Introduction to Neural Net

1. Introduction to Neural Net CS480 Computer Science Seminar Fall 2002

2. Characteristics not present in von Neumann or modern parallel computers

3. Typical tasks a neural net is capable of performing • Pattern classification • Clustering/categorization • Function approximation • prediction/forecasting • Optimization • Content-addressable memory • control

22. Kohonen’s Self-Organizing Map

25. Neural network definition • A machine that is designed to model the way in which the brain performs a particular task or function of interest. • It is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles brain in two respects: 1. Knowledge is acquired through learning process, 2. Interneuron connection strengths known as synaptic weights are used to stored the knowledge.

26. Some interesting facts • Silicon gate speed: 10-9 sec • Neural event: 10-3 sec • # gates on Pentium III: < 107 • # neurons in human brain: 1010 with 60x1012 synapses or connections • Power consumption: for human brain---10-16 joules per operations per second; for today's best computer---10-6 joules per operations per second

27. Some interesting facts (cont’d) • The brain is a highly complex, nonlinear, and parallel processor. • Brain is superior in performing pattern recognition, perception, and motor control), e.g., it takes a brain 100-200 msec to recognize a familiar face embedded in an unfamiliar scene (will take days for the computer to do the similar tasks)

28. Some interesting facts (cont’d) • Brain has the ability to build up its own rules through “experience”over the years with most dramatic development in the first two years from birth (about 106 synapses formed per second)

29. Neural net architecture • Feed-forward neural net • Single layer • Multi-layer • Recurrent neural net • There are closed loops (feedback) paths.

30. Training the neural net • Training: setting the weights • Supervised • Unsupervised

31. Supervised learning • Supervised training: presenting a sequence of training vectors or patterns, each is associated with an associated target output vector. The weight is then adjusted according to a learning algorithm. • Examples • Pattern classification: the output is either 1 or –1 (belong or not belong to the category) • Patten association: to associate a set of input vectors with a corresponding set of output vectors (the neural net is called associative memory). After training, the the neural net can identify input vectors that are sufficiently close to (but not necessary the same as the input vectors).

32. History of neural net • 1940s: McCulloch-Pitts neurons (perform logic/combinational functions); introduced the idea of “threshold”. • 1949: Hebb learning algorithm---if two neurons are active, the connection strength (weight) should be increased. • 1950s and 1960s: the first golden age of neural net • Perceptrons (Rosenblatt) for pattern recognition • Adaline (adaptive linear neurons). • 1970s: the quiet years (research funding stopped) • Kohonen, Anderson, Grossberg, and Carpenter

33. History of neural net (cont’d) • 1980s: • Backpropagation (of errors) learning algorithm • Hopfield nets: capable of solving constraint satisfaction problems such as traveling salesman problem • Neocognitron: a self-organizing neural for pattern recognition (position or rotation-distorted characters) • Boltzmann machine: non-deterministic neural net (weights or activations are changed on the basis of a probabilistic density function) • Hardware implementation: digital and analog implementations using using VLSI technology

34. Neural net architecture • Feed-forward neural net • Single layer • Multi-layer • Recurrent neural net • There are closed loops (feedback) paths.

35. Training the neural net • Training: setting the weights • Supervised • Unsupervised

36. Supervised learning • Supervised training: presenting a sequence of training vectors or patterns, each is associated with an associated target output vector. The weight is then adjusted according to a learning algorithm. • Examples • Pattern classification: the output is either 1 or –1 (belong or not belong to the category) • Patten association: to associate a set of input vectors with a corresponding set of output vectors (the neural net is called associative memory). After training, the net is the neural net can identify input vectors that are sufficiently close to (but not necessary the same as the input vecotrs)

37. A simple example: McCulloch-Pitts neurons that perform logic operations • Presumption: • Binary activation: neuron either fires or does not fire • Neurons are connected by directed, weighted paths • A connection path is excitatory if the weight on the path is positive; otherwise, its inhibitory • Each neuron has a fixed threshold such that if the net input into a neuron is greater than the threshold, the neuron fires. • The threshold is set so that inhibition is absolute, i.e., any nonzero inhibitory input will prevent the neuron from firing • It takes one time step for a signal to pass over one connection link

38. McCulloch-Pitts Neuron: AND function The threshold on y is 2

39. McCulloch-Pitts Neuron: OR function

40. McCulloch-Pitts Neuron: OR function The threshold on y is 2

41. McCulloch-Pitts Neuron: AND-NOT function

42. McCulloch-Pitts Neuron: AND-NOT function The threshold on y is 2

43. McCulloch-Pitts Neural net: XOR function The threshold on y is 2

44. McCulloch-Pitts Neural net: XOR function The threshold on y is 2

45. McCulloch-Pitts Neural net application: modeling the perception of heat and cold • Interesting physiological phenomenon: if cold stimulus is applied to a person’s skin for a very short period of time, the person will perceive heat. If the same stimulus is applied for a longer period, the person will perceive cold.

46. McCulloch-Pitts Neural net: modeling the perception of heat and cold (time step functions are included in the modeling)

47. A cold stimulus applied for one time step

48. A cold stimulus applied for two time steps

49. Another example: character recognition

50. Noisy input