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CS 621 Artificial Intelligence
Lecture 33 - 07/11/05
Guest Lecture byProf. Rohit Manchanda
Biological Neurons - I
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The Perceptron Model A perceptron is a computing element with input lines having associated weights and the cell having a threshold value. The perceptron model is motivated by the biological neuron.
Output = y
wnWn-1
w1
Xn-1
x1
Threshold = θ
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Step function / Threshold functiony = 1 for Σ > θ, y >1
=0 otherwise
Σwixi > θ
θ
1y
Σwixi
Features of Perceptron
• Input output behavior is discontinuous and the derivative does not exist at Σwixi = θ • Σwixi - θ is the net input denoted as net
• Referred to as a linear threshold element - linearity because of x appearing with power 1
• y= f(net): Relation between y and net is non-linear
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Perceptron vs. the point neuron
• Incoming signals from synapses are summed up at the soma
• , the biological “inner product”• On crossing a threshold, the cell “fires”
generating an action potential in the axon hillock region
The McCulloch and Pitt’s neuron
Synaptic inputs: Artist’s conception
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The biological neuron
Pyramidal neuron, from the amygdala (Rupshi et al. 2005)
A CA1 pyramidal neuron (Mel et al. 2004)
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What makes neuronal computation special ?
• Electrical activity in neurons• Traveling action potentials• Leaky, conducting membrane• Highly branched structures• A variety of electrical connections between neurons• A varied range of possibilities in neural coding of
information
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Dendritic computation
• Time delay• Attenuation, duration increase• Spatial and temporal
summation• Non linear intra branch
summation• Multiple layer configuration• Retrograde propagation of
signals into the dendritic arbor– Backprogating action
potentials
Spatial and temporal summation of proximal and distal inputs (Nettleton et al. 2000)
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Dendritic computationComparison of within-branch andbetween-branch summation.
(a-f)Black: individually Activated Re: simultaneously activatedBlue: arithmetic sum of individual responses.
(g) Summary plot of predicted versus actual combined responses. Coloured circles: within-branch summationDashed line: linear summation. Green diamonds: between-branch summation
(h) Modeling data: summation of EPSPsRed circles: within-branch summation Open green circles: between-branch summation
(Mel et al. 2003, 2004)
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Possible computational consequences of non-linear summation in dendritic sub-trees (Mel et al. 2003)
Dendritic computation: Single neuron as a neural
network
Another possibility
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Single neuron as a neural network
3 Layered Neural Network2 Layered Neural Network
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A multi neuron pathway in the hippocampus
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Summary
Classical Picture Emerging Picture
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Recent neurobiological discoveries
Changes as a result of stress (CIS)– Dendritic atrophy
Consequences– Loss of computational subunits– Changes in connectivity of the
network
Atrophy and de-branching as seen in the CA3 pyramidal cells from (Ajai et al. 2002)
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Increase in spine count (Amygdaloid neurons) (Rupshi et al. 2005)
Changes as a result of stress (CIS)
•Arbor growth•Increase in spine count
Consequences
•Increase in computational subunits•Synaptic site increase
Recent neurobiological discoveries