The Blessing and the Curse of Multiplicative Updates

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Multiplicative updates multiply nonnegative weights and recover Bayes via prior×likelihood, implemented physically with 10^20 strands in in vitro selection using PCR amplification; raw multiplicative dynamics give exponential growth but wipe out diversity so one strand wins. Proven fixes include conservative/Winnow thresholding (blind selection with sample-based dot products, bound ≈ k·log(n/k)), mix in 1% uniform to preserve a lower-bound, capping to create exponentially many corners, and a two-cup cross-pouring protocol that produces long-term memory and works empirically in simulated tube experiments.

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" chapters (31)

1. 0:00Intro
2. 0:37Definition of multiplicative updates
3. 1:19Machine learning vs nature
4. 6:11Basic scheme
5. 6:52Duplicating DNA with PCR
6. 8:46The caveat
7. 9:19Mathematical description of in-vitro selection
8. 11:28Update Good RNA in tubes
9. 12:33Implementing Bayes rule in RNA
10. 13:34Iterating Bayes Rule with same data likelihoods
11. 15:07The best are too good
12. 15:57View of evolution
13. 16:43Another tube experiment
14. 18:33Boundaries prevent the curse
15. 18:55A first key problem
16. 20:41Solution
17. 25:25Nature 2: Coupling preserves diversity
18. 25:55A second problem
19. 27:39Key problem 2
20. 29:04Related machine learning problem
21. 31:05Normalized Winnow Algorithm (N. Littlestone)
22. 34:42ML 1: prevent overtraining with conservative update
23. 35:38Super predator
24. 35:54cap weights
25. 36:20Why capping?
26. 37:45What if environment changes over time
27. 38:27Disk spindown problem
28. 47:27ML 4: sleeping
29. 48:11Blind in-vitro implementation of sleeping
30. 50:12Summary
31. 50:46Final question