Cohen & Andersen (2002) Nat Rev Neurosci 3
description
Transcript of Cohen & Andersen (2002) Nat Rev Neurosci 3
![Page 1: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/1.jpg)
Learning and Adaptation Strategies in an Obstacle - Avoidance Task
Performed in Monkeys
CALTECH
Biology Division – Andersen Lab
Elizabeth B. TorresRichard Andersen
![Page 2: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/2.jpg)
Motivation: What is encoded in the PRR region of the Posterior Parietal Cortex of
the Monkey (Macaca Mulatta)
Cohen & Andersen (2002) Nat Rev Neurosci 3
Lewis & Van Essen (2000) J Comp Neuroll 428
Goal? or
Hand path? Posture ?
![Page 3: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/3.jpg)
Experimental Design:
Obstacle Avoidance, 2 very different handpath solutions ??
![Page 4: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/4.jpg)
![Page 5: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/5.jpg)
![Page 6: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/6.jpg)
![Page 7: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/7.jpg)
![Page 8: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/8.jpg)
![Page 9: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/9.jpg)
Handpaths constrained to a plane
![Page 10: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/10.jpg)
Handpaths constrained to a plane
![Page 11: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/11.jpg)
Results
1 – Subutilize 3D space
![Page 12: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/12.jpg)
Results
1 - Subutilize 3D space
2 - Adaptation
![Page 13: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/13.jpg)
Obstacles
![Page 14: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/14.jpg)
No Obstacles - Aftereffect
![Page 15: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/15.jpg)
No Obstacle - Deadapted
![Page 16: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/16.jpg)
Results
1 - Subutilize 3D space
2 – Adaptation
3 – Speed Independence (during learning)
![Page 17: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/17.jpg)
Learning Period Speed Independence
As the subject learns,
More consistent, shorter motions,
approach bell-shaped speed profiles
From geometric (local) strategy
(decoupled from speed) to
Kinetic-based (global) optimization
(eventually smooth, ballistic motion)
![Page 18: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/18.jpg)
Kalaska’s experim loads effect on PD
M1 A5 Dorsal
![Page 19: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/19.jpg)
![Page 20: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/20.jpg)
The Straight-line Path of a Curved World
![Page 21: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/21.jpg)
Metric Tensor ijg
Generalized Pythagorean Theorem (curved world)
2 2 211 1 12 1 2 22 2ds g dx g dx dx g dx
Euclidean Case (flat world)
2 2 21 2
ij ij
ds dx dx
g
![Page 22: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/22.jpg)
1 nij
1
1 np
n
b
X Y g u ua a
b
, ,, , ,
Inner Product (norm)
1 0
flat world
0 1
11 1
1
curved n
n nn
g x g x
g x g x
![Page 23: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/23.jpg)
f
mR
q
nR
x
XQ
rR
r f q
TARGET WORLD
ij
gPOSTURE WORLD
kl
g ?
tkl ij
g J g J Pullback the Metric of X into Q
1f
targetx 1 targetf x
Local Isometric Imbedding
![Page 24: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/24.jpg)
The gradient flow generates geodesics paths (“straight-line”
paths of a space whose curvature is task-dependent,
because we have optimized with respect to a geometry
dictated by the norm/cost the task dictates:
i.e. dictated by the TARGET !!!
Given this, What norm could we optimize in order to
approximate these solution paths in hand space?, i.e. to
capture the geometry (curvature) of task space and that of
the underlying parameter space?
![Page 25: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/25.jpg)
Via Point
Temporally, speed-based
Spatially-based
![Page 26: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/26.jpg)
3 62 2ViaPoint target
1 21 4
i i i ii i
r x f q x f q
11
1
1traversedd D
e
22
1
1traversedd D
e
D1D2
Target
ViaPoint
Init Hand
Norm in this TASK Space
-100 -50 50 100
0.2
0.4
0.6
0.8
1
-100 -50 50 100
0.2
0.4
0.6
0.8
1
![Page 27: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/27.jpg)
1. Obstacles Weight such that first priority is Via Point
2. No Obstacle (Deadaptation residual aftereffects) More weight to Main Target, Via Point is not as important
3. No Obstacle Straight-line Paths 0 weight for Via Point, 1 for Main Target
Solving the Task
D1D2
Target
ViaPoint
Init Hand
![Page 28: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/28.jpg)
Apply Method to Data Paths
curved 'sijg
flat 'sijg
![Page 29: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/29.jpg)
Simulations
![Page 30: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/30.jpg)
Future Work
• Neural Recordings
• Neural Systems Identification
![Page 31: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/31.jpg)
Acknowledgements
Sloan-Swartz Foundation
Richard Andersen
All members of the Andersen Lab for their immense help and incredible patience while teaching me
![Page 32: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/32.jpg)
Nobody asked questions related to this, but I had included the following 2 slides here in case someone wanted to know more about the model implementation of the theory in general
![Page 33: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/33.jpg)
Equation describing the autonomous flow of geometric motion
1 target,qdq G r f q x t
t
q m n n mf qm m n nG J G J
target f qrr f q x
f q q
,
target targetn 2
i ii 1
r f q x x f q ,
![Page 34: Cohen & Andersen (2002) Nat Rev Neurosci 3](https://reader036.fdocuments.us/reader036/viewer/2022062423/56814577550346895db2482a/html5/thumbnails/34.jpg)
Compatibility Condition q Q q Q W p
nq Q R : M
nQ RnQ R
1 1 1q q q W q W :
nq Q R : M
|
|
i1 1
j
i1 1
j
qq q Q Q J q q
q
qq q Q Q J q q
q
:
:
ijg rsg
r st1 1
ij rs rs i jrs
q qg J q q g J q q g
q q
2 i j r sij rs
ij rsds g dq dq g dq dq
1 1 1q q q W q W :
1q 1q