Artificial Neural Networks Neural networks to the rescue

Artificial Neural Networks

Neural networks to the rescue Neural network: information processing paradigm inspired by biological nervous systems, such as our brain p Structure: large number of highly interconnected processing elements (neurons) working together p Like people, they learn from experience (by example) p

Neural networks to the rescue p p Neural networks are configured for a specific application, such as pattern recognition or data classification, through a learning process In a biological system, learning involves adjustments to the synaptic connections between neurons same for artificial neural networks (ANNs)

Where can neural network systems help When we can't formulate an algorithmic solution. p When we can get lots of examples of the behavior we require. ‘learning from experience’ p When we need to pick out the structure from existing data. p

Inspiration from Neurobiology p p A neuron: many-inputs / one-output unit output can be excited or not excited incoming signals from other neurons determine if the neuron shall excite ("fire") Output subject to attenuation in the synapses, which are junction parts of the neuron

Mathematical representation The neuron calculates a weighted sum of inputs and compares it to a threshold. If the sum is higher than the threshold, the output is set to 1, otherwise to -1. Non-linearity

The Mc. Culloch-Pitts Model of Neuron Figure : Symbolic Illustration of Linear Threshold Gate The Mc. Culloch-Pitts model of a neuron is simple yet has substantial computing potential. It also has a precise mathematical definition. However, this model is so simplistic that it only generates a binary output and also the weight and threshold values are fixed. The neural computing algorithm has diverse features for various applications. Thus, we need to obtain the neural model with more flexible computational features. p

A simple perceptron p p It’s a single-unit network Change the weight by an amount proportional to the difference between the desired output and the actual output. Δ Wi = η * (D-Y). Ii Input Learning rate Actual output Desired output Perceptron Learning Rule

Example: A simple single unit adaptive network p The network has 2 inputs, and one output. All are binary. The output is n n p 1 if W 0 I 0 + W 1 I 1 + Wb > 0 0 if W 0 I 0 + W 1 I 1 + Wb ≤ 0 We want it to learn simple OR: output a = 1 if either I 0 or I 1 is 1.

A simplest network 10

Solving XOR problem using the simplest network 11

Solving XOR problem using the simplest network Neuron 1 Neuron 2 Neuron 3 Inputs # XOR= Z output 1) 1 1 5 1 1 2) 1 -1 -5 -1 7 1 -1 -1 -1 3) -1 1 7 1 -1 -1 -1 4) -1 -1 1 1 5 1 1 12

Learning From experience: examples / training data p Strength of connection between the neurons is stored as a weight-value for the specific connection p Learning the solution to a problem = changing the connection weights p

Operation mode Fix weights (unless in online learning) p Network simulation = input signals flow through network to outputs p Output is often a binary decision p Inherently parallel p Simple operations and threshold: fast decisions and real-time response p

Single-Layer Network p p structure of connecting neurons into a network is by layers. input layer : neurons are to only pass and distribute the inputs and perform no computation. Thus, the only true layer of neurons is the on the right. Each of the inputs x 1, x 2, …x. N is connected to every artificial neuron in the output layer through the connection weight.

Single-Layer Network p p Since every value of outputs y 1, y 2, …y. N is calculated from the same set of input values, each output is varied based on the connection weights. Although the presented network is fully connected, the true biological neural network may not have all possible connections - the weight value of zero can be represented as ``no connection".

Multilayer Network p p p To achieve higher level of computational capabilities, a more complex structure of neural network is required. Figure shows the multilayer neural network which distinguishes itself from the single-layer network by having one or more hidden layers. In this multilayer structure, the input nodes pass the information to the units in the first hidden layer, then the outputs from the first hidden layer are passed to the next layer, and so on.

Multilayer Network p p p Multilayer network can be also viewed as cascading of groups of single-layer networks. The level of complexity in computing can be seen by the fact that many singlelayer networks are combined into this multilayer network. The designer of an artificial neural network should consider how many hidden layers are required, depending on complexity in desired computation.

Multilayer Network - Inter-layer connections p Fully connected n p Partially connected n p n There is another set of connections carrying the output of the neurons of the second layer into the neurons of the first layer. Feed forward and bi-directional connections could be fully- or partially connected. Hierarchical n p The neurons on the first layer send their output to the neurons on the second layer, but they do not receive any input back form the neurons on the second layer. Bi-directional n p A neuron of the first layer does not have to be connected to all neurons on the second layer. Feed forward n p Each neuron on the first layer is connected to every neuron on the second layer. If a neural network has a hierarchical structure, the neurons of a lower layer may only communicate with neurons on the next level of layer. Resonance n The layers have bi-directional connections, and they can continue sending messages across the connections a number of times until a certain condition is achieved.

Evolving networks p Continuous process of: n n n p Evaluate output Adapt weights Take new inputs “Learning” ANN evolving causes stable state of the weights, but neurons continue working: network has ‘learned’ dealing with the problem

Learning performance Network architecture p Learning method: p n n n p Supervised learning: have a teacher, telling you where to go Unsupervised learning: no teacher, net learns by itself Reinforcement learning: have a critic, wrong or correct Type of learning used depends on task at hand.

Where are NN used? Recognizing and matching complicated, vague, or incomplete patterns p Data is unreliable p Problems with noisy data p n n n Prediction Classification Data association Data conceptualization Filtering Planning

Applications p Prediction: learning from past experience n n n p pick the best stocks in the market predict weather identify people with cancer risk Classification n Image processing Predict bankruptcy for credit card companies Risk assessment

Applications p Recognition n p Pattern recognition: SNOOPE (bomb detector in U. S. airports) Character recognition Handwriting: processing checks Data association n Not only identify the characters that were scanned but identify when the scanner is not working properly

Strengths of a Neural Network p p Power: Model complex functions, nonlinearity built into the network Ease of use: n n p Learn by example Very little user domain-specific expertise needed Intuitively appealing: based on model of biology, will it lead to genuinely intelligent computers/robots? Neural networks cannot do anything that cannot be done using traditional computing techniques, BUT they can do some things which would otherwise be very difficult.

General Advantages p Advantages n n n p Disadvantages n n p Adapt to unknown situations Robustness: fault tolerance due to network redundancy Autonomous learning and generalization Not exact Large complexity of the network structure For motion planning?