# AI News, Neural Nets in Azure ML &ndash; Introduction to Net#

## Neural Nets in Azure ML &ndash; Introduction to Net#

One of the challenges when using neural networks is how to define a network topology given the variety of possible layer types, connections among them, and activation functions.

The network has 3 layers of neurons: an input layer of size 28*28 = 784, one hidden layer of size 100, and the output layer of size 10.

Here is the corresponding network definition in Net#: input Picture [28, 28];// Note that alternatively we could declare input layer as:// input Picture [28 * 28];// or just // input Picture [784];// Net# compiler will be able to infer the number of dimensions automatically. //

This defines a fully-connected (to the input layer &#39;Picture&#39;)// hidden layer of size 100 with sigmoid activation function// (which is a default activation function).hidden H [100] from Picture all; //

add a Net# definition to a neural network module in Azure ML, you drag the learner module onto the canvas (in this case &ldquo;Multiclass Neural Network&rdquo;) and in the properties window for the module, under &ldquo;Hidden layer specification,&rdquo;

this topology, you can run a simple experiment using default values for learning rate and initial weight diameter, while reducing number of iterations to 30 to result in faster training.

The experiment should run for less than 2 minutes, providing an accuracy of 97.7% (or 2.3% error), which is not bad given such a simple net and short training time. Net#&rsquo;s

constant literals are similar to C#, including decimal and hexadecimal integer literals, floating point literals, and string literals (including verbatim string literals) with escape sequence support. Prefixing

net, which should take about 4 minutes (30 iterations), you should get an accuracy of about 98.1% (error is 1.9%) which is certainly better than our previous single hidden layer net.

Using this topology, you can run a simple experiment using default values for learning rate and initial weight diameter, while reducing number of iterations to 30 to result in faster training.

The experiment should run for less than 2 minutes, providing an accuracy of 97.7% (or 2.3% error), which is not bad given such a simple net and short training time.

net, which should take about 4 minutes (30 iterations), you should get an accuracy of about 98.1% (error is 1.9%) which is certainly better than our previous single hidden layer net.

## Convolutional neural network

In machine learning, a convolutional neural network (CNN, or ConvNet) is a class of deep, feed-forward artificial neural networks, most commonly applied to analyzing visual imagery.

CNNs use a variation of multilayer perceptrons designed to require minimal preprocessing.[1] They are also known as shift invariant or space invariant artificial neural networks (SIANN), based on their shared-weights architecture and translation invariance characteristics.[2][3] Convolutional networks were inspired by biological processes[4] in that the connectivity pattern between neurons resembles the organization of the animal visual cortex.

A very high number of neurons would be necessary, even in a shallow (opposite of deep) architecture, due to the very large input sizes associated with images, where each pixel is a relevant variable.

The convolution operation brings a solution to this problem as it reduces the number of free parameters, allowing the network to be deeper with fewer parameters.[8] For instance, regardless of image size, tiling regions of size 5 x 5, each with the same shared weights, requires only 25 learnable parameters.

In this way, it resolves the vanishing or exploding gradients problem in training traditional multi-layer neural networks with many layers by using backpropagation[citation needed].

Convolutional networks may include local or global pooling layers[clarification needed], which combine the outputs of neuron clusters at one layer into a single neuron in the next layer.[9][10] For example, max pooling uses the maximum value from each of a cluster of neurons at the prior layer.[11] Another example is average pooling, which uses the average value from each of a cluster of neurons at the prior layer[citation needed].

Work by Hubel and Wiesel in the 1950s and 1960s showed that cat and monkey visual cortexes contain neurons that individually respond to small regions of the visual field.

Provided the eyes are not moving, the region of visual space within which visual stimuli affect the firing of a single neuron is known as its receptive field[citation needed].

Their 1968 paper[12] identified two basic visual cell types in the brain: The neocognitron [13] was introduced in 1980.[11][14] The neocognitron does not require units located at multiple network positions to have the same trainable weights.

This idea appears in 1986 in the book version of the original backpropagation paper.[15]:Figure 14 Neocognitrons were developed in 1988 for temporal signals.[clarification needed][16] Their design was improved in 1998,[17] generalized in 2003[18] and simplified in the same year.[19] LeNet-5, a pioneering 7-level convolutional network by LeCun et al.

