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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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- 1. ngoodman@ stanford.edu (Reverse) Engineering Intelligence Noah D. Goodman Stanford University H+ Summit, June 12, 2010
- 3. What is thought? • How are thoughts structured?
- 4. What is thought? • How are thoughts structured? • How does this structure support ﬂexible, successful thinking?
- 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. 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?
- 8. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means”
- 9. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” ..a big green bear who loves chocolate..
- 10. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” ..a big green bear who loves chocolate..
- 11. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” p=mv
- 12. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” p=mv
- 13. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” p=mv Compositional representations
- 14. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” Compositional representations
- 15. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” Compositional representations
- 16. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” Compositional representations
- 17. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” Compositional representations
- 18. Composition and probability Thought is productive: “the inﬁnite use of ﬁnite means” Compositional representations
- 19. Composition and probability Thought is productive: Thought is useful “the inﬁnite use of in an uncertain ﬁnite means” world Compositional representations
- 20. Composition and probability Thought is productive: Thought is useful “the inﬁnite use of in an uncertain ﬁnite means” world Compositional representations
- 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. 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. 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. 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. Composition and probability Thought is productive: Thought is useful “the inﬁnite use of in an uncertain ﬁnite means” world Compositional Probabilistic representations inference
- 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. 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. 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. 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. Composition and probability Thought is productive: Thought is useful “the inﬁnite use of in an uncertain ﬁnite means” world Compositional Probabilistic representations inference
- 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. 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. 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
- 35. A probabilistic language Lambda calculus:
- 36. A probabilistic language Lambda calculus: (define double (λ (x) (+ x x)))
- 37. A probabilistic language Lambda calculus: (define double (double 3) => 6 (λ (x) (+ x x)))
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Bob’s box Goodman, Baker, Tenenbaum (2009; in prep.)
- 49. Bob’s box • Bob has a box with two buttons and a light. A B Goodman, Baker, Tenenbaum (2009; in prep.)
- 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. 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. 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. 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. 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. 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. 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. 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. 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. Scalar implicature Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
- 60. Scalar implicature Desires: -informative Beliefs -parsimonious Actions: “...” Some of the plants have sprouted (Plants usually sprout.) Goodman, et al (in prep)
- 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. 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. 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. 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. Summary • The probabilistic language of thought combines composition and probability. • We can explain complex, ﬂexible human thinking... • And engineer ﬂexible computer intelligence.

- History: Two computational principles... To explain real cognition we need both. My research: unify these ideas, Tackle new areas - the real payoff.
- History: Two computational principles... To explain real cognition we need both. My research: unify these ideas, Tackle new areas - the real payoff.
- History: Two computational principles... To explain real cognition we need both. My research: unify these ideas, Tackle new areas - the real payoff.
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- Named for Alonzo Church
- We have a formalism for stochastic functions ..church is universal for both representation and inference. rest of talk -- schematic church.. broader framework..
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- Intuition: why would he have pressed both buttons unless he had to?
- But where do actions come from, and why are actions diagnostic of cs-world?
- B-D-A: remember this from BN?