Topics in Brain Computer Interfaces
CS295-7, Fall 2002
Neural Coding
Michael J. Black
Brown University
Department Computer Science
Michael J. Black, © 2002
Neural Prosthetics
“One might think of the computer in
this case as a prosthetic device. Just
as a man who has his arm amputated
can receive a mechanical equivalent
of the lost arm, so a brain-damaged
man can receive a mechanical aid to
overcome the effects of brain
damage. … It makes the computer a
high-class wooden leg.”
Michael Crichton,
The Terminal Man, 1972
Michael J. Black, © 2002
Matlab
Note that CIS released a new version of Matlab yesterday.
Both are available, but the older version is the default.
The links are
/usr/local/bin/matlab
/usr/local/bin/matlab61
/usr/local/bin/matlab65
The first two point to the same thing.
Michael J. Black, © 2002
Announcements
Thursday: Matt Fellows: Detecting and Discriminating
Neural Signals
See Syllabus for reading.
Tuesday: Moran and Schwartz – need presenter
Assignment 1 – currently being updated with new data.
Michael J. Black, © 2002
NEURAL PROSTHETICS
Sensation
Action
Michael J. Black, © 2002
NEURAL PROSTHETICS
Sensation
Action
Michael J. Black, © 2002
Nicolelis, Nature 2001.
Michael J. Black, © 2002
VISUALIZING THE PLAYERS
Single cells of
the nervous system
NEURON
source: David Sheinberg
Michael J. Black, © 2002
Pyramidal Cells
source: Tanya McGraw
Michael J. Black, © 2002
NeuronNeuron
source: Health South Press
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Action Potentials (Spikes)
Source: Chudler
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SINGLE UNIT ACTIVITY
Spikes
2/1000’s second
1/10 mm
source: David Sheinberg
Michael J. Black, © 2002
Neurons
Michael J. Black, © 2002
BRAIN VERSUS COMPUTER
Computational Elements
100,000,000,000
Neurons
100,000,000
Transistors
Speed (operations/second/element)
30-300
1.5 * 109
Michael J. Black, © 2002
MOORE’S LAW
source: Intel
Michael J. Black, © 2002
MASSIVE CONNECTIVITY
SYNAPSES
source: David Sheinberg
Michael J. Black, © 2002
Neural “Coding”
• How do cells represent information?
• ie, how is representation “coded” in action
potentials.
• If we understand the encoding then we can tackle
the “decoding” problem.
• inference – from activity to encoded property
Michael J. Black, © 2002
Neural Coding
What are the possibilities?
1. Localist encoding in on/off response .
2. Rate coding.
3. Precise timing – pattern of spiking carries
information.
4. Ensembles code information that individuals can’t.
5. Synchronous firing within and across ensembles (it
is the interdependencies that matter).
Michael J. Black, © 2002
Neural Coding
• Localist view – each neuron codes a particular value
• “computer”-like model where neurons are binary
• at the low level cells represent things like
orientation
• at the high level they represent complex
information
• Problems?
Michael J. Black, © 2002
Neural Coding
Population codes
• distributed representation
• information encoded in the overall activity of many
cells
• graded response – level of activity conveys
information. Not binary.
Michael J. Black, © 2002
Orientation Selectivity
Hubel & Weisel, 1962
Michael J. Black, © 2002
Rate Coding
source: Zemel & McNaughton, NIPS2000 tutorial
rate = (# of spikes in time bin) / (length of time bin)
Rate is related to the probability the cell will spike in a
given time interval
Michael J. Black, © 2002
Rate Coding
Source: Rob Kass
Michael J. Black, © 2002
Orientation Tuning
Watkins & Berkley ‘74
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Direction Tuning
Snowden ‘94
Michael J. Black, © 2002
Michael J. Black, © 2002
DECODING NEURAL MESSAGES
Performance
Reaction Time
BEHAVIOR
Eye Position
NEURAL
SIGNAL
10ms
source: David Sheinberg
Michael J. Black, © 2002
source: David Sheinberg
Source: David Sheinberg
Michael J. Black, © 2002
Center-Out Task
Possible targets
Mov em ent target
C e n te r h old
Position Feedback Cursor
VideoMonitor
Digitizin
Tablet
g
Digitizing
Tablet
A
B
C
Georgopoulos, Schwartz, & Kettner, ’86. Moran & Schwartz, ‘99
Michael J. Black, © 2002
Center-Out Task
Moran & Schwartz, J Neurophysiology ‘99
Data averaged over multiple animals and multiple trials.
Michael J. Black, © 2002
Single-Cell Activity
Single cells from multiple
animals.
Average rate over RT and
MT to each target (300-600
ms).
Fit with cosine model.
Moran & Schwartz, ’99
f j1/ 2 = b0 + bx sin(θ j ) + by cos(θ j )
Infer firing conditioned on
speed by assuming a bellshaped function and
factoring out direction
effects.
Michael J. Black, © 2002
Population Vectors
Georgopuolos, Schwartz & Vetter ‘86
• Take each cell’s “preferred” direction and weight it by its
current activity.
• Summing all the weighted directions gives some measure
of the current direction.
• Populations computed from multiple animals.
Michael J. Black, © 2002
Population Vector
θˆ = ∑ rθ
i i
i
Michael J. Black, © 2002