Similarly, a shift invariant neural network was proposed for image character recognition in 1988.[2][3] The architecture and training algorithm were modified in 1991[20] and applied for medical image processing[21] and automatic detection of breast cancer in mammograms.[22] A

This design was modified in 1989 to other de-convolution-based designs.[24][25] The feed-forward architecture of convolutional neural networks was extended in the neural abstraction pyramid[26] by lateral and feedback connections.

Following the 2005 paper that established the value of GPGPU for machine learning,[27] several publications described more efficient ways to train convolutional neural networks using GPUs.[28][29][30][31] In 2011, they were refined and implemented on a GPU, with impressive results.[9] In 2012, Ciresan et al.

significantly improved on the best performance in the literature for multiple image databases, including the MNIST database, the NORB database, the HWDB1.0 dataset (Chinese characters), the CIFAR10 dataset (dataset of 60000 32x32 labeled RGB images),[11] and the ImageNet dataset.[32] While traditional multilayer perceptron (MLP) models were successfully used for image recognition[example needed], due to the full connectivity between nodes they suffer from the curse of dimensionality, and thus do not scale well to higher resolution images.

For example, in CIFAR-10, images are only of size 32x32x3 (32 wide, 32 high, 3 color channels), so a single fully connected neuron in a first hidden layer of a regular neural network would have 32*32*3 = 3,072 weights.

Also, such network architecture does not take into account the spatial structure of data, treating input pixels which are far apart in the same way as pixels that are close together.

Weight sharing dramatically reduces the number of free parameters learned, thus lowering the memory requirements for running the network and allowing the training of larger, more powerful networks.

The layer's parameters consist of a set of learnable filters (or kernels), which have a small receptive field, but extend through the full depth of the input volume.

During the forward pass, each filter is convolved across the width and height of the input volume, computing the dot product between the entries of the filter and the input and producing a 2-dimensional activation map of that filter.

Every entry in the output volume can thus also be interpreted as an output of a neuron that looks at a small region in the input and shares parameters with neurons in the same activation map.

When dealing with high-dimensional inputs such as images, it is impractical to connect neurons to all neurons in the previous volume because such a network architecture does not take the spatial structure of the data into account.

Convolutional networks exploit spatially local correlation by enforcing a local connectivity pattern between neurons of adjacent layers: each neuron is connected to only a small region of the input volume.

Since all neurons in a single depth slice share the same parameters, then the forward pass in each depth slice of the CONV layer can be computed as a convolution of the neuron's weights with the input volume (hence the name: convolutional layer).

The result of this convolution is an activation map, and the set of activation maps for each different filter are stacked together along the depth dimension to produce the output volume.

The pooling layer serves to progressively reduce the spatial size of the representation, to reduce the number of parameters and amount of computation in the network, and hence to also control overfitting.

The most common form is a pooling layer with filters of size 2x2 applied with a stride of 2 downsamples at every depth slice in the input by 2 along both width and height, discarding 75% of the activations.

Average pooling was often used historically but has recently fallen out of favor compared to max pooling, which works better in practice.[34] Due to the aggressive reduction in the size of the representation, the trend is towards using smaller filters[35] or discarding the pooling layer altogether.[36] Region of Interest pooling (also known as RoI pooling) is a variant of max pooling, in which output size is fixed and input rectangle is a parameter.[37] Pooling is an important component of convolutional neural networks for object detection based on Fast R-CNN[38] architecture.

Preserving more information about the input would require keeping the total number of activations (number of feature maps times number of pixel positions) non-decreasing from one layer to the next.

In stochastic pooling,[43] the conventional deterministic pooling operations are replaced with a stochastic procedure, where the activation within each pooling region is picked randomly according to a multinomial distribution, given by the activities within the pooling region.

Since the degree of model overfitting is determined by both its power and the amount of training it receives, providing a convolutional network with more training examples can reduce overfitting.

Since these networks are usually trained with all available data, one approach is to either generate new data from scratch (if possible) or perturb existing data to create new ones.

