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Chapter 11 Neural Networks http://www.msnbc.msn.com/id/10401930 http://www.msnbc.msn.com/id/15014341/ http://www.msnbc.msn.com/id/10401930 1 2 Neural Network What is a neural network? Neural Networks are a different paradigm for computing: von Neumann machines are based on the processing/memory abstraction of human information processing. neural networks are based on the parallel architecture of animal brains. 3 Neural networks are a form of multiprocessor computer system, with simple processing elements a high degree of interconnection simple scalar messages adaptive interaction between elements 4 A biological neuron may have as many as 10,000 different inputs, and may send its output (the presence or absence of a short-duration spike) to many other neurons. Neurons are wired up in a 3dimensional pattern. Real brains, however, are orders of magnitude more complex than any artificial neural network so far considered. 5 Neural networks are being used: in investment analysis: to attempt to predict the movement of stocks currencies etc., from previous data. There, they are replacing earlier simpler linear models. in signature analysis: as a mechanism for comparing signatures made (e.g. in a bank) with those stored. This is one of the first large-scale applications of neural networks in the USA, and is also one of the first to use a neural network chip. 6 in process control: there are clearly applications to be made here: most processes cannot be determined as computable algorithms. In monitoring: networks have been used to monitor – the state of aircraft engines. By monitoring vibration levels and sound, early warning of engine problems can be given. – British Rail have also been testing a similar application monitoring diesel engines. in marketing: networks have been used to improve marketing mail shots. One technique is to run a test mailshot, and look at the pattern of returns from this. The idea is to find a predictive mapping from the data known about the clients to how they have responded. This mapping is then used to direct further mailshots. 7 New Applications New Application areas: Pen PC's PC's where one can write on a tablet, and the writing will be recognized and translated into (ASCII) text. Speech and Vision recognition systems Not new, but Neural Networks are becoming increasingly part of such systems. They are used as a system component, in conjunction with traditional computers. White goods and toys As Neural Network chips become available, the possibility of simple cheap systems which have learned to recognize simple entities (e.g. walls looming, or simple commands like Go, or Stop), may lead to their incorporation in toys and washing machines etc. Already the Japanese are using a related technology, fuzzy logic, in this way. There is considerable interest in the combination of fuzzy and neural technologies. 8 Chapter 11 Contents (1) Biological Neurons Artificial Neurons Perceptrons Multilayer Neural Networks Backpropagation 9 Chapter 11 Contents (2) Recurrent Networks Hopfield Networks Bidirectional Associative Memories Kohonen Maps Hebbian Learning Evolving Neural Networks 10 Human Brains 11 12 13 The human brain has a huge number of synapses. Each of the 1012 neurons (1,000 billion, i.e. 1 trillion) has on average 7,000 synaptic connections to other neurons. It hast been estimated that the brain of a three-year-old child has about 1016 synapses (10,000 trillion). This number declines with age, stabilizing by adulthood. Estimates vary for an adult, ranging from 1015 to 5 x 1015 synapses (1,000 to 5,000 trillion).[3] 14 Biological Neurons The human brain is made up of billions of simple processing units – neurons. Inputs are received on dendrites, and if the input levels are over a threshold, the neuron fires, passing a signal through the axon to the synapse which then connects to another neuron. 15 True Neuron We Know Now 16 Functions of Neurons Neurons are cells that send and receive electro-chemical signals to and from the brain and nervous system. There are about 100 billion neurons in the brain. There are many more glial cells; they provide support functions for the neurons, and are far more numerous than neurons. 17 Neuron Neurons are nerve cells that transmit nerve signals to and from the brain at up to 200 mph. The neuron consists of a cell body (or soma) with branching dendrites (signal receivers) and a projection called an axon, which conducts the nerve signal. At the other end of the axon, the axon terminals transmit the electro-chemical signal across a synapse (the gap between the axon terminal and the receiving cell). The word "neuron" was coined by the German scientist Heinrich Wilhelm Gottfried von Waldeyer-Hartz in 1891 (he also coined the term "chromosome"). 18 Types of Neurons There are many type of neurons. They vary in size from 4 microns (.004 mm) to 100 microns (.1 mm) in diameter. Their length varies from a fraction of an inch to several feet. 19 Axon The axon, a long extension of a nerve cell, and take information away from the cell body. Bundles of axons are known as nerves or, within the CNS (central nervous system), as nerve tracts or pathways. Dendrites bring information to the cell body. 20 Myelin Myelin coats and insulates the axon (except for periodic breaks called nodes of Ranvier), increasing transmission speed along the axon. Myelin is manufactured by Schwann's cells, and consists of 7080% lipids (fat) and 20-30% protein. 21 Cell Body -- Soma The cell body (soma) contains the neuron's nucleus (with DNA and typical nuclear organelles). Dendrites branch from the cell body and receive messages. 22 Neuron A typical neuron has about 1,000 to 10,000 synapses (that is, it communicates with 1,000-10,000 other neurons, muscle cells, glands, etc.). 23 Life Span of a Neuron Unlike most other cells, neurons cannot re-grow after damage (except neurons from the hippocampus). Fortunately, there are about 100 billion neurons in the brain. 