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Models in neuroscience
Lee, Rohrer & Sparks 1988:
population coding of saccades in SC
Gunnar
July 30, 2018CoSMo 2018 - G. Blohm2
population coding of saccades in SC
July 30, 2018CoSMo 2018 - G. Blohm3
Lidocaine
inactivation
Andy Ruina’s passive walkers
(e.g. Collins & Ruina, 2005)
Konrad
July 30, 2018CoSMo 2018 - G. Blohm4
https://www.youtube.com/watch?v=-
nh4EPmGlEE&feature=youtu.be
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Zipser & Andersen 1988: Gain
fields
Gunnar
July 30, 2018CoSMo 2018 - G. Blohm6
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
July 30, 2018CoSMo 2018 - G. Blohm8
Reference frame transformations
Zipser & Andersen, Nature 1988Eye position gain modulation
of hidden layer units
Gain modulation
July 30, 2018CoSMo 2018 - G. Blohm9
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
July 30, 2018CoSMo 2018 - G. Blohm12
Biophysical model of decisions and WM
July 30, 2018CoSMo 2018 - G. Blohm13
Biophysical model of decisions and WM
July 30, 2018CoSMo 2018 - G. Blohm14
Vilares & Kording 2017:
dopamine represents uncertainty
Konrad
July 30, 2018CoSMo 2018 - G. Blohm15
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
July 30, 2018CoSMo 2018 - G. Blohm20
( 1) ( ) ( ) ( )
( ) ( ) ( )
1( ) ( ) ( ) ( 1) ( 1) ( 1)
0
( ) ( ) ( )
( 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
G
A AK C
x x u ε
y x ε
u u y y
u x
x x y y u
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
July 30, 2018CoSMo 2018 - G. Blohm21
Example: tennis
Optimal control reproduces backward swing
Torodov & Jordan, 2002
Nichols & Houk 1976: stretch
reflex simplifies feedback control
Konrad
July 30, 2018CoSMo 2018 - G. Blohm22
Stretch reflex simplifies feedback control
July 30, 2018CoSMo 2018 - G. Blohm23
More models…
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Daye et al. 2014: hierarchical
control of eye-head saccades
July 30, 2018CoSMo 2018 - G. Blohm25
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
July 30, 2018CoSMo 2018 - G. Blohm27
Emergent rhythms in thalamocortical model
July 30, 2018CoSMo 2018 - G. Blohm28
Izhikevich & Edelman PNAS (2008)
Mazurek etal. 2003: drift
diffusion modelling
July 30, 2018CoSMo 2018 - G. Blohm29
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
July 30, 2018CoSMo 2018 - G. Blohm31
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
July 30, 2018CoSMo 2018 - G. Blohm33
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!
July 30, 2018CoSMo 2018 - G. Blohm34