For example, input images could be asymmetrically cropped by a few percent to create new examples with the same label as the original.[45] One of the simplest methods to prevent overfitting of a network is to simply stop the training before overfitting has had a chance to occur.

Another simple way to prevent overfitting is to limit the number of parameters, typically by limiting the number of hidden units in each layer or limiting network depth.

Limiting the number of parameters restricts the predictive power of the network directly, reducing the complexity of the function that it can perform on the data, and thus limits the amount of overfitting.

simple form of added regularizer is weight decay, which simply adds an additional error, proportional to the sum of weights (L1 norm) or squared magnitude (L2 norm) of the weight vector, to the error at each node.

after seeing a new shape once they can recognize it from a different viewpoint.[47] Currently, the common way to deal with this problem is to train the network on transformed data in different orientations, scales, lighting, etc.

The pose relative to retina is the relationship between the coordinate frame of the retina and the intrinsic features' coordinate frame.[48] Thus, one way of representing something is to embed the coordinate frame within it.

The vectors of neuronal activity that represent pose ('pose vectors') allow spatial transformations modeled as linear operations that make it easier for the network to learn the hierarchy of visual entities and generalize across viewpoints.

In 2012 an error rate of 0.23 percent on the MNIST database was reported.[11] Another paper on using CNN for image classification reported that the learning process was 'surprisingly fast';

in the same paper, the best published results as of 2011 were achieved in the MNIST database and the NORB database.[9] When applied to facial recognition, CNNs achieved a large decrease in error rate.[50] Another paper reported a 97.6 percent recognition rate on '5,600 still images of more than 10 subjects'.[4] CNNs were used to assess video quality in an objective way after manual training;

the resulting system had a very low root mean square error.[51] The ImageNet Large Scale Visual Recognition Challenge is a benchmark in object classification and detection, with millions of images and hundreds of object classes.

The winner GoogLeNet[53] (the foundation of DeepDream) increased the mean average precision of object detection to 0.439329, and reduced classification error to 0.06656, the best result to date.

That performance of convolutional neural networks on the ImageNet tests was close to that of humans.[54] The best algorithms still struggle with objects that are small or thin, such as a small ant on a stem of a flower or a person holding a quill in their hand.

For example, they are not good at classifying objects into fine-grained categories such as the particular breed of dog or species of bird, whereas convolutional neural networks handle this.

One approach is to treat space and time as equivalent dimensions of the input and perform convolutions in both time and space.[56][57] Another way is to fuse the features of two convolutional neural networks, one for the spatial and one for the temporal stream [58][59][60].

CNN models are effective for various NLP problems and achieved excellent results in semantic parsing,[63] search query retrieval,[64] sentence modeling,[65] classification,[66] prediction[67] and other traditional NLP tasks.[68] CNNs have been used in drug discovery.

In 2015, Atomwise introduced AtomNet, the first deep learning neural network for structure-based rational drug design.[69] The system trains directly on 3-dimensional representations of chemical interactions.

Similar to how image recognition networks learn to compose smaller, spatially proximate features into larger, complex structures,[70] AtomNet discovers chemical features, such as aromaticity, sp3 carbons and hydrogen bonding.

Subsequently, AtomNet was used to predict novel candidate biomolecules for multiple disease targets, most notably treatments for the Ebola virus[71] and multiple sclerosis.[72] CNNs have been used in the game of checkers.

The learning process did not use prior human professional games, but rather focused on a minimal set of information contained in the checkerboard: the location and type of pieces, and the piece differential[clarify].

Ultimately, the program (Blondie24) was tested on 165 games against players and ranked in the highest 0.4%.[73][74] It also earned a win against the program Chinook at its 'expert' level of play.[75] CNNs have been used in computer Go.

In December 2014, Clark and Storkey published a paper showing that a CNN trained by supervised learning from a database of human professional games could outperform GNU Go and win some games against Monte Carlo tree search Fuego 1.1 in a fraction of the time it took Fuego to play.[76] Later it was announced that a large 12-layer convolutional neural network had correctly predicted the professional move in 55% of positions, equalling the accuracy of a 6 dan human player.

