1. of 29 May 2, 2011 Semantic Communication @ Northwestern1 Universal Semantic Communication Madhu Sudan Microsoft Research Joint with Oded Goldreich (Weizmann) and Brendan Juba (MIT). TexPoint fonts used in EMF. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A Read the TexPoint manual before you delete this box.: A A A A

2. of 29 May 2, 2011Semantic Communication @ Northwestern 2 The Meaning of Bits Is this perfect communication? Is this perfect communication? What if Alice is trying to send instructions? What if Alice is trying to send instructions? Aka, an algorithm Aka, an algorithm Does Bob understand the correct algorithm? Does Bob understand the correct algorithm? What if Alice and Bob speak in different (programming) languages? What if Alice and Bob speak in different (programming) languages? Question important theoretically, and in practice of computing/communication. Question important theoretically, and in practice of computing/communication. Channel Alice Bob Bob 01001011 01001011 Bob Freeze!

3. of 29 This talk Meaning of information: Meaning via Goal- oriented communication Meaning of information: Meaning via Goal- oriented communication Example: Computational Goal Example: Computational Goal Going Beyond Example Going Beyond Example General Goals General Goals Efficiency via compatible beliefs Efficiency via compatible beliefs Semantics in general Semantics in general May 2, 2011Semantic Communication @ Northwestern 3

4. of 29 Meaning? A first attempt Sender is sending instructions/algorithms Sender is sending instructions/algorithms Can we understand/execute it? Can we understand/execute it? Answer: NO! Answer: NO! Under sufficient richness of language (any finite length string means anything), can never achieve this state. Under sufficient richness of language (any finite length string means anything), can never achieve this state. So what should we try to achieve? So what should we try to achieve? May 2, 2011Semantic Communication @ Northwestern 4

5. of 29 Communications as a means to an end Communication is painful: Communication is painful: Unreliability of communication medium, misunderstanding, loss of privacy, secrecy. Unreliability of communication medium, misunderstanding, loss of privacy, secrecy. So why do it? So why do it? Must be some compensating gain. Must be some compensating gain. Communication should strive to achieve some goal. Communication should strive to achieve some goal. “Understanding Meaning” is when we can achieve the goal in the absence of common language. “Understanding Meaning” is when we can achieve the goal in the absence of common language. May 2, 2011Semantic Communication @ Northwestern 5

6. of 29 Part II: Computational Motivation May 2, 2011 6 Semantic Communication @ Northwestern

7. of 29 Computational Goal for Bob Why does Bob want to learn algorithm? Why does Bob want to learn algorithm? Presumably to compute some function f Presumably to compute some function f (A is expected to compute this function.) Lets focus on the function f. Lets focus on the function f. Setting: Setting: Bob is prob. poly time bounded. Bob is prob. poly time bounded. Alice is computationally unbounded, does not speak same language as Bob, but is “helpful”. Alice is computationally unbounded, does not speak same language as Bob, but is “helpful”. What kind of functions f? What kind of functions f? E.g., uncomputable, PSPACE, NP, P? E.g., uncomputable, PSPACE, NP, P? May 2, 2011Semantic Communication @ Northwestern 7

8. of 29 qkqkqkqk May 2, 2011Semantic Communication @ Northwestern 8 Setup Bob Alice Server User f(x) = 0/1? R Ã $$$ q1q1q1q1 a1a1a1a1 akakakak Computes P(x,R,a 1,…,a k ) Hopefully P(x,…) = f(x)! Different from interactions in cryptography/security: There, User does not trust Server, while here he does not understand her.

