9.54 Shimon Ullman + Tomaso Poggio Danny Harari + Daniel Zysman + - - PowerPoint PPT Presentation

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9.54 Shimon Ullman + Tomaso Poggio Danny Harari + Daniel Zysman + - - PowerPoint PPT Presentation

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9.54 Shimon Ullman + Tomaso Poggio Danny Harari + Daniel Zysman + Darren Seibert 9.54, fall semester 2014 9.54 class 3 Biophysics of Computation: Synapses, dendritic trees, computational primitives, including Hebb-like plasticity rules

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9.54, fall semester 2014

9.54

Shimon Ullman + Tomaso Poggio

Danny Harari + Daniel Zysman + Darren Seibert

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9.54, fall semester 2014

9.54 class 3

Biophysics of Computation: Synapses, dendritic trees, computational primitives, including Hebb-like plasticity rules

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9.54, fall semester 2014

Traditional view (McCullogh Pitts, 1943 and Neural Nets, ~1980-2015): basic mechanism

  • threshold mechanism of the spike
  • Biophysics of Computation

Dendritic computation (~1970): basic mechanisms (examples)

  • passive : shunting inhibition
  • active: V and t dependent channels in dendrites
  • others
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Threshold units

  • Threshold units are universal
  • The threshold mechanism can be identified with spike generation in the soma of a

neuron

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Threshold units are universal

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Threshold units can be identified with neuron’s spike mechanisms

Hodgkin-Huxley equations Leaky-integrator approximation

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Perceptrons and Neural networks

  • These systems - not Boolean — are

also universal in the sense of ability of approximating any continuous function (polynomial are dense in the space of continuous functions)

  • Active properties of neurons can also

implement

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9.54, fall semester 2014

Traditional view (McCullogh Pitts, 1943 and Neural Nets, ~1980-2015): basic mechanism

  • threshold mechanism of the spike
  • Biophysics of Computation

Dendritic computation (~1970): basic mechanisms (examples)

  • passive : shunting inhibition
  • active: V and t dependent channels in dendrites
  • others
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Katz Miledi 1964

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Relative motion

Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

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Relative motion: feedforward model

Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

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The circuit uses normalization (pre-Heeger), gain control and max-like operation

yi = (xi)r β + ( x j)q

j=1 N

∑

where y are the outputs after shunting inhibition, x are the inputs and r, q are approximations of pre-postsynaptic nonlinearities

Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

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Katz Miledi 1964

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9.54, fall semester 2014

Biophysics of Computation

Background on neurons and synapses (many slides from a course by Rao; see 9.40)

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Dendritic Computation

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Passive (linear) cable

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General solution

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9.54, fall semester 2014

Biophysics of Computation

Dendritic computations

  • passive nonlinearities: shunting inhibition
  • active nonlinearities: V and t dependent channels in dendrites
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e3 ANDNOT (i1 OR i2 OR i3)] OR [e2 ANDNOT (i1 OR i2) OR (e1 ANDNT i1 ) (e1 ANDNOT i1) OR (e2 ANDNOT i2 ) OR {[(e3 ANDNOT i3) OR (e4 ANDNOT i4) OR (e6 AND-NOT i6) OR (e6 AND-NOT i6)] ANDNOT i7 }

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9.54, fall semester 2014

Biophysics of Computation

Dendritic computations

  • passive nonlinearities: shunting inhibition
  • active nonlinearities: V and t dependent channels in dendrites
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9.54, fall semester 2014

Biophysics of Computation

Background on active membranes and spikes

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New model for CS cells (see later in class)

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Traditional circuits for simple and complex cells since HW

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How to compile into one cell

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  • Plasticity and Learning: Adapting the Connections
  • We will see in the next few classes on supervised learning how synaptic

weights can be modifies during training to solve useful tasks.

  • But…how does the brain modify synaptic weights? What are the

biophysical mechanisms?

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  • Unsupervised Learning
  • Synapses adapted based solely on inputs
  • Network self-organizes in response to statistical patterns in input
  • Similar to Probability Density Estimation in statistics
  • Supervised Learning
  • Synapses adapted based on inputs and desired outputs
  • External “teacher”provides desired output for each input
  • Goal: Function approximation
  • Reinforcement Learning
  • Synapses adapted based on inputs and (delayed) reward/punishment
  • Goal: Pick outputs that maximize total expected future reward
  • Similar to optimization based on Markov decision processes

Learning algorithms and biophysical mechanisms

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Biophysical mechanisms for learning

  • Hebb rule for unsupervised learning
  • Hebb rule + supervised modulation of neural threshold and gain

for supervised learning

  • Dopamine machinery for RL
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Hebb rule + supervised modulation of neural threshold and gain for supervised learning

  • Hebb rule
  • with normalization

decreases error

  • with
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LTP and LTD

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LTP and LTD

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LTP and LTD

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LTP

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LTP

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LTP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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STDP

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9.54, fall semester 2014