24 GLIAL CELLS GLIAL CELLS Glial cells make up 90 percent of the brain's cells. Glial cells are nerve cells that don't carry nerve impulses. The various glial (meaning "glue") cells perform many important functions, including: digestion of parts of dead neurons, manufacturing myelin for neurons, providing physical and nutritional support for neurons, and more. Types of glial cells include Schwann's Cells, Satellite Cells, Microglia, Oligodendroglia, and Astroglia. 25 Artificial Neurons 26 Artificial Neurons (1) Artificial neurons are based on biological neurons. Each neuron in the network receives one or more inputs. An activation function is applied to the inputs, which determines the output of the neuron – the activation level. The charts on the right show three typical activation functions. 27 Artificial Neurons (2) A typical activation function works as follows: Each node i has a weight, wi associated with it. The input to node i is xi. t is the threshold. So if the weighted sum of the inputs to the neuron is above the threshold, then the neuron fires. 28 Perceptrons (1) A perceptron is a single neuron that classifies a set of inputs into one of two categories (usually 1 or -1). If the inputs are in the form of a grid, a perceptron can be used to recognize visual images of shapes. The perceptron usually uses a step function, which returns 1 if the weighted sum of inputs exceeds a threshold, and –1 otherwise. 29 Perceptrons (2) The perceptron is trained as follows: First, inputs are given random weights (usually between –0.5 and 0.5). An item of training data is presented. If the perceptron mis-classifies it, the weights are modified according to the following: e is the size of the error, and a is the learning rate, between 0 and 1. 30 Perceptrons (3) Perceptrons can only classify linearly separable functions. The first of the following graphs shows a linearly separable function (OR). The second is not linearly separable (Exclusive-OR). 31 Multilayer Neural Networks Multilayer neural networks can classify a range of functions, including non linearly separable ones. Each input layer neuron connects to all neurons in the hidden layer. The neurons in the hidden layer connect to all neurons in the output A feed-forward network layer. 32 Backpropagation (1) Multilayer neural networks learn in the same way as perceptrons. However, there are many more weights, and it is important to assign credit (or blame) correctly when changing weights. Backpropagation networks use the sigmoid activation function, as it is easy to differentiate: 33 Backpropagation (2) For node j, Xj is the output Yj is the output n is the number of inputs to node j j is the threshold for j After values are fed forward through the network, errors are fed back to modify the weights in order to train the network. For each node, we calculate an error gradient. 34 Backpropagation (3) For a node k in the output layer, the error ek is the difference between the desired output and the actual output. The error gradient for k is: Similarly, for a node j in the hidden layer: Now the weights are updated as follows: is the learning rate, (a positive number below 1) 35 Recurrent Networks Feed forward networks do not have memory. Recurrent networks can have connections between nodes in any layer, which enables them to store data – a memory. Recurrent networks can be used to solve problems where the solution depends on previous inputs as well as current inputs (e.g. predicting stock market movements). 36 Hopfield Networks A Hopfield Network is a recurrent network. Use a sign activation function: If a neuron receives a 0 as an input it does not change state. Inputs are usually represented as matrices. The network is trained to represent a set of attractors, or stable states. Any input will be mapped to an output state which is the attractor closest to the input. A Hopfield network is autoassociative – it can only associate an item with itself or a similar37 one. Bidirectional Associative Memories A BAM is a heteroassociative memory: Like the brain, it can learn to associate one item with another completely unrelated item. The network consists of two fully connected layers of nodes – every node in one layer is connected to every node in the other layer. 38 Kohonen Maps An unsupervised learning system. Two layers of nodes: an input layer and a cluster (output) layer. Uses competitive learning: Every input is compared with the weight vectors of each node in the cluster node. The node which most closely matches the input, fires. This is the classification of the input. Euclidean distance is used. The winning node has its weight vector modified to be closer to the input vector. 39 Kohonen Maps It is also called self-organizing feature maps. It uses the winner-take-all algorithm. -- only one neuron provides the output of the network in response to a given input. It will be the neuron that has the highest activation level. 40 The input and the weight 1 wi 2 1 3 xj 1 2 41 The input and the weight di n wi xj 2 =4 j 1 42 The neuron for which that has the smallest di is the winner This neuron will have its weight vector updated as follows: Wij Wij + α(xj – Wij) 43 44 Kohonen Maps (example) The nodes in the cluster layer are arranged in a grid, as shown: The diagram on the left shows the training data. Initially, the weights are arranged as shown here: 45 Kohonen Maps (example) After training, the weight vectors have been rearranged to match the training data: 46 Hebbian Learning (1) Hebb’s law: “When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased”. Hence, if two neurons that are connected together fire at the same time, the weights of the connection between them is strengthened. 47 Hebbian Learning (2) The activity product rule is used to modify the weights of a connection between two nodes that fire at the same time: is the learning rate; xi is the input to node i and yi is the output of node i. Hebbian networks usually also use a forgetting factor, which decreases the weight of the connection between if two nodes if they fire at different times. 48 Evolving Neural Networks Neural networks can be susceptible to local maxima. Evolutionary methods (genetic algorithms) can be used to determine the starting weights for a neural network, thus avoiding these kinds of problems. 49