The Algorithmic Lens on the Sciences

1. The Algorithmic Lenson the Sciences Christos H. Papadimitriou UC Berkeley

2. What is Computer Science? “CS is the only scientific discipline that cannot be defined in a single sentence”

3. (now seriously folks…) What is Computer Science? • Applied science? • Engineering discipline? • Narrative of a transformative technology? • (in the era of the Internet) Also a natural and social science?

4. Mathematics: “The queen and servant of sciences” • Queen: Power, authority, pride, beauty • Servant: Influences and transforms by being useful, powerful, and universal • My point: CS is the new math

6. Perturbing Physics The algorithmic worldview provides new insights into, and tests, some of the most prestigious theories about the universe

7. Statistical Physics and Algorithms How does the lake freeze? The mystery of phase transitions vs. the convergence of algorithms

8. Quantum computation: reinventing the bit many electrons bit: a wire can have few electrons close to the nucleus qubit: an electron can be far

9. Big difference • A bit is either 0 or 1 • A qubit is in both states Q =  |0 +  |1 • An n-qubit system is in 2n states at the same time! complex numbers “probabilities”

10. Three possible reactions • How curious, Nature is extravagant! 2. Oh my God, how do you simulate such a system on a computer? • But what if we built a computer out of these things?

11. How to factor a 1000-bit integerin ~1000 easy steps(on a quantum computer) output (measurement) 1000 bits input 1000 bits the “probabilities” of 21000 states maintained throughout

12. But can we build these computers?The three eventualities • Yes! • No, because of a thousand annoying little problems and details (plus, eventually, lack of funding…) • No, because Quantum Physics breaks down for large numbers of particles!!!

13. “Quantum computation is as much about testing Quantum Physics as it is about building powerful computers.” Umesh Vazirani

14. Equilibria: Behavior predictions in Economics

15. The Story of Equilibria They exist in two-player zero-sum games,1928 John Nash 1950: all games have one!

16. In markets too!Price equilibria (Arrow-Debreu 1954) “The Nash equilibrium lies at the foundations of modern economic thought.” Roger Myerson

17. Universality (Nash’s theorem) is important “Nobody would take seriously a solution concept that is empty for some games.” Roger Myerson

18. Surprise! Finding equilibria is an intractable problem!

19. And intractability meansNash equilibrium’s universality is suspect “If your laptop can’t find it, neither can the market” Kamal Jain

20. Next • New, more “algorithmic” solution concept based on player dynamics?

21. Evolution under the Lens

22. “What algorithm could have created all this in a mere 1012 steps?”

23. The Origin of Species • Possibly the world’s most masterfully compelling scientific argument • Natural selection • Common ancestry

24. Evolution Theory since 1859 • Genetics (Mendel, 1866 – really, 1901) • The crisis (1901 – 1930) • The synthesis through math (1930 – ) • The genomics revolution (1980 – )

25. The Synthesis: The Fisher-Wright-Haldane model Entries: fitness of the genotype (exp. # offspring, normalized) 1.05 1.00 0.96 1.01 1.03 1.02 0.94 1.02 0.99 Rows: alleles of gene A Columns: alleles of gene B

26. The Fisher-Wright-Haldane model:frequencies at current generation 0.33 0.33 0.33 0.33 1.05 1.00 0.96 0.33 1.01 1.03 1.02 0.33 0.94 1.02 0.99

27. The Fisher-Wright-Haldane model:frequencies at next generation 0.33 0.35 0.32 0.34 1.05 1.00 0.96 0.34 1.01 1.03 1.02 0.31 0.94 1.02 0.99

28. Brilliant theory, a deluge of data -- and yet most important questions unanswered • Why so much genetic diversity? • What is the role of sex/recombination? • Is Evolution optimizing something?

29. Btw: 100 generations later? 1.05 1.00 0.96 1.01 1.03 1.02 0.94 1.02 0.99

30. Btw: 100 generations later? 0.30 0.63 0.07 0.24 1.05 1.00 0.96 0.73 1.01 1.03 1.02 0.03 0.94 1.02 0.99

31. Mixability Theory of the Role of Sex: [LPF 2007]:good mixers win! 0.30 0.63 0.07 0.24 1.05 1.00 0.96 0.73 1.01 1.03 1.02 0.03 0.94 1.02 0.99

32. Contrast: In asexual speciesthe fittest genotype wins 1.05 1.00 0.96 1.01 1.03 1.02 0.94 1.02 0.99

33. Surprising connection with algorithms [CLPV 2014] • The Fisher-Wright-Haldane model is mathematically equivalent to a repeated game between genes: • The strategies of each gene are its alleles • The probabilities of play are the frequencies • The commonutility is the organism’s fitness • The genes update their probabilities of play through the multiplicative updates algorithm!

34. Multiplicative updates! • (Also known as no-regret learning) • A simple, common-sense algorithm known in CS for its surprising aptness at solving many sophisticated problems • At each step, increase the weight of allele i by a factor of (1 + ε fi) • fiis the allele’s fitness in the current environment created by the other genes

35. Multiplicative updates:Dual interpretation Convex optimization duality: Each gene “seeks to optimize” the sum of two quantities: allele frequencies cumulative fitness maxx Φ(x) = H(x) + s F x entropy selection strength

36. Recall the Big Questions • Why so much genetic diversity? • What is the role of sex/recombination? • Is Evolution optimizing something? • “What algorithm could have done this in a mere 1012 steps?”

37. Finally: The frontier in our head

38. Brain and Computation: The Great Disconnects • Babies vscomputers • Clever algorithms vswhat happens in cortex • Understanding Brain anatomy and function vsunderstandingthe emergence of the Mind • How does one think computationally about the Brain?

39. A possible approach • (Current work with Santosh Vempala, and Wolfgang Maas and his group in Graz) • What is the boundary between “subsymbolic” and “symbolic” brain processes? • One candidate: Assemblies of excitatory neurons in MTL

40. The experiment by [Ison et al. 2016]

41. The experiment by [Ison et al. 2016]

42. The experiment by [Ison et al. 2016]

43. The experiment by [Ison et al. 2016]

44. The experiment by [Ison et al. 2016]

45. The experiment by [Ison et al. 2016]

46. The experiment by [Ison et al. 2016]

47. Interpretation • Each “thing” is represented by an assembly of many neurons (~0,5% of all) • Every time we are thinking of the “thing”all these neurons fire • If two “things” become related, these assemblies are “JOINed:” some neurons fire on either “thing”

48. Questions • Can this interpretattion be predicted by a realistic mathematicalmodel of neurons and synapses? (It is predicted in simulations) • How about operations besides JOIN such as LINK or BIND (e.g., “kick” is a “verb”)? • Can assemblies be the right conceptualinterface between CS and Brain Science? • Connection with language?

49. Soooo… • CS is worth teaching not only because it is (a) a fascinating and open-ended subject; (b) useful and in dmand; (c) as central and present in the world today as mass, energy, and life… …but also because (just like math) • (d) without a solid understanding of computation you are handicapped as a scientist

50. Danke! Merci! Grazie! Engrazie! Ευχαριστώ!