1 of 22

The neural code�Variability and correlations

Kenneth D Harris, UCL

2 of 22

Allen Institute mouse visual cortex data

  • Neuropixels recordings from visual cortex (and other regions), mouse passively viewing stimuli
  • Lots of visual stimuli, including 118 natural scenes and 1 gray screen presented 50 times each:

​

Siegle et al Nature 2021. https://www.nature.com/articles/s41586-020-03171-x

3 of 22

Spike count variability: more than Poisson

4 of 22

Spike count variance vs mean

  •  

Cell 180

Cell 181

Cell 0

5 of 22

Allen Institute mouse visual cortex data

  • Neuropixels recordings from visual cortex (and other regions), mouse passively viewing stimuli
  • Lots of visual stimuli, including 118 natural scenes and 1 gray screen presented 50 times each:

​

Siegle et al Nature 2021. https://www.nature.com/articles/s41586-020-03171-x

6 of 22

Trial-to-trial variability in population responses to same stimulus

Repeat (sorted by rate in first 50ms)

time (ms)

cell

7 of 22

Variability above Poisson is related to correlations

  • How can we study correlations?

​

1. Cross-correlogram (provides fast-timescale information)

​

2. Spike count correlation across trials

8 of 22

Cross-correlogram

  •  

9 of 22

Identifying synaptic connections from CCGs

  • In cortex, narrow waveforms come from one specific type of inhibitory neuron (“Pvalb cells”)
  • Wide waveforms from all other neurons (so mostly excitatory cells)
  • Sometimes you see peaks just offset from 0 that match expected direction => probably synaptic

10 of 22

Confirming connectivity by stimulating excitatory cells

11 of 22

Spike count correlation

  • Neurons can be correlated for two reasons:

​

​

  • Stimulus-dependent correlation
    • Both neurons respond to the same sensory stimuli
    • (Sometimes called “signal correlation”)
    • You would see this even for responses different repeats of a stimulus
    • Or even for neurons in different brains

​

​

  • Stimulus-independent correlation
    • Both neurons are driven by the same stimulus-independent factors
    • (Sometimes called “noise correlation”)
    • Requires a genuinely simultaneous recording

​

12 of 22

Estimating stimulus-dependent correlations

  •  

 

 

“Noise”, i.e. variability between presentations of stimulus

 

13 of 22

Estimating stimulus-dependent correlations

Mean responses of cell 1

Mean responses of cell 2

0

1

2

3

cell 1501 response

0

0.2

0.4

0.6

0.8

1

c

e

l

l

5

3

5

6

r

e

s

p

o

n

s

e

traditional signal correlation

r = 0.4071

p <1e-5

repeat 1

repeat 2

14 of 22

Estimating stimulus-dependent correlations

0

1

2

3

cell 1501 response

0

0.2

0.4

0.6

0.8

1

c

e

l

l

5

3

5

6

r

e

s

p

o

n

s

e

Correlation within repeat

r = 0.4071

p <1e-5

0

0.5

1

1.5

cell 1501 response

0

0.5

1

1.5

c

e

l

l

5

3

5

6

r

e

s

p

o

n

s

e

Correlation between repeats

r = 0.0146

p = 0.8786

Mean responses of cell 1: block 1

Mean responses of cell 1: block 2

Mean responses of cell 2: block 1

Mean responses of cell 2: block 2

  • Finite number of repeats
  • Correlated fluctuations not fully averaged out
  • Contribute to apparent stimulus correlation

repeat 1

repeat 2

15 of 22

Estimating stimulus-dependent correlations

0

1

2

3

cell 1501 response

0

0.2

0.4

0.6

0.8

1

c

e

l

l

5

3

5

6

r

e

s

p

o

n

s

e

r = 0.4071

p <1e-5

0

0.5

1

1.5

cell 1501 response

0

0.5

1

1.5

c

e

l

l

5

3

5

6

r

e

s

p

o

n

s

e

r = 0.0146

p = 0.8786

0

1

2

3

cell 6800 response

0

1

2

3

c

e

l

l

1

1

0

1

r

e

s

p

o

n

s

e

r = 0.37

p <1e-4

0

1

2

3

cell 6800 response

0

1

2

3

4

5

c

e

l

l

1

1

0

1

r

e

s

p

o

n

s

e

r = 0.5765

p <1e-10

Mean responses of cell 1: block 1

Mean responses of cell 1: block 2

Mean responses of cell 2: block 1

Mean responses of cell 2: block 2

Correlation within repeat

Correlation between repeats

16 of 22

Around 2% of cell pairs show genuine stimulus-dependent correlation

0

0.5

1

p value

0

5

10

15

n

u

m

b

e

r

o

f

p

a

i

r

s

10

5

pair distribution

uniform distribution

Mean responses of cell 1: block 1

Mean responses of cell 1: block 2

Mean responses of cell 2: block 1

Mean responses of cell 2: block 2

17 of 22

Similarity of spontaneous and evoked activity?

  • Boltzmann machine: simple recurrent ANN model
  • Visible units: clamped to sensory input
  • Hidden units: learn to represent latent factors for probability distribution of sensory input

​

  • Learning rule: two phases
  • “Wake”: Hebbian plasticity between all units, visible units clamped to sensory input
  • “Sleep”: Anti-Hebbian plasticity, visible units free-run

​

  • Produces “dreams” in sleep phase that resemble sensory inputs

​

18 of 22

Are spontaneous and evoked patterns really similar?

  • A lot of papers say yes …

19 of 22

But it might be down to one shared dimension

  • Population rate = summed activity of all neurons
  • Movements and up phases increase population rate
  • Sensory stimuli increase population rate
  • This might be the only dimension they have in common
  • Might explain similarity of population patterns

20 of 22

Additive and multiplicative variability

 

21 of 22

The coding equation

  •  

22 of 22

Current model for sensory coding

  •