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4_16_09_EnergyMinimization_1

4_16_09_EnergyMinimization_1 - Swimming uses half centers...

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Swimming uses half centers, with cross inhibition ending mainly by local inhibition.
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The bifurcation diagram shows fixed points and limit cycles of varying frequencies as one modulates the tonic excitation to C neurons).
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David Marr’s three levels of understanding computations.
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To understand the computation of a neural network, consider a simple feedforward case.
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A network like this is a resistive network, which, in steady state, minimizes electrical energy.
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Computations performed by neural networks can be expressed as energy minimization.
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The advantage to do so is emphasizing the computational strategy not the implementation.
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Example: Aperture problem: small receptive fields can only measure components of velocity parallel to luminance gradients.
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The variables of the aperture problem are the components of velocity parallel ( V (s)) and perpendicular ( V (s)) to the moving contour.
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V s ( ) = v T s ( ) T s ( ) + v s ( ) N s ( ) The true velocity at each position of the contour obeys However, we can only measure N (s) and V .
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