models in neuroscience
TRANSCRIPT
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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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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x x u ε
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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
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)()|,(),|(
VAp
XpXVApVAXp
)|()|()|,( XApXVpXVAp
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),|(
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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