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

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 9.54, fall semester 2014

Biophysics of Computation Traditional view (McCullogh Pitts, 1943 and Neural Nets, ~1980-2015): basic mechanism � • threshold mechanism of the spike � Dendritic computation (~1970): basic mechanisms (examples) � • passive : shunting inhibition • active: V and t dependent channels in dendrites • others � 9.54, fall semester 2014

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

Threshold units are universal

Threshold units can be identified with neuron’s spike mechanisms Hodgkin-Huxley equations Leaky-integrator approximation

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

Biophysics of Computation Traditional view (McCullogh Pitts, 1943 and Neural Nets, ~1980-2015): basic mechanism � • threshold mechanism of the spike � Dendritic computation (~1970): basic mechanisms (examples) � • passive : shunting inhibition • active: V and t dependent channels in dendrites • others � 9.54, fall semester 2014

Katz Miledi 1964

Relative motion 11 Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

Relative motion: feedforward model 12 Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

The circuit uses normalization (pre-Heeger), gain control and max-like operation ( x i ) r y i = ∑ N β + ( x j ) q j = 1 where y are the outputs after shunting inhibition, x are the inputs and r, q are approximations of pre-postsynaptic nonlinearities 13 Towards the neural circuitry, Reichardt, Poggio, Hausen, 1983

Katz Miledi 1964

Biophysics of Computation Background on neurons and synapses (many slides from a course by Rao; see 9.40) � � � 9.54, fall semester 2014

Dendritic Computation

Passive (linear) cable

General solution

Biophysics of Computation Dendritic computations � • passive nonlinearities: shunting inhibition • active nonlinearities: V and t dependent channels in dendrites � � 9.54, fall semester 2014

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 }

Biophysics of Computation Dendritic computations � • passive nonlinearities: shunting inhibition • active nonlinearities: V and t dependent channels in dendrites � � 9.54, fall semester 2014

Biophysics of Computation Background on active membranes and spikes � � � 9.54, fall semester 2014

New model for CS cells (see later in class)

Traditional circuits for simple and complex cells since HW

How to compile into one cell

� 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?

Learning algorithms and biophysical mechanisms � 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 74

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 � 75

Hebb rule + supervised modulation of neural threshold and gain for supervised learning � Hebb rule � � � � with normalization � � � decreases error � with 76

LTP and LTD 77

LTP and LTD 9.54, fall semester 2014

STDP 9.54, fall semester 2014

9.54, fall semester 2014