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Artificial neural networks ANN or connectionist systems are computing systems that are inspired by, but not identical to, biological neural networks that constitute animal brains. Such systems "learn" to perform tasks by considering examples, generally without being programmed with 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.

They do this without any prior knowledge of cats, for example, that they have fur, tails, whiskers and cat-like faces. Instead, they automatically generate identifying characteristics from the examples that they process. An ANN is based on a collection of connected units or nodes called artificial neurons , which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

An artificial neuron that receives a signal then processes it and can signal neurons connected to it. In ANN implementations, the "signal" at a connection is a real number , and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a weight that adjusts as learning proceeds.


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The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer the input layer , to the last layer the output layer , possibly after traversing the layers multiple times. The original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology.

ANNs have been used on a variety of tasks, including computer vision , speech recognition , machine translation , social network filtering, playing board and video games , medical diagnosis and even in activities that have traditionally been considered as reserved to humans, like painting [1]. Warren McCulloch and Walter Pitts [2] opened the subject by creating a computational model for neural networks.

Hebb [4] created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Farley and Clark [5] first used computational machines, then called "calculators", to simulate a Hebbian network. Rosenblatt [6] created the perceptron. In , Linnainmaa published the general method for automatic differentiation AD of discrete connected networks of nested differentiable functions.

In , he applied Linnainmaa's AD method to neural networks in the way that became widely used. In , max-pooling was introduced to help with least shift invariance and tolerance to deformation to aid in 3D object recognition. Hinton et al. In , Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images. Ciresan and colleagues [27] showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks. ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had had little success.

They soon reoriented towards improving empirical results, mostly abandoning attempts to remain true to their biological precursors. Neurons are connected to each other in various patterns, to allow the output of some neurons to become the input of others. The network forms a directed , weighted graph. ANNs retained the biological concept of artificial neurons , which receive input, combine the input with their internal state activation and an optional threshold using an activation function , and produce output using an output function.

The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.

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The important characteristic of the activation function is that it provides a smooth transition as input values change, i. The network consists of connections, each connection providing the output of one neuron as an input to another neuron. Each connection is assigned a weight that represents its relative importance.

The propagation function computes the input to a neuron from the outputs of its predecessor neurons and their connections as a weighted sum. The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer.

In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be fully connected , with every neuron in one layer connecting to every neuron in the next layer.

They can be pooling , where a group of neurons in one layer connect to a single neuron in the next layer, thereby reducing the number of neurons in that layer. A hyperparameter is a parameter whose value is set before the learning process begins. The values of parameters are derived via learning.

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Examples of hyperparameters include learning rate , the number of hidden layers and batch size. For example, the size of some layers can depend on the overall number of layers. Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights and optional thresholds of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate.

Convolutional Neural Networks - The Math of Intelligence (Week 4)

Even after learning, the error rate typically does not reach 0. If after learning, the error rates too high, the network typically must be redesigned.

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Practically this is done by defining a cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output almost certainly a cat and the correct answer cat is small. Learning attempts to reduce the total of the differences across the observations.

The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation. A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy.

Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate.

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A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change. While it is possible to define a cost function ad hoc , frequently the choice is determined by the functions desirable properties such as convexity or because it arises from the model e. Backpropagation is a method to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections.

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Technically, backprop calculates the gradient the derivative of the cost function associated with a given state with respect to the weights. The weight updates can be done via stochastic gradient descent or other methods, such as Extreme Learning Machines , [45] "No-prop" networks, [46] training without backtracking, [47] "weightless" networks, [48] [49] and non-connectionist neural networks.

The three major learning paradigms are supervised learning , unsupervised learning and reinforcement learning. They each correspond to a particular learning task. Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case the cost function is related to eliminating incorrect deductions.