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Information in “Associative” Learning

Information in “Associative” Learning. C. R. Gallistel Rutgers Center for Cognitive Science. Temporal Pairing. Thought to be essential for the formation of associations Assumed to be the critical variable in work on neurobiology of learning (LTP)

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Information in “Associative” Learning

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

  2. 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 Sloan-Swartz 7/22/08

  3. 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) Sloan-Swartz 7/22/08

  4. 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 Sloan-Swartz 7/22/08

  5. Not Sufficient • The truly random control (Rescorla, 1968) • It is the mutual information between CS & US that is critical • Not their temporal pairing Sloan-Swartz 7/22/08

  6. 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 Sloan-Swartz 7/22/08

  7. 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%) Sloan-Swartz 7/22/08

  8. 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 Sloan-Swartz 7/22/08

  9. 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 Sloan-Swartz 7/22/08

  10. Rate-Change Protocols Information communicated by CS Sloan-Swartz 7/22/08

  11. Delay Protocols • Two sources of information: 1) The rate change 2) The fixed delay • They are additive • Only one depends on protocol parameters Sloan-Swartz 7/22/08

  12. Gibbon & Balsam • Reinforcements to acquisition, as a function of theIus-us/Ics-us ratio • Slope (log-log) ~ -1 Sloan-Swartz 7/22/08

  13. 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) Sloan-Swartz 7/22/08

  14. Associability • where Ncs-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 Sloan-Swartz 7/22/08

  15. 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 Sloan-Swartz 7/22/08

  16. A Simple Quantitative Law Sloan-Swartz 7/22/08

  17. 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! Sloan-Swartz 7/22/08

  18. Conclusion 1 • Temporal pairing is • Undefinable • Insufficient • Unnecessary • “Trials” are a pernicious fiction. Banish them from your models Sloan-Swartz 7/22/08

  19. 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 Sloan-Swartz 7/22/08

  20. 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 Sloan-Swartz 7/22/08

  21. Thank You • Collaborators • The late John Gibbon • Peter Balsam • Stephen Fairhurst • Daniel Gottlieb • Support • RO1 MH68073 Time and Associative Learning Sloan-Swartz 7/22/08

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