When the trained convolutional network was used directly to play games of Go, without any search, it beat the traditional search program GNU Go in 97% of games, and matched the performance of the Monte Carlo tree search program Fuego simulating ten thousand playouts (about a million positions) per move.[77] A

couple of CNNs for choosing moves to try ('policy network') and evaluating positions ('value network') driving MCTS were used by AlphaGo, the first to beat the best human player at the time.[78] For many applications, little training data is available.

Other deep reinforcement learning models preceded it.[81] Convolutional deep belief networks (CDBN) have structure very similar to convolutional neural networks and are trained similarly to deep belief networks.

time delay neural network allows speech signals to be processed time-invariantly, analogous to the translation invariance offered by CNNs.[84] They were introduced in the early 1980s.

## 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] 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] 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.

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).

i

&#x2211;

i

w

i

g

i

(

x

)

(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.

i

1

2

n

&#x2217;

&#x2217;

&#x2217;

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.

(

f

(

x

)

&#x2212;

y

)

2

D

D

C

&#x005E;

1

N

i

=

1

N

i

i

2

D

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.

exp

&#x2061;

(

x

j

)

&#x2211;

k

exp

&#x2061;

(

x

k

)

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).

2

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).

t

t

t

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.

s

1

s

n

a

1

a

m

t

t

t

t

t

+

1

t

t

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&#160;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.

x

&#x007E;

x

&#x007E;

x

&#x007E;

x

&#x007E;

x

&#x007E;

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.

Each block estimates the same final label class y, and its estimate is concatenated with original input X to form the expanded input for the next block.

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&#160;– 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.

In the section on linear classification we computed scores for different visual categories given the image using the formula $$s = W x$$, where $$W$$ was a matrix and $$x$$ was an input column vector containing all pixel data of the image.

In the case of CIFAR-10, $$x$$ is a [3072x1] column vector, and $$W$$ is a [10x3072] matrix, so that the output scores is a vector of 10 class scores.

There are several choices we could make for the non-linearity (which we’ll study below), but this one is a common choice and simply thresholds all activations that are below zero to zero.

Notice that the non-linearity is critical computationally - if we left it out, the two matrices could be collapsed to a single matrix, and therefore the predicted class scores would again be a linear function of the input.

three-layer neural network could analogously look like $$s = W_3 \max(0, W_2 \max(0, W_1 x))$$, where all of $$W_3, W_2, W_1$$ are parameters to be learned.

The area of Neural Networks has originally been primarily inspired by the goal of modeling biological neural systems, but has since diverged and become a matter of engineering and achieving good results in Machine Learning tasks.

Approximately 86 billion neurons can be found in the human nervous system and they are connected with approximately 10^14 - 10^15 synapses.

The idea is that the synaptic strengths (the weights $$w$$) are learnable and control the strength of influence (and its direction: excitory (positive weight) or inhibitory (negative weight)) of one neuron on another.

Based on this rate code interpretation, we model the firing rate of the neuron with an activation function $$f$$, which represents the frequency of the spikes along the axon.

Historically, a common choice of activation function is the sigmoid function $$\sigma$$, since it takes a real-valued input (the signal strength after the sum) and squashes it to range between 0 and 1.

An example code for forward-propagating a single neuron might look as follows: In other words, each neuron performs a dot product with the input and its weights, adds the bias and applies the non-linearity (or activation function), in this case the sigmoid $$\sigma(x) = 1/(1+e^{-x})$$.

As we saw with linear classifiers, a neuron has the capacity to “like” (activation near one) or “dislike” (activation near zero) certain linear regions of its input space.

With this interpretation, we can formulate the cross-entropy loss as we have seen in the Linear Classification section, and optimizing it would lead to a binary Softmax classifier (also known as logistic regression).

The regularization loss in both SVM/Softmax cases could in this biological view be interpreted as gradual forgetting, since it would have the effect of driving all synaptic weights $$w$$ towards zero after every parameter update.

The sigmoid non-linearity has the mathematical form $$\sigma(x) = 1 / (1 + e^{-x})$$ and is shown in the image above on the left.

