1. Remembering to decide: discrimination of temporally separated stimuli (selecting the best apple) Paul Miller Brandeis University

2. Parametric Working Memory and Sequential Discrimination Experiments by group of R. Romo et al., UNAM Nature 399:470 (1999), Cereb. Cort. 13:1196 (2003)

3. Choose f1 > f2 f2f1

4. or f2 > f1 f1f2

5. Rastergram: f1(Hz) 10 14 18 22 26 30 34 basedelay Trial-averaged firing rate Firing rate (Hz) 0 30 Time (sec)0.5 3.5 (from Miller et al. Cerebral Cortex 2003) Tuning curve of memory activity Firing rate (Hz) Stimulus, f1 (Hz) 5 18 1034 Romo et al. Nature 1999

6. A continuous attractor acts as an integrator Time Input Memory activity

7. ... but integration yields magnitude x time Time Input Memory activity

8. Problem: How can a network compare an incoming stimulus with an earlier one in memory? Especially as discrimination ≡ subtraction whereas integration ≡ addition Sequential Discrimination Integral feedback control: memory neurons (M) inhibit their inputs (D). Solution: - + ∫ r D dt Input

9. rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 1 low cue1delaycue2

10. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 1 low cue1delaycue2

11. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 2 higher cue1delaycue2

12. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 2 lower Threshold not reached cue1delaycue2

13. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 1 high cue1delaycue2

14. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 2 lower Threshold not reached cue1delaycue2

15. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue1delaycue2 cue 2 higher

16. A continuous attractor for memory

18. Feedback too high Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

19. Feedback too high Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

20. Feedback too high Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

21. Feedback too low Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

22. Feedback too low Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

23. Feedback too low Gradient is proportional to difference between current needed to produce a firing rate and the feedback current generated by that firing rate.

24. Continuous or discrete memory? Note psychophysics: for most continuous quantities, we can only remember (even recognize?) them in discrete categories Except when quantity is encoded across different neurons (eg vision, pitch)

25. Simulation results Look at Discriminating neuron Memory = Discrete Integrator

26. Activity of model discriminating neuron. basedelaycomparison

27. basedelaycomparison Activity of model discriminating neuron.

28. Trial-averaged firing rate through time of model discriminating neuron for different pairs of stimuli f1 = 34Hz f1 = 10Hz f2>f1 f2<f1 Base, f1 Delay Comparison, f2 Time (sec) 0 0.5 3.5 4 0 100 Firing rate (Hz) f1 = 22Hz Miller and Wang, PNAS 2006

29. Base tuning Comparison tuning Delay tuning f2>f1 f2<f1

30. Trial-averaged firing rate through time from experimental data of Romo (prefrontal cortex) Base, f1 Delay Comparison, f2 Time (sec) 0 0.5 3.5 4 0 35 Firing rate (Hz) f2>f1 f2<f1 f1=12Hz f1=20Hz f1=28Hz

31. PFC cell from Romo's data: Initial tuning +ve to f1 : final tuning to +f2-f1 Base, f1 Delay Comparison, f2 Time (sec) 0 0.5 3.5 4 0 60 Firing rate (Hz) f2>f1 f2<f1 f1=10Hz f1=22Hz f1=34Hz

32. PFC cell from Romo's data Initial tuning -ve to f1 : final tuning to +f1-f2 Base, f1 Delay Comparison, f2 Time (sec) 0 0.5 3.5 4 0 35 Firing rate (Hz) f2<f1 f2>f1 f1=10Hz f1=22Hz f1=28Hz

33. Decision-making as a competition between pools

34. f1=22Hz Probability of choosing f2>f1 from simulations

35. f1=14Hz f1=22Hz Probability of choosing f2>f1 from simulations

36. f1=14Hz f1=22Hz f1=30Hz Probability of choosing f2>f1 from simulations Miller, in preparation

37. Probability of choosing f2>f1 from experiment f1 = 20Hzf1 = 30Hz f2

38. Probability of choosing f2>f1 from experiment = fix f2 (20Hz), vary f1 = fix f1 (20Hz), vary f2

39. Probability of choosing f2>f1 from experiment Hernandez et al, 1997 = fix f2 (20Hz), vary f1 = fix f1 (20Hz), vary f2 = fix f2 (30Hz), vary f1 = fix f1 (30Hz), vary f2

40. fixed f1=22Hzfixed f1=30Hz Probability of choosing f2>f1 from simulations

41. fixed f1=22Hzfixed f1=30Hz Probability of choosing f2>f1 from simulations fixed f2=22Hzfixed f2=30Hz

42. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 1:low Is magnitude dissociated from duration of input?

43. Input rDrD rMrM I D =Input -W MD r M t t t t cue1delaycue2 cue1 delay cue2 cue 1:longer Is magnitude dissociated from duration of input?

44. Duration of initial stimulus:= 0.5s Is magnitude dissociated from duration of input? Simulation results

45. Duration of initial stimulus:= 0.5s = 0.25s Is magnitude dissociated from duration of input? Simulation results

46. Duration of initial stimulus:= 0.5s = 0.25s = 0.75s + Is magnitude dissociated from duration of input? Simulation results

47. From Luna et al., Nat Neurosci 2005 Is magnitude dissociated from duration of input? Experimental results