Models of the brain hardware Meet the Neurons Models of the brain hardware

A Real Neuron The Neuron                                                                                                           

Mcculloch-pitts 1940’s Y = f(next) = f( S wi xi + b) Wi are weights Xi are inputs B is a bias term F() is activation function F = 1 if next >= 0 else -1

Activation Functions Modified Mcculloch-pitts The function shown before is a threshold function Tanh function Logistic

Human Brain Neuron Speed - 10-3 seconds per operation Brain weights about 3 pounds and at rest consumes 20% of the bodies oxygen. Estimates place neuron count at 1012 to 1014 Connectivity can be 10,000

What is the capacity of the brain? Estimate the MIPS of a brain Estimate the MIPS needed by a computer to simulate the brain

Structure The cortex is estimated to be 6 layers The brain does recognition type computations is 100-200 milliseconds The brain clearly uses some specialized structures.

Survey of Artificial Neural Networks

The Perceptron Rosenblatt - 1950’s Linear classifiers Mcculloch-pitts neurons: x1 1 y1 x2 y2 2 xn m ym

Multi-layer Feed Forward x1 1 1 x2 2 2 xn m m

Training Vs. Learning Learning is ‘self directed” Training is externally controlled Set of pairs of inputs and desired outputs

Learning Vs. Training Hebbian learning: Training: Strengthen connections that are fired at same time Training: Back propagation Hopfield networks Boltzman machines

Back Propagation Present input then measure desired vs.. Actual outputs Correct weights by back propagating error though net Hidden layers are corrected in proportion to the weight they provide to output stage. Need a constant, used to prevent rapid training

Back Propagation The Math Number the Levels: 0 is input N is output All neurons in level i is connected to each neuron in i+1 Weights from level i to i+1 form a matrix Wi Input is a vector x and Training data is a vector t The vector yi is the input to level i: y0 = x yi+1 = fi ( Wi * yi + bi)

The Math (cont.) Error is dn= t – yn Back propagate the error di = (WTi+1 di+1) (fi(net)) Where WT is a transpose matrix of W Update the W matrices and bias terms DWi = a di yTi-1 D bi = a di b

Hopfield Networks Single layer Each neuron receives and input Each neuron has connections to all others Training by “clamping” and adjusting weights

Boltzman Machines Change f() in McCulloch-Pitts to be probabilistic The energy gap between 0 and 1 outputs is related to a “temperature” pk = 1 / [ 1 + e t] t = -DEk / T Learning: Hold inputs and outputs according to training data Anneal temperature while adjusting weights

PDP - an turning point Parallel Distributed Processing (1985) Properties: Learning similar to observed human behavior Knowledge is distributed! Robust

Connectionism Superposition principle Distributed “knowledge representation” Separation of process and “knowledge representation” Knowledge representation is not symbolic in the same sense as symbolic AI!

Example 1 Face recognition – Gary Cottrell Input a 64x64 grid Hidden layer 80 neurons Output layer 8 neurons – face yes,no, 2 bits for gender and 5 bits for name Results: Recognized the input set – 100% Face / no-face on new faces – 100% Male / female determination on new faces – 81%

Example 2 SRI worked on a net to spot tanks Used pictures of tanks and non-tanks Pictures were both exposed and hidden vehicles! When it worked, exposed it to new pictures It failed! Why?

Example 3 The nature of Sub-symbolic Categorize words by lexical type based on word order (Elman 1991)

Elman’s Network output Hidden Layer Input Context Units

Training Set build from sample sentences 29 words 10,000 two and three word sentences Training sample is input word and following word pair No unique answer – output is a set of words Analysis of the trained network – No symbol in the hidden layer corresponding to words or word pairs!!

Connectionisms challenge Fodor’s Language of the Mind Folk Psychology mind states and our tags for them How does the brain get to these? Marr’s type 1 theory – competence with out explanations See Associative Engines by Andy Clark for more!

Pulsed Systems Real neurons pulse! Pulsed neurons have computing power over level

Spike Response Model Variable ui describes the internal state Firing times are: Fi = {ti(f) ; i< f < n} = {t | ui(t) = threshold } After a spike, the state variable's value is lowered Inputs ui= S wij eij(t - tj(f))

Models Full Models Spike Models Simulate continuous functions Can integrate other factors Currents other than dendrite Chemical states Spike Models Simplify and treat output as an impulse

Computational Power Spiked Neurons Power All the neurons are Turing Computable Can do some things cheaper in neuron count

Encoding Problem How does the human brain use the spike trains? Rate Coding Spike density Rate over population Pulse Coding Time to first spike Phase Correlation

Where Next? Build a brain model! Analyze the operation of real brains

Interesting Work Computational Cockroach by Randall D Beer Systems of Igor Aleksander Imagination and Consciousness Cat brain of Hugo DeGrais