Transcript From vision to action - The Swartz Foundation

Noise reduction and addition in
sensory-motor processing
Stephen G. Lisberger
Howard Hughes Medical Institute
Department of Physiology, UCSF
Can we learn something important by
analyzing trial-by-trial variation?
• We know that the responses of single neurons vary substantially across
identical trials.
• We want to understand how the brain deals with the variation across
many neurons on one trial.
• We want to know about noise reduction and noise addition at each level
of sensory-motor processing.
Noise reduction depends on the degree of independence of neural
responses across the population (RNN)
Downstream noise addition (2DS) depends on lots of factors
Can we learn something important by
analyzing trial-by-trial variation?
• What can we measure?
Trial-by-trial variation in responses of individual neurons (2FR)
Trial-by-trial variations in behavioral outputs (2EYE)
Correlations between trial-by-trial variations in neural
responses and behavior (RNB)
To some degree, correlations between trial-by-trial variations
in responses of pairs of neurons (RNN)
• How do we get from what we can measure to what we want to know?
Two simple intuitions
• Higher correlations between neurons in the
population lead to higher neuron-behavior
correlations -- less noise reduction
• More noise added downstream leads to lower
neuron-behavior correlations
(These intuitions break if the population of neurons is really small)
Equations that make these intuitions concrete
Neuron-behavior correlations
Variance reduction

RNB 
RNN

RNN 

2
DS
2
FR
2
2
 EYE
 DS
 RNN  2
2
 FR
 FR
(These are for large numbers of neurons in the population)

Solving the equations allows us to compute what
we want to know from what we can measure
2
 EYE
2
 FR
Neuron-neuron correlations
RNN  RNB

Noise added downstream
2
2
 DS
 EYE
 2  RNN
2
 FR  FR
Smooth pursuit eye movements
Pursuit is
somewhat
variable
Neural
responses are
variable, too
Neural responses are variable, too
Eye velocity
Target velocity
Neural responses are variable, too
Eye velocity
Target velocity
What we can measure in single unit recordings
Neuron-behavior correlations
RNB
Noise reduction between
neuron and behavior
2
 EYE
2
 FR

(To make these measurements meaningful in an
absolute sense, we derive a surrogate of eye
movement with the units of firing rate, spikes/s.)

What we can measure in single unit recordings
Neuron-behavior correlations
RNB
Noise reduction between
neuron and behavior
2
 EYE
2
 FR

Ý
fr(t)  aEÝ
(t) bEÝ(t) cE(t) rr

Surrogate of eye movement (spikes/s)
Neuron-behavior correlations
Measurements from the data
Measurements from the data
Recall the equations that allow us to
compute what we want to know from
what we can measure
Neuron-neuron correlations
RNN  RNB

Noise added downstream


2
DS
2
FR



2
 EYE
2
 FR
2
EYE
2
FR
 RNN
Neuronneuron
correlations
Downstream
noise
The bigger picture
Neural population
FR, 2FR, RNN, N
Decoding
, Avg, VAvg, …
2DS, C/Dvergence
Behavior
2EYE, RNB
The bigger picture
Neural population
FR, 2FR, RNN, N
Decoding
, Avg, VAvg, …
2DS, C/Dvergence
Neural population
FR, 2FR, RNN, N
Behavior
2EYE, RNB
Collaborators
Leslie Osborne
Javier Medina
Bill Bialek
Research supported by the Sloan and Swartz Foundations, the
Howard Hughes Medical Institute, the National Eye Institute, the
National Institute for Neurological Disease and Stroke, and the
National Institute for Mental Health