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(Reverse) Engineering Intelligence - Noah Goodman - H+ Summit @ Harvard

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What computational principles explain the success of human intelligence? I will describe recent work that combines together the unbounded flexibility of mathematical logic with the robustness of statistical inference. This combination brings us several steps closer to understanding human intelligence -- and to the tools for true intelligence engineering.

Noah D. Goodman is a research scientist in the Department of Brain and Cognitive Sciences at MIT, and a member of the Computer Science and Artificial Intelligence Laboratory. He studies the computational basis of human thought, merging behavioral experiments with formal methods from statistics and logic. He received his Ph.D. in mathematics from the University of Texas at Austin. After a brief stint as a Chicago real estate developer, he joined the Computational Cognitive Science group at MIT. Goodman has published more than thirty publications in psychology, cognitive science, artificial intelligence, and mathematics. Several of these papers have won awards.

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(Reverse) Engineering Intelligence - Noah Goodman - H+ Summit @ Harvard

  1. 1. ngoodman@ stanford.edu (Reverse) Engineering Intelligence Noah D. Goodman Stanford University H+ Summit, June 12, 2010
  2. 2. What is thought?
  3. 3. What is thought? • How are thoughts structured?
  4. 4. What is thought? • How are thoughts structured? • How does this structure support flexible, successful thinking?
  5. 5. What is thought? • How are thoughts structured? • How does this structure support flexible, successful thinking? What mathematical principles can help us understand thought?
  6. 6. What is thought? • How are thoughts structured? • How does this structure support flexible, successful thinking? e ngi ne e r What mathematical principles can help us understand thought?
  7. 7. Composition and probability
  8. 8. Composition and probability Thought is productive: “the infinite use of finite means”
  9. 9. Composition and probability Thought is productive: “the infinite use of finite means” ..a big green bear who loves chocolate..
  10. 10. Composition and probability Thought is productive: “the infinite use of finite means” ..a big green bear who loves chocolate..
  11. 11. Composition and probability Thought is productive: “the infinite use of finite means” p=mv
  12. 12. Composition and probability Thought is productive: “the infinite use of finite means” p=mv
  13. 13. Composition and probability Thought is productive: “the infinite use of finite means” p=mv Compositional representations
  14. 14. Composition and probability Thought is productive: “the infinite use of finite means” Compositional representations
  15. 15. Composition and probability Thought is productive: “the infinite use of finite means” Compositional representations
  16. 16. Composition and probability Thought is productive: “the infinite use of finite means” Compositional representations
  17. 17. Composition and probability Thought is productive: “the infinite use of finite means” Compositional representations
  18. 18. Composition and probability Thought is productive: “the infinite use of finite means” Compositional representations
  19. 19. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional representations
  20. 20. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional representations
  21. 21. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Why did he yell at me? Compositional representations
  22. 22. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Why did he yell at me? He wanted to hurt me. He thought I was a telemarketer. Compositional representations
  23. 23. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Why did he yell at me? Belief Desire Action He wanted to hurt me. He thought I was a telemarketer. Compositional representations
  24. 24. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Why did he yell at me? Belief Desire Action He wanted to hurt me. He thought I was a telemarketer. Compositional Probabilistic representations inference
  25. 25. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional Probabilistic representations inference
  26. 26. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional Probabilistic representations inference
  27. 27. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world a+b+c = Compositional Probabilistic representations inference
  28. 28. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world a+b+c = 0 1 2 3 Compositional Probabilistic representations inference
  29. 29. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world a+b+c = 0 1 2 3 P (H|d) ∝ P (d|H)P (H) Compositional Probabilistic representations inference
  30. 30. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional Probabilistic representations inference
  31. 31. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world Compositional Probabilistic representations inference
  32. 32. Composition and probability Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world ∀x King(x) =⇒ M an(x) ∀y M an(y) ⇐⇒ ¬W oman(y) Compositional Probabilistic representations inference
  33. 33. Composition and probability Probabilistic language of thought hypothesis Thought is productive: Thought is useful “the infinite use of in an uncertain finite means” world ∀x King(x) =⇒ M an(x) ∀y M an(y) ⇐⇒ ¬W oman(y) Compositional Probabilistic representations inference
  34. 34. A probabilistic language
  35. 35. A probabilistic language Lambda calculus:
  36. 36. A probabilistic language Lambda calculus: (define double (λ (x) (+ x x)))
  37. 37. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x)))
  38. 38. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x)))))
  39. 39. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12
