Functional Link Network

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Support Vector Machines

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Support Vector Machines

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Two Spiral Problem

SVM architecture

Application: text classification

• Reuters “newswire” messages

• Bag-of-words representation

• Dimension reduction

• Training SVM

Results

Break-even point = precision value at which precision and recall are nearly equal

Results

Application 2: face recognition

False detections

System architecture

Results

Results

Skin detection and real-time recognition

Neural Networks

Ccortex is a massive spiking neuron network emulation and will mimic the human cortex, the outer layer of gray matter at the cerebral hemispheres, largely responsible for higher brain functions. The emulation covers up to 20 billion layered neurons and 2 trillion 8-bit connections.

Spiking Neural Networks

• From neurones to neurons• Artificial Spiking Neural Networks

(ASNN)– Dynamic Feature Binding– Computing with spike-times

Neural Networks

• Artificial Neural Networks– (neuro)biology -> Artificial Intelligence (AI)

– Model of how we think the brain processes information

• New data on how the brain works!– Artificial Spiking Neural Networks

Real Neurons

• Real cortical neurons communicate with spikes or action potentials

Real Neurons

• The artificial sigmoidal neuron models the rate at which spikes are generated

• artificial neuron computes function of weighted input:

x = f( )w x ij ijjx

w x ij i

Artificial Neural Networks

• Artificial Neural Networks can:– approximate any function

• (Multi-Layer Perceptrons)

– act as associative memory• (Hopfield networks, Sparse Distributed Memory)

– learn temporal sequences• (Recurrent Neural Networks)

ANN’s

• BUT....

for understanding the brain the neuron model is wrong

• individual spikes are important, not just rate

Binding Problem

• When humans view a scene containing a red circle and a green square, some neurons – signal the presence of red,– signal the presence of green, – signal the circle shape,– Signal the square shape.

• The binding problem: – how does the brain represent the pairing of color and shape?

• Specifically, are the circles red or green?

Binding

• Synchronizing spikes?

New Data!

• neurons belonging to same percept tend to synchronize (Gray & Singer, Nature 1987)

• timing of (single) spikes can be remarkably reproducible

• Spikes are rare: average brain activity < 1Hz– “rates” are not energy efficient

Computing with Spikes

• Computing with precisely timed spikes is more powerful than with “rates”.(VC dimension of spiking neuron models)[W. Maass and M. Schmitt., 1999]

• Artificial Spiking Neural Networks??[W. Maass Neural Networks, 10, 1997]

Artificial Spiking Neuron

• The “state” (= membrane potential) is a weighted sum of impinging spikes– spike generated when potential crosses threshold, reset

potential

Artificial Spiking Neuron

• Spike-Response Model:

where ε(t) is the kernel describing how a single spike changes the potential:

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Artificial Spiking Neural Network

• Network of spiking neurons:

Error-backpropagation in ASNN

• Encode “X-OR” in (relative) spike-times

XOR in ASNN

• Change weights according to gradient descent using error-backpropagation (Bohte et al, Neurocomputing 2002)

• Also effective for unsupervised learning(Bohte etal, IEEE Trans Neural Net. 2002)

Oil Application