what is the neural code?
DESCRIPTION
What is the neural code?. What is the neural code?. Alan Litke, UCSD. What is the neural code?. What is the neural code?. Encoding : how does a stimulus cause a pattern of responses? what are the responses and what are their characteristics? neural models: - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/1.jpg)
What is the neural code?
![Page 2: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/2.jpg)
Alan Litke, UCSD
What is the neural code?
![Page 3: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/3.jpg)
What is the neural code?
![Page 4: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/4.jpg)
What is the neural code?
Encoding: how does a stimulus cause a pattern of responses?
• what are the responses and what are their characteristics?• neural models:
what takes us from stimulus to response;descriptive and mechanistic models, and the relation between them.
Decoding: what do these responses tell us about the stimulus?
• Implies some kind of decoding algorithm• How to evaluate how good our algorithm is?
![Page 5: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/5.jpg)
What is the neural code?
Single cells:spike ratespike timesspike intervals
![Page 6: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/6.jpg)
What is the neural code?
Single cells:spike rate: what does the firing rate correspond to?spike times: what in the stimulus triggers a spike?spike intervals: can patterns of spikes convey extra information?
![Page 7: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/7.jpg)
What is the neural code?
Populations of cells:population codingcorrelations between responsessynergy and redundancy
![Page 8: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/8.jpg)
Receptive fields and tuning curves
Tuning curve: r = f(s)
Gaussian tuning curve of a cortical (V1) neuron
![Page 9: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/9.jpg)
Receptive fields and tuning curves
Tuning curve: r = f(s)
Cosine tuning curve of a motor cortical neuron
Hand reaching direction
![Page 10: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/10.jpg)
Receptive fields and tuning curves
Sigmoid/logistic tuning curve of a “stereo” V1 neuron
Retinal disparity for a “near”object
![Page 11: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/11.jpg)
Higher brain areas represent increasingly complex features
Quian Quiroga, Reddy, Kreiman, Koch and Fried, Nature (2005)
![Page 12: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/12.jpg)
![Page 13: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/13.jpg)
![Page 14: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/14.jpg)
![Page 15: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/15.jpg)
More generally, we are interested in determining the relationship:
P(response | stimulus)
Due to noise, this is a stochastic description.
Problem of dimensionality, both in response and in stimulus
P(stimulus | response)
encoding
decoding
![Page 16: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/16.jpg)
Reverse correlation
Fast modulation of firing by dynamic stimuli
Feature extraction
Use reverse correlation to decide what each of these spiking eventsstands for, and so to either:
-- predict the time-varying firing rate-- reconstruct the stimulus from the spikes
![Page 17: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/17.jpg)
Reverse correlation
Typically, use Gaussian, white noise stimulus: an unbiased stimulus which samples all directions equally
S(t)
r(t)
Basic idea: throw random stimuli at the system and collect the onesthat cause a response
![Page 18: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/18.jpg)
Reverse correlation
Spike-conditionalensemble
Goal: simplify!
![Page 19: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/19.jpg)
stimulus = fluctuating potential
(generates electric field)
Example: a neuron in the ELL of a fish
Spike-triggered Average
![Page 20: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/20.jpg)
This can be done with other dimensions of stimulus as well
Spatio-temporal receptive field
![Page 21: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/21.jpg)
spike-triggering stimulus feature
stimulus X(t)
decision function
spike output Y(t)x1
f1
P(s
pike
|x1
)x1
Decompose the neural computation into a linear stage and a nonlinear stage.
Modeling spike encoding
Given a stimulus, when will the system spike?
To what feature in the stimulus is the system sensitive?
Gerstner, spike response model; Aguera y Arcas et al. 2001, 2003; Keat et al., 2001
Simple example: the integrate-and-fire neuron
![Page 22: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/22.jpg)
spike-triggering stimulus feature
stimulus X(t)
decision function
spike output Y(t)x1
f1
P(s
pike
|x1
)
x1
The decision function is P(spike|x1). Derive from data using Bayes’ theorem:
P(spike|x1) = P(spike) P(x1 | spike) / P(x1)
P(x1) is the prior : the distribution of all projections onto f1
P(x1 | spike) is the spike-conditional ensemble : the distribution of all projections onto f1 given there has been a spike
P(spike) is proportional to the mean firing rate
Modeling spike encoding
![Page 23: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/23.jpg)
Models of neural function
spike-triggering stimulus feature
stimulus X(t)
decision function
spike output Y(t)x1
f1
P(s
pike
|x1
)
x1
Weaknesses
![Page 24: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/24.jpg)
STA
Gaussian priorstimulus distribution
Spike-conditional distribution
covariance
Reverse correlation: a geometric view
![Page 25: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/25.jpg)
Dimensionality reduction
Cij = < S(t – ti) S(t - tj)> - < STA(t - ti) STA (t - tj)> - < I(t - ti) I(t - tj)>
The covariance matrix is given by
Properties:
•If the computation is low-dimensional, there will be a few eigenvalues significantly different from zero
•The number of eigenvalues is the relevant dimensionality•The corresponding eigenvectors span the subspace of the relevant features
Stimulus prior
Bialek et al., 1997
![Page 26: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/26.jpg)
Functional models of neural function
spike-triggering stimulus feature
stimulus X(t)
decision function
spike output Y(t)x1
f1
P(s
pike
|x1
)
x1
![Page 27: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/27.jpg)
spike-triggering stimulus features
stimulus X(t)
multidimensionaldecision function
spike output Y(t)
x1
x2
x3
f1
f2
f3
Functional models of neural function
![Page 28: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/28.jpg)
?
spike-triggering stimulus features
?
stimulus X(t)
decision function
spike history feedback
spike output Y(t)
x1
x2
x3
f1
f2
f3
?
