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Information in “Associative” Learning

Information in “Associative” Learning

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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