  40. 40. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  41. 41. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: (define a (flip 0.3)) (define b (flip 0.3)) (define c (flip 0.3)) (+ a b c) Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  42. 42. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: (define a (flip 0.3)) => 1 (define b (flip 0.3)) => 0 (define c (flip 0.3)) => 1 (+ a b c) => 2 Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  43. 43. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: (define a (flip 0.3)) => 1 0 (define b (flip 0.3)) => 0 0 (define c (flip 0.3)) => 1 0 (+ a b c) => 2 0 Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  44. 44. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: (define a (flip 0.3)) => 1 0 0 (define b (flip 0.3)) => 0 0 0 (define c (flip 0.3)) => 1 0 1 (+ a b c) => 2 0 1 Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  45. 45. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: (define a (flip 0.3)) => 1 0 0 (define b (flip 0.3)) => 0 0 0 (define c (flip 0.3)) => 1 0 1 (+ a b c) => 2 0 1 .. Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  46. 46. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x))) (define repeat (λ (f) (λ (x) (f (f x))))) ((repeat double) 3) => 12 Probabilistic lambda calculus: probability / frequency (define a (flip 0.3)) => 1 0 0 (define b (flip 0.3)) => 0 0 0 (define c (flip 0.3)) => 1 0 1 (+ a b c) => 2 0 1 .. 0 1 2 3 Goodman, Mansinghka, Roy, Bonawitz, Tenenabum (2008)
  47. 47. Hypothesis • The probabilistic language of thought hypothesis: Mental representations are functions in a probabilistic lambda calculus. • Thoughts are built compositionally (like molecules). • Thinking is probabilistic inference. http://projects.csail.mit.edu/church
  48. 48. Bob’s box Goodman, Baker, Tenenbaum (2009; in prep.)
  49. 49. Bob’s box • Bob has a box with two buttons and a light. A B Goodman, Baker, Tenenbaum (2009; in prep.)
  50. 50. Bob’s box • Bob has a box with two buttons and a light. A B • He presses both buttons, and the light comes on. Goodman, Baker, Tenenbaum (2009; in prep.)
  51. 51. Bob’s box • Bob has a box with two buttons and a light. A B • He presses both buttons, and the light comes on. • How does the box work? A A A A A B B B B B C C C C C A alone B alone A or B A and B Nothing causes C. causes C. cause C. causes C. causes C. Goodman, Baker, Tenenbaum (2009; in prep.)
  52. 52. Human judgements Social 50 * 40 Social condition Mean Bets ($) 30 Physical 50 20 Physical condition 40 ns 30 10 20 0 A B AorB A&B none 10 N=15 0 A B AorB A&B none A alone B alone A or B A and B Nothing causes C. causes C. cause C. causes C. causes C.
  53. 53. Purely causal learning Causal!only model 0.5 (query Causal-only (define world-cs (cs-prior)) 0.4 (define action (uniform)) Probability 0.3 (define outcome (world-cs init-state 0.2 action)) 0.1 world-cs (and (press-A action) 0 A B AorB A&B none A or B A&B B only none A only (press-B action) Cause of C (light-on outcome))) No conclusion is possible. The evidence is confounded.
  54. 54. Explaining actions Beliefs: Desires: A B C Decision Rational action: Actions: (define decide (λ (state causal-model utility) (query (define action (action-prior)) action (flip (utility (causal-model state action))))))
  55. 55. Causal learning models Causal!only model 0.5 Causal-only model Causal-only Causal-only (define world-cs (cs-prior)) 0.4 (define action (uniform)) model Probability (define outcome (world-cs 0.3 init-state 0.2 action)) 0.1 0 A B AorB A&B none A or B A&B B only none A only Cause of C (define world-cs (cs-prior)) (define utility (uniform)) Social & causal (define cs-belief world-cs) Knowledgeable (define action (decide init-state agent assumption cs-belief Rational utility)) (define outcome (world-cs agent assumption init-state action))
  56. 56. Causal learning models Causal!only model 0.5 Causal-only model Causal-only Causal-only (define world-cs (cs-prior)) 0.4 (define action (uniform)) model Probability (define outcome (world-cs 0.3 init-state 0.2 action)) 0.1 0 A B AorB A&B none A or B A&B B only none A only Cause of C (define world-cs (cs-prior)) (define utility (uniform)) Social & causal (define cs-belief world-cs) (define action (decide init-state cs-belief utility)) (define outcome (world-cs init-state action))
  57. 57. Causal learning models Causal!only model 0.5 Causal-only model Causal-only (define world-cs (cs-prior)) 0.4 (define action (uniform)) Probability (define outcome (world-cs 0.3 init-state 0.2 action)) 0.1 0 A B AorB A&B none A or B A&B B only none A only Cause of C (define world-cs (cs-prior)) (define utility (uniform)) Social & causal (define cs-belief world-cs) (define action (decide init-state cs-belief utility)) (define outcome (world-cs init-state action))
  58. 58. Causal learning models Causal!only model 0.5 Causal-only model Causal-only (define world-cs (cs-prior)) 0.4 (define action (uniform)) Probability (define outcome (world-cs 0.3 init-state 0.2 action)) 0.1 0 A B AorB A&B none A or B A&B B only none A only Cause of C (define world-cs (cs-prior)) (define utility (uniform)) Social & causal Social!causal model 0.5 (define cs-belief world-cs) Social + causal model (define action (decide 0.4 init-state Posterior probability Probability 0.3 cs-belief utility)) 0.2 (define outcome (world-cs init-state 0.1 action)) 0 A B AorB A&B none
  59. 59. Scalar implicature Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  60. 60. Scalar implicature Desires: -informative Beliefs -parsimonious Actions: “...” Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  61. 61. Scalar implicature Desires: Model: -informative Beliefs -parsimonious Plausibility (Z-score) 2 1 0 -1 Actions: -2 “...” 0:5 1:5 2:5 3:5 4:5 5:5 Number sprouted Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  62. 62. Scalar implicature Desires: Model: -informative Beliefs -parsimonious Plausibility (Z-score) 2 1 0 -1 Actions: -2 “...” 0:5 1:5 2:5 3:5 4:5 5:5 Number sprouted Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  63. 63. Scalar implicature Desires: Model: Partial -informative Full knowledge knowledge Beliefs -parsimonious Plausibility (Z-score) 2 1 0 -1 Actions: -2 “...” 0:5 1:5 2:5 3:5 4:5 5:5 0:5 1:5 2:5 3:5 4:5 5:5 Number sprouted Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  64. 64. Scalar implicature Desires: Model: Partial -informative Full knowledge knowledge Beliefs -parsimonious Plausibility (Z-score) 2 1 0 -1 Actions: -2 “...” 0:5 1:5 2:5 3:5 4:5 5:5 0:5 1:5 2:5 3:5 4:5 5:5 Number sprouted Human: Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
  65. 65. Summary • The probabilistic language of thought combines composition and probability. • We can explain complex, flexible human thinking... • And engineer flexible computer intelligence.

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