Introduction to Neural Networks

1. Introduction to Neural Networks

2. Neural Networks in the Brain • Human brain “computes” in an entirely different way from conventional digital computers. • The brain is highly complex, nonlinear, and parallel. • Organization of neurons to perform tasks much faster than computers. (Typical time taken in visual recognition tasks is 100–200 ms.) • Key features of the biological brain: experience shapes the wiring through plasticity, and hence learning becomes the central issue in neural networks.

3. Neural Networks as an Adaptive Machine • A neural network is a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experimental knowledge and making it available for use. • Neural networks resemble the brain: • Knowledge is acquired from the environment through a learning process. • Iner neuron connection strengths, known as synaptic weights, are used to store the acquired knowledge. • Procedure used for learning: learning algorithm. Weights, or even the topology can be adjusted.

4. Benefits of Neural Networks • Nonlinearity: nonlinear components, distributed nonlinearity • Input-output mapping: supervised learning, nonparametric statistical inference (model-free estimation, no prior assumptions) • Adaptivity: either retain or adapt. Can deal with non-stationary environments. Must overcome stability-plasticity dilemma. • Evidential response: decision plus confidence of the decision can be provided. • Contextual information: Every neuron in the network potentially influences every other neuron, so contextual information is dealt with naturally

5. Benefits of Neural Networks • Fault tolerance: performance degrades gracefully. • VLSI implementability: network of simple components. • Uniformity of analysis and design: common components (neurons), sharability of theories and learning algorithms, and seamless integration based on modularity. • Neurobiological analogy: Neural nets motivated by neurobiology, and neurobiology also turning to neural networks for insights and tools.

6. Human Brain • Stimulus → Receptors ⇔ Neural Net ⇔ Effectors → Response: Arbib (1987) • Neurons are slow: 10−3 s per operation, compared to 10−9 s of modern CPUs. • Huge number of neurons and on nections: 1010 neurons, 6 × 1013 connections in human brain. • Highly energy efficient: 10−16J in the brain vs. 10−6 J in modern computers

7. The Biological Neuron • Each neuron is a cell that uses biochemical reactions to receive, process and transmit information. • Each terminal button is connected to other neurons across a small gap called a synapse. • A neuron's dendritic tree is connected to a thousand neighbouring neurons. When one of those neurons fire, a positive or negative charge is received by one of the dendrites. The strengths of all the received charges are added together through the processes of spatial and temporal summation

8. Bias b x1 w1 Activation function Induced Field v Output y Input values x2 w2 Summing function xm wm weights Models of Neurons

9. Activation Functions

10. Stochastic Model • Instead of deterministic activation, stochastic activation can be done. • State of neuron +1,-1} • Probability of firing • Typical choice of where is a pseudo temperature. • When → 0, the neuron becomes deterministic. • Think of computer simulation

11. Signal Flow Graph • Nodes and links • Links: synaptic links and activation links. • Incoming edges: summation • Outgoing edges: replication • Architectural graph simplifies the above and abstracts out internal neuronal function.

12. Signal Flow Graph Example • Turn the above into a signal-flow graph

13. Feedback • Feedback gives dynamics (temporal aspect), and it is found in almost every part of the nervous system in every animal.

14. Feedback

15. Feedback • : • converge (infinite memory, fading) • linearly diverge • exponentially diverge

16. Definition of Neural Networks • An information processing system that has been developed as a generalization of mathematical models of human cognition or neurobiology, based on the assumptions that • Information processing occurs at many simple elements called neurons. • Signals are passed between neurons over connection links. • Each connection link has an associated weight, which typically multiplies the signal transmitted. • Each neuron applies an activation function (usually non-linear) to its net input (sum of weighted input signals) to determine its output signal.

17. Network Architectures • The connectivity of a neural network is intimately linked with the learning algorithm. • Single-layer feedforward networks: one input layer, one layer of computing units (output layer), acyclic connections. • Multilayer feedforward networks: one input layer, one (or more)hidden layers, and one output layer. Recurrent networks: feedback loop exists. • Recurrent networks: feedback loop exists. • Layers can be fully connected or partially connected.

18. Similarity Measures • Similar inputs from similar classes should produce similar representations, leading to classification into the same category. • Reciprocal of Euclidean distance == • Dot product(inner product) == • The two are related, when =1 ==

19. Similarity Measure • When two vectors and are drawn from two distributions: • Mean vector: • Mahalanobis distance: = • Covariance matrix