Models in neuroscience

Models in neuroscience

Lee, Rohrer & Sparks 1988:

population coding of saccades in SC

Gunnar

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population coding of saccades in SC

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Lidocaine

inactivation

Andy Ruina’s passive walkers

(e.g. Collins & Ruina, 2005)

Konrad

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https://www.youtube.com/watch?v=-

nh4EPmGlEE&feature=youtu.be

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Zipser & Andersen 1988: Gain

fields

Gunnar

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Gain modulation

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= change of receptive field strength with secondary input

E.g. eye position gain modulation of visual receptive fields in

posterior parietal cortex

Blohm, Khan, Crawford, 2009 (adapted from Andersen, et al., 1985)

Gain modulation

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Reference frame transformations

Zipser & Andersen, Nature 1988Eye position gain modulation

of hidden layer units

Gain modulation

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Powerful computational means for

Cue combination

Reference frame transformations

Multi-sensory integration...

Blohm & Crawford, 2009

Mnih et al., 2013: Deep learning

for playing games

Konrad

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Deep reinforcement learning for games

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https://arxiv.org/pdf/1312.5602.pdf

Standage & Pare 2011: biophysical

model of decisions and WM

Gunnar

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Biophysical model of decisions and WM

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Biophysical model of decisions and WM

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Vilares & Kording 2017:

dopamine represents uncertainty

Konrad

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Dopamine represents uncertainty

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Dopamine represents uncertainty

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Todorov & Jordan 2002: Optimal

feedback movement control

Gunnar

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Motor planning & control

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Motor planning is the result of all previous steps…

Sensory processing

Transformations & multi-sensory integration

Target selection & decision making

Motor control

Execution of the motor plan…

Task Selection (Reaching)

Target Position

Initial Arm Position

Nominal Speed

Scott, 2004

Optimal feedback control

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( ) ( ) ( )

1( ) ( ) ( ) ( 1) ( 1) ( 1)

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( 1) ( ) ( ) ( ) ( ) ( )

ˆ

ˆ ˆ ˆˆ ˆ ˆ

k k k ku

k k ky

pk T k k k T k k

k

k k k

k k k k k k

A C

B

J L T

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A AK C

x x u ε

y x ε

u u y y

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motor noise

sensory noise

Sensory state of our body and the world we interact with

What we can observe about the state

Cost to minimize

Feedback control policy

Belief about state

motor command

Predicted sensory consequences

Measured sensory consequences

Optimal feedback control

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Example: tennis

Optimal control reproduces backward swing

Torodov & Jordan, 2002

Nichols & Houk 1976: stretch

reflex simplifies feedback control

Konrad

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Stretch reflex simplifies feedback control

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More models…

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Daye et al. 2014: hierarchical

control of eye-head saccades

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Hierarchical control

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Eye-head Saccades

Endpoint control

Vs. trajectory control

Head motion =

perturbation to gaze goal

Daye, Optican, Blohm, Lefèvre (2014)

Izhiekevich & Edelman 2008:

rhythms in thalamocortical model

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Emergent rhythms in thalamocortical model

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Izhikevich & Edelman PNAS (2008)

Mazurek etal. 2003: drift

diffusion modelling

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Diffusion models for decision making

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Example: left-right decisions

Integrated decision model (Mazurek, et al. 2003)

Ma et al. 2006: Multi-sensory

integration in PPC

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Bayesian multi-sensory integration

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Cue combination

Optimal Bayesian observer

Independent observations A, V

If uniform priors, then

The brain always uses all available useful information.

Information from different sources is combined in a statistically optimal fashion

likelih

ood )|( XVp

)|( XAp

)|,( XVAp

),(

)()|,(),|(

VAp

XpXVApVAXp

)|()|()|,( XApXVpXVAp

)|()|(

),|(

XApXVp

VAXp

Bayesian computations in population codes

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Representing uncertainty with population codes

Probabilistic population codes

Poisson-like neural noise

Variance inversely

related to gains of

population code

Ma et al. (2006)

That’s all folks!

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