internal models, adaptation, and uncertainty reza shadmehr johns hopkins school of medicine ali...
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Internal models, adaptation, and uncertainty
Reza ShadmehrJohns Hopkins School of Medicine
Ali Ghazizadeh
Maurice Smith
Konrad Koerding
Siavash VaziriJoern Diedrichsen
Duhamel, Colby, & Goldberg Science 255, 90-92 (1992)
Internal models predict the sensory consequences of motor commands
musclesMotor commandsforce
Body partState change
Sensory system
ProprioceptionVision
Audition
Measured sensory
consequences
Forward model
Predicted sensory consequences
Integration
Bayesian
mixture
Vaziri, Diedrichsen, Shadmehr, J Neurosci 2006
Reach endpoints with respect to targetTime (msec)
Vaziri, Diedrichsen, Shadmehr, J Neurosci 2006
Variance in reach errors indicates an integration of the predicted and actual sensory consequence of oculomotor
commands
Motor commands
Sensory system
Measured sensory input
Forward model
Predicted sensory consequences
Integration
Estimate of target location
Motor commands musclesforce
Body partState change
Sensory system
ProprioceptionVision
Audition
Measured sensory
consequences
Forward model
Predicted sensory consequences
Integration
Bayesian
mixture
What are internal models good for?
Improve ability to sense the world. By predicting the sensory consequences of motor commands, and then integrating it with the actual sensory feedback, the brain arrives at an estimate that is better than is possible from sensation alone.
Equivalent to muscles being too strong
McLaughlin 1967
TargetEye X
30%
Saccadic target jump experiments: gain reduction
Kojima et al. (2004) J Neurosci 24:7531.
Result 1: After changes in gain, monkeys exhibit recall despite behavioral evidence for washout.
+ _ + _ + _
Savings: when adaptation is followed by de-adaptation, motor system still exhibits recall
Saccade gain = Target displacement
Eye displacement
Result 2: Following changes in gain and a period of darkness, monkeys exhibit a “jump” in memory.
+ _ +
Offline learning: with passage of time and without explicit training, the motor system still appears to learn
Kojima et al. (2004) J Neurosci 24:7531.
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( 1) ( ) ( )2 22 2
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Motor adaptation as concurrent learning in two systems:A fast learning system that forgets quicklyA slow learning system that hardly forgets
Smith, Ghazizadeh, Shadmehr PLOS Biology, 2006
prediction
Prediction error
Learning
Savings: de-adaptation may not erase adaptation
Task reversal periodre-adaptation
Trial number
Smith, Ghazizadeh, Shadmehr PLOS Biology, 2006
A
1w
y
x
Hid
den
sta
tes
Context
perturbation
2w
mw
t
1w
y
x
2w
mw
t
Slow change
fast change
The Bayesian learner’s interpretation of prediction error
Offline learning: Passage of time has asymmetric affects on the fast
and slow systems
Smith, Ghazizadeh, Shadmehr PLOS Biology, 2006
Task reversal period
“dark” period
re-adaptation
Trial number
Slow stateFast state
-
( 1) ( ) ( )1 11 1
( 1) ( ) ( )2 22 2
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n n n
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y a y b y
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1. Perturbations that can affect the motor plant have multiple time scales.Some perturbations are fast: muscles recover from fatigue quickly.Some perturbations are slow: recovery from disease may be slow.
2. Faster perturbations are more variable (have more noise).
3. Disturbances result in error, which can be observed, but with sensory noise.
4. The problem of learning is one of credit assignment: when I observe a disturbance, what is the time-scale of this perturbation?
5. To solve this problem, the brain must keep a measure of uncertainty about each possible timescale of perturbation.
The learner’s view about the cause of motor errors
( ) (1 1/ ) ( )disturbance t disturbance t
0, /N c
( ) ( )observation t disturbance t
Koerding, Tenenbaum, Shadmehr, unpublished
Savings: de-adaptation does not washout the
adapted system
Simulation
Koerding, Tenenbaum, Shadmehr, unpublished
Spontaneous recovery
Model 1 (Smith et al.): Error causes changes in multiple adaptive processes. Fast adaptive processes are highly responsive to error, but quickly forget. Slowly adaptive processes respond poorly to error, but retain their changes.
Prediction: When actions are performed with zero error, states of the adaptive processes decay, but at different rates.
Model 2 (Koerding et al.): Motor system is disturbed by processes that have various timescale (fatigue vs. disease). Credit assignment of error depends on uncertainty regarding what is the timescale of the disturbance.
Prediction: When there are actions but the sensory consequences cannot be observed, states decay at various rates, but uncertainty grows. Increased uncertainty encourages learning.
What prediction dissociates the two models?
Trial number
Slow stateFast state
Task reversal period
“dark” period
re-adaptation
-
Model 1: After a period of “darkness”, there will be spontaneous recovery, but rate of re-adaptation will be the same as initial learning.
Adapting without uncertainty
Smith, Ghazizadeh, Shadmehr PLOS Biology 2006
Model 2: After a period of “darkness”, there will be spontaneous recovery, but the rate of re-adaptation will be faster than initial learning.
Adapting with uncertainty
Monkey data from Kojima et al. (2004). Simulations from Koerding, Tenenbaum, Shadmehr, unpublished
Bayesian learner
1 1000 2000 3000
Saccade number
Dark
ness
Robinson et al. J Neurophysiol, in press
Sensory deprivation may increase uncertainty, resulting in faster learning
Monkeys were trained each day, but between training sessions they put on dark goggles, reducing their ability to sense consequences of their own motor commands.
Dark
ness
Adapting with uncertainty: some predictions
Sensory deprivation Faster subsequent rate of learning.
Example: A subject that spends a bit of time in the dark will subsequently learn faster than a subject that spends that time with the lights on.
Why: In the dark, uncertainty about state of the motor system increases.
Longer inter-stimulus interval Better retention.
Example: A subject that trains on n trials with long ITI will show less forgetting than one that trains on the same n trials with short ITI.
Why: events that take place spaced in time will be interpreted as having a long timescale.
Ali Ghazizadeh Maurice Smith
Konrad Koerding
Siavash VaziriJoern Diedrichsen
By combining the predictions of internal models with sensory measurements, the brain ends up with less noisy estimates of the environment than is possible with either source of information alone.
Fast and slow adaptive processes arose because disturbances to the motor system have various timescales (fatigue vs. disease). When faced with error, the brain faces a credit assignment problem: what is the timescale of the disturbance? To solve this problem, the brain likely keeps a measure of uncertainty about the timescales.
A prediction error causes changes in multiple adaptive systems. Some are highly responsive to error, but rapidly forget. Others are poorly responsive to error but have high retention. This explains savings and spontaneous recovery.
Summary