2. Information in “Associative” Learning C. R. Gallistel Rutgers Center for Cognitive Science

3. Sloan-Swartz 7/22/081 Temporal Pairing Thought to be essential for the formation of associations Assumed to be the critical variable in work on neurobiology of learning (LTP) Basis of unsupervised learning in neural net models

4. Sloan-Swartz 7/22/082 But It’s never been objectively defined for any paradigm: What is the critical interval? Neither necessary nor sufficient for development of a conditioned response to the CS (the warning signal)

5. Sloan-Swartz 7/22/083 Not Necessary Subjects develop a conditioned response to a CS that is never paired with the US (the predicted event)--conditioned inhibition Pavlov and Hull struggled with this problem It has not been solved

6. Sloan-Swartz 7/22/084 Not Sufficient The truly random control (Rescorla, 1968) –It is the mutual information between CS & US that is critical –Not their temporal pairing

7. Sloan-Swartz 7/22/085 It’s Information! People believe in “temporal pairing” because they are intuitively sensitive to the fact that a relatively more proximal warning gives more information It’s the information that matters, not the temporal pairing

8. Sloan-Swartz 7/22/086 Information Derives From Temporal Representation Information-theoretic analysis explains BOTH cue competition AND the data on the temporal pairing Founded on the assumption that animals learn the intervals AND, they represent the uncertainty with which they can remember them (about +/- 15%)

9. Sloan-Swartz 7/22/087 Principles I Subjects respond only to stimuli (CSs) that provide information about the timing of future events (USs) CSs inform to the extent they change the subject’s uncertainty about the time to the next US

10. Sloan-Swartz 7/22/088 Principles II Bandwidth maximization by minimizing number of information-carrying CSs attended to Information carried by intervals and numbers They are what is learned Weber’s law: uncertainty scales with delay:  =wT

11. Sloan-Swartz 7/22/089 Rate-Change Protocols Information communicated by CS

12. Sloan-Swartz 7/22/0810 Delay Protocols They are additive Only one depends on protocol parameters Two sources of information: 1) The rate change 2) The fixed delay

13. Sloan-Swartz 7/22/0811 Gibbon & Balsam Reinforcements to acquisition, as a function of the I us-us /I cs-us ratio Slope (log-log) ~ -1

14. Sloan-Swartz 7/22/0812 Trials Don’t Matter These two protocols are equi-effective! The number of trials is not in and of itself a learning-relevant parameter of a training protocol Gottlieb (2008)

15. Sloan-Swartz 7/22/0813 Associability where N cs-us = the number of CS reinforcements required to produce an anticipatory response. (The onset of conditioned responding is abrupt) Definition parallels definition of sensitivity (1/Intensity) in sensory psychophysics Purely operational: no implication that associations exist

16. Sloan-Swartz 7/22/0814 Informativeness We define the ratio of the background rate to the rate in presence of CS to be the informativeness of the CS-US relation in an associative learning protocol Thus, the information conveyed is the log of the informativeness

17. Sloan-Swartz 7/22/0815 A Simple Quantitative Law

18. Sloan-Swartz 7/22/0816 Why trials don’t matter When there are 8 times fewer trials, the trials are 8 times more informative Provided one maintains total protocol duration The only way to speed up learning is to increase informativeness of the CS-US relation. Adding trials won’t do it!

19. Sloan-Swartz 7/22/0817 Conclusion 1 Temporal pairing is –Undefinable –Insufficient –Unnecessary “Trials” are a pernicious fiction. Banish them from your models

20. Sloan-Swartz 7/22/0818 Conclusion 2 What matters is the mutual information (between CS and US), a component of which is the change in US rate when the CS comes on The informativeness of the CS-US relation is the factor by which CS onset changes the expected time to the next US Associability is proportional to informativeness That’s why people believe in in temporal pairing

21. Sloan-Swartz 7/22/0819 Conclusions 3 Focus on mutual information gives an empirically supported quantitative account of the notion of temporal pairing And an account of “cue competition:” how the system solves the multivariate prediction problem (aka the assignment-of-credit problem; what is predicting what), the other problem posed by Rescorla’s experiment

22. Sloan-Swartz 7/22/0820 Thank You Collaborators –The late John Gibbon –Peter Balsam –Stephen Fairhurst –Daniel Gottlieb Support –RO1 MH68073 Time and Associative Learning