The sigmoid function has seen frequent use historically since it has a nice interpretation as the firing rate of a neuron: from not firing at all (0) to fully-saturated firing at an assumed maximum frequency (1).

Also note that the tanh neuron is simply a scaled sigmoid neuron, in particular the following holds: $$\tanh(x) = 2 \sigma(2x) -1$$.

Other types of units have been proposed that do not have the functional form $$f(w^Tx + b)$$ where a non-linearity is applied on the dot product between the weights and the data.

TLDR: “What neuron type should I use?” Use the ReLU non-linearity, be careful with your learning rates and possibly monitor the fraction of “dead” units in a network.

For regular neural networks, the most common layer type is the fully-connected layer in which neurons between two adjacent layers are fully pairwise connected, but neurons within a single layer share no connections.

Working with the two example networks in the above picture: To give you some context, modern Convolutional Networks contain on orders of 100 million parameters and are usually made up of approximately 10-20 layers (hence deep learning).

The full forward pass of this 3-layer neural network is then simply three matrix multiplications, interwoven with the application of the activation function: In the above code, W1,W2,W3,b1,b2,b3 are the learnable parameters of the network.

Notice also that instead of having a single input column vector, the variable x could hold an entire batch of training data (where each input example would be a column of x) and then all examples would be efficiently evaluated in parallel.

Neural Networks work well in practice because they compactly express nice, smooth functions that fit well with the statistical properties of data we encounter in practice, and are also easy to learn using our optimization algorithms (e.g.

Similarly, the fact that deeper networks (with multiple hidden layers) can work better than a single-hidden-layer networks is an empirical observation, despite the fact that their representational power is equal.

As an aside, in practice it is often the case that 3-layer neural networks will outperform 2-layer nets, but going even deeper (4,5,6-layer) rarely helps much more.

We could train three separate neural networks, each with one hidden layer of some size and obtain the following classifiers: In the diagram above, we can see that Neural Networks with more neurons can express more complicated functions.

For example, the model with 20 hidden neurons fits all the training data but at the cost of segmenting the space into many disjoint red and green decision regions.

The subtle reason behind this is that smaller networks are harder to train with local methods such as Gradient Descent: It’s clear that their loss functions have relatively few local minima, but it turns out that many of these minima are easier to converge to, and that they are bad (i.e.

Conversely, bigger neural networks contain significantly more local minima, but these minima turn out to be much better in terms of their actual loss.

In practice, what you find is that if you train a small network the final loss can display a good amount of variance - in some cases you get lucky and converge to a good place but in some cases you get trapped in one of the bad minima.

10.4: Neural Networks: Multilayer Perceptron Part 1 - The Nature of Code

In this video, I move beyond the Simple Perceptron and discuss what happens when you build multiple layers of interconnected perceptrons ("fully-connected ...

Convolutional Neural Networks (CNNs) explained

21 in Machine Leaning / Deep Learning for Programmers Playlist In this video, ..

How Convolutional Neural Networks work

A gentle guided tour of Convolutional Neural Networks. Come lift the curtain and see how the magic is done. For slides and text, check out the accompanying ...

Max Pooling in Convolutional Neural Networks explained

In this video, we start out by explaining what max pooling is, and we show how it's calculated by looking at some examples. We then discuss the motivation for ...

Neural Networks (1): Basics

The basic form of a feed-forward multi-layer perceptron / neural network; example activation functions.

Recurrent Neural Networks - Ep. 9 (Deep Learning SIMPLIFIED)

Our previous discussions of deep net applications were limited to static patterns, but how can a net decipher and label patterns that change with time?

Layers in a Neural Network explained

In this video, we explain the concept of layers in a neural network and show how to create and specify layers in code with Keras. Follow deeplizard on Twitter: ...

Neural Networks 6: solving XOR with a hidden layer

Neural Networks Demystified [Part 4: Backpropagation]

Backpropagation as simple as possible, but no simpler. Perhaps the most misunderstood part of neural networks, Backpropagation of errors is the key step that ...

Building Deep Multiple Hidden Layer Neural Network with TensorFlow

In this lesson you will learn how to: -- Build a deep neural network -- Choose number of layers and neurons -- Training a deep densely connected net Hope you ...