Functional models of neural function
![Page 29: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/29.jpg)
Covariance analysis
Let’s develop some intuition for how this works: the Keat model
Keat, Reinagel, Reid and Meister, Predicting every spike. Neuron (2001)
• Spiking is controlled by a single filter• Spikes happen generally on an upward threshold crossing of
the filtered stimulus expect 2 modes, the filter F(t) and its time derivative F’(t)
![Page 30: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/30.jpg)
-1.0
-0.5
0.0
0.5
1.0
Eig
en
valu
e
50403020100Mode Index
-1.0
-0.5
0.0
0.5
1.0
Eig
en
valu
e
50403020100Mode Index
-1.0
-0.5
0.0
0.5
1.0
Eig
en
valu
e
50403020100Mode Index
6
4
2
0
-2P
roje
ctio
n o
nto
Mo
de
26420-2
Projection onto Mode 1
6
4
2
0
-2P
roje
ctio
n o
nto
Mo
de
2
6420-2
Projection onto Mode 1
6
4
2
0
-2P
roje
ctio
n o
nto
Mo
de
2
6420-2
Projection onto Mode 1
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Sp
ike
-Tri
gg
ere
d A
vera
ge
-0.5 -0.4 -0.3 -0.2 -0.1 0.0Time before Spike (s)
Covariance analysis
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Sp
ike
-Tri
gg
ere
d A
vera
ge
-0.5 -0.4 -0.3 -0.2 -0.1 0.0Time before Spike (s)
![Page 31: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/31.jpg)
Covariance analysis
Let’s try a real neuron: rat somatosensory cortex (Ras Petersen, Mathew Diamond, SISSA)
0 200 400 600 800 1000
-400
-200
0
200
400
Time (ms)
Stim
ulat
or
posi
tion
(m
)
Record from single units in barrel cortex
![Page 32: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/32.jpg)
Covariance analysis
Spike-triggered average:
-20020406080100120140160180-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Pre-spike time (ms)
No
rma
lise
d ve
loci
ty
![Page 33: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/33.jpg)
Covariance analysis
Is the neuron simply not very responsive to a white noise stimulus?
![Page 34: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/34.jpg)
Covariance analysis
Prior Spike-triggered
Difference
![Page 35: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/35.jpg)
Covariance analysis
0 20 40 60 80 100-1
0
1
2
3
4
Feature number
No
rmal
ised
vel
oci
ty2
050100150-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Pre-spike time (ms)
Vel
oci
ty
Eigenspectrum
Leading modes
![Page 36: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/36.jpg)
-3 -2 -1 0 1 2 30
2
4
6
8
10
Normalised "acceleration"
No
rmal
ised
firi
ng r
ate
-3 -2 -1 0 1 2 30
2
4
6
8
10
12
Normalised "velocity"
No
rmal
ised
firi
ng r
ate
-2 0 2
-3
-2
-1
0
1
2
3
"acceleration"
"vel
oci
ty"
0
2
4
6
8
10
0 1 2 30
2
4
6
8
10
"vel"2+"acc"2
No
rmal
ised
firi
ng r
ate
Input/outputrelations wrtfirst two filters,alone:
and in quadrature:
Covariance analysis
![Page 37: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/37.jpg)
050100150-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Pre-spike time (ms)
Velo
city (
arb
itra
ry u
nits)
050100150-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Pre-spike time (ms)V
elo
city
(a
rbitr
ary
un
its)
How about the other modes?
Next pair with +ve eigenvalues Pair with -ve eigenvalues
Covariance analysis
![Page 38: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/38.jpg)
Covariance analysis
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
"Energy"N
orm
alis
ed f
iring
rat
e
-3 -2 -1 0 1 2-3
-2
-1
0
1
2
Filter 100
Filt
er 1
01
0.2
0.4
0.6
0.8
1
1.2
1.4
Firing rate decreases with increasing projection: suppressive modes
Input/output relations for negative pair
![Page 39: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/39.jpg)
Beyond covariance analysis
1. Single, best filter determined by the first moment
2. A family of filters derived using the second moment
3. Use the entire distribution: information theoretic methods
Find the dimensions that maximize the mutual informationbetween stimulus and spike
Removes requirement for Gaussian stimuli
![Page 40: What is the neural code?](https://reader035.vdocument.in/reader035/viewer/2022062500/56814fd9550346895dbd9f47/html5/thumbnails/40.jpg)
Limitations
Not a completely “blind” procedure: have to have some idea of the appropriate stimulus space
Very complex stimuli: does a geometrical picture work or make sense?
Adaptation:stimulus representations change with experience!