1. Noise reduction and addition in sensory-motor processing Stephen G. Lisberger Howard Hughes Medical Institute Department of Physiology, UCSF

2. 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 (R NN ) Downstream noise addition (  2 DS ) depends on lots of factors

3. Can we learn something important by analyzing trial-by-trial variation? What can we measure? Trial-by-trial variation in responses of individual neurons (  2 FR ) Trial-by-trial variations in behavioral outputs (  2 EYE ) Correlations between trial-by-trial variations in neural responses and behavior (R NB ) To some degree, correlations between trial-by-trial variations in responses of pairs of neurons (R NN ) How do we get from what we can measure to what we want to know?

5. 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)

6. Equations that make these intuitions concrete Variance reduction Neuron-behavior correlations (These are for large numbers of neurons in the population)

7. Solving the equations allows us to compute what we want to know from what we can measure Noise added downstream Neuron-neuron correlations

8. Smooth pursuit eye movements

9. Pursuit is somewhat variable

10. Neural responses are variable, too

11. Target velocity Eye velocity

12. Neural responses are variable, too Target velocity Eye velocity

13. What we can measure in single unit recordings Noise reduction between neuron and behavior Neuron-behavior correlations (To make these measurements meaningful in an absolute sense, we derive a surrogate of eye movement with the units of firing rate, spikes/s.)

14. What we can measure in single unit recordings Noise reduction between neuron and behavior Neuron-behavior correlations

15. Surrogate of eye movement (spikes/s)

16. Measurements from the data

18. Recall the equations that allow us to compute what we want to know from what we can measure Noise added downstream Neuron-neuron correlations

19. Neuron- neuron correlations Downstream noise

20. The bigger picture Neural population Decoding Behavior FR,  2 FR, R NN, N , Avg, VAvg, …  2 DS, C/Dvergence  2 EYE, R NB

21. The bigger picture Neural population Decoding Neural population Behavior FR,  2 FR, R NN, N , Avg, VAvg, …  2 DS, C/Dvergence  2 EYE, R NB FR,  2 FR, R NN, N

22. 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