviours. Because unsupervised and reinforcement learning strategies do not require that data be labelled they can be applied to under-formulated problems where the correct output is not known.

Self Organizing Maps are essentially a multi-dimensional scaling technique which construct an approximation of the probability density function of some underlying data set, \textbf{Z}, whilst preserving the topological structure of that data set. This is done by mapping input vectors, \textbf{z}_i, in the data set, \textbf{Z}, to weight vectors, \textbf{v}_j, (neurons) in the feature map, \textbf{V}.

In the context of financial markets (and game playing) reinforcement learning strategies are particularly useful because the neural network learns to optimize a particular quantity such as an appropriate measure of risk adjusted return.  Back to the top

One of the inputs is the price of the security and we are using the Sigmoid activation function. However, most of the securities cost between 5$ and 15$ per share and the output of the Sigmoid function approaches 1.0.

Neural networks trained on unprocessed data produce models where 'the lights are on but nobody's home' Outlier removal - an outlier is value that is much smaller or larger than most of the other values in some set of data.

Outliers can cause problems with statistical techniques like regression analysis and curve fitting because when the model tries to 'accommodate' the outlier, performance of the model across all other data deteriorates, The illustration shows that trying to accommodate an outlier into the linear regression model results in a poor fits of the data set.

Remove redundancy - when two or more of the independent variables being fed into the neural network are highly correlated (multiplecolinearity) this can negatively affect the neural networks learning ability. Highly correlated inputs also mean that the amount of unique information presented by each variable is small, so the less significant input can be removed.

For example, fund managers wouldn't know how a neural network makes trading decisions, so it is impossible to assess the risks of the trading strategies learned by the neural network. Similarly, banks using neural networks for credit risk modelling would not be able to justify why a customer has a particular credit rating, which is a regulatory requirement. That having been said, state of the art rule-extraction algorithms have been developed to vitrify some neural network architectures.

This is the difference between predicate and propositional logic. If we had a simple neural network which Price (P), Simple Moving Average (SMA), and Exponential Moving Average (EMA) as inputs and we extracted a trend following strategy from the neural network in propositional logic, we might get rules like this,

Therefore for traders there is no way to determine the confidence of these results. Fuzzy logic overcomes this limitation by introducing a membership function which specifies how much a variable belongs to a particular domain.

This article describes how to evolve security analysis decision trees using genetic programming. Decision tree induction is the term given to the process of extracting decision trees from neural networks.

Webpage - http://h2o.ai/ GitHub Repositories - https://github.com/h2oai H2O is not strictly a package for machine learning, instead they expose an API for doing fast and scalable machine learning for smarter applications which use big data.

Webpage - https://azure.microsoft.com/en-us/services/machine-learning GitHub Repositories - https://github.com/Azure?utf8=%E2%9C%93&query=MachineLearning  The machine learning / predictive analytics platform in Microsoft Azure is a fully managed cloud service that enables you to easily build, deploy, and share predictive analytics solutions.

This software basically allows you to drag and drop pre-built components (including machine learning models) and custom-built components which manipulate data sets into a process. This flow-chart is then compiled into a program and can be deployed as a web-service.

We have designed it with the following functionality in mind: 1) Support for commonly used models and examples: convnets, MLPs, RNNs, LSTMs, autoencoders, 2) Tight integration with nervanagpu kernels for fp16 and fp32 (benchmarks) on Maxwell GPUs, 3) Basic automatic differentiation support, 4) Framework for visualization, and 5) Swappable hardware backends ...'

A summary of core features include an N-dimensional array, routines for indexing, slicing, transposing, an interface to C, via LuaJIT, linear algebra routines, neural network, energy-based models, numeric optimization routines, Fast and efficient GPU support, Embeddable, with ports to iOS, Android and FPGA' - Torch Webpage (November 2015).

It is built on NumPy, SciPy, and matplotlib Open source, and exposes implementations of various machine learning models for classification, regression, clustering, dimensionality reduction, model selection, and data preprocessing.

Before committing to any one solution I would recommend doing a best-fit analysis to see which open source or proprietary machine learning package or software best matches your use-cases.

Despite this, they have a bad reputation due to the many unsuccessful attempts to use them in practice. In most cases, unsuccessful neural network implementations can be traced back to inappropriate neural network design decisions and general misconceptions about how they work.

For readers interested in getting more information, I have found the following books to be quite instructional when it comes to neural networks and their role in financial modelling and algorithmic trading. 

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