9. of 29 May 2, 2011Semantic Communication @ Northwestern 9 Intelligence & Cooperation? For User to have a non-trivial interaction, Server must be: For User to have a non-trivial interaction, Server must be: Intelligent: Capable of computing f(x). Intelligent: Capable of computing f(x). Cooperative: Must communicate this to User. Cooperative: Must communicate this to User. Formally: Formally: Server S is helpful (for f) if Server S is helpful (for f) if 9 some (other) user U’ s.t. 9 some (other) user U’ s.t. 8 x, starting states ¾ of the server 8 x, starting states ¾ of the server (U’(x) $ S( ¾ )) outputs f(x) (U’(x) $ S( ¾ )) outputs f(x)

10. of 29 May 2, 2011Semantic Communication @ Northwestern 10 Successful universal communication Universality: Universal User U should be able to talk to any (every) helpful server S to compute f. Universality: Universal User U should be able to talk to any (every) helpful server S to compute f. Formally: Formally: U is f-universal, if U is f-universal, if 8 helpful S, 8 ¾, 8 x (U(x) $ S( ¾ )) = f(x) (w.h.p.) What happens if S is not helpful? What happens if S is not helpful? Paranoid view ) output “f(x)” or “?” Paranoid view ) output “f(x)” or “?” Benign view ) Don’t care (everyone is helpful) Benign view ) Don’t care (everyone is helpful)

11. of 29 May 2, 2011Semantic Communication @ Northwestern 11 Main Theorems [Juba & S. ‘08] If f is PSPACE-complete, then there exists a f- universal user who runs in probabilistic polynomial time. If f is PSPACE-complete, then there exists a f- universal user who runs in probabilistic polynomial time. Extends to checkable problems Extends to checkable problems (NP Å co-NP, breaking cryptosystems) (NP Å co-NP, breaking cryptosystems) S not helpful ) output is safe S not helpful ) output is safe Conversely, if there exists a f-universal user, then f is PSPACE-computable. Conversely, if there exists a f-universal user, then f is PSPACE-computable. Scope of computation by communication is limited by misunderstanding (alone). Scope of computation by communication is limited by misunderstanding (alone).

12. of 29 Implications No universal communication protocol  No universal communication protocol  If there were, should have been able to solve every problem (not just (PSPACE) computable ones). If there were, should have been able to solve every problem (not just (PSPACE) computable ones). But there is gain in communication: But there is gain in communication: Can solve more complex problems than on one’s own, but not every such problem. Can solve more complex problems than on one’s own, but not every such problem. Resolving misunderstanding? Learning Language? Resolving misunderstanding? Learning Language? Formally No! No such guarantee. Formally No! No such guarantee. Functionally Yes! If not, how can user solve such hard problems? Functionally Yes! If not, how can user solve such hard problems? May 2, 2011Semantic Communication @ Northwestern 12

13. of 29 Positive result: Enumeration + Interactive Proofs Positive result: Enumeration + Interactive Proofs Guess: Interpreter; b 2 {0,1} (value of f(x)) Guess: Interpreter; b 2 {0,1} (value of f(x)) Proof works ) f(x) = b. Proof works ) f(x) = b. If it doesn’t ) {Interpreter or b} incorrect. If it doesn’t ) {Interpreter or b} incorrect. May 2, 2011Semantic Communication @ Northwestern 13 Few words about the proof: Positive result Server Prover User Interpreter

14. of 29 May 2, 2011Semantic Communication @ Northwestern 14 Proof of Negative Result L not in PSPACE ) User makes mistakes. L not in PSPACE ) User makes mistakes. Suppose Server answers every question so as to minimize the conversation length. Suppose Server answers every question so as to minimize the conversation length. (Reasonable effect of misunderstanding). (Reasonable effect of misunderstanding). Conversation comes to end quickly. Conversation comes to end quickly. User has to decide. User has to decide. Conversation + Decision simulatable in PSPACE (since Server’s strategy can be computed in PSPACE). Conversation + Decision simulatable in PSPACE (since Server’s strategy can be computed in PSPACE). f is not PSPACE-computable ) User wrong. f is not PSPACE-computable ) User wrong. Warning: Only leads to finitely many mistakes. Warning: Only leads to finitely many mistakes.

15. of 29 Part III: Beyond Example III.1 General Goals May 2, 2011Semantic Communication @ Northwestern 15

16. of 29 General Goals Limitations of example: Limitations of example: Gain is computational Gain is computational Gain possible only if Server more powerful than User (asymmetric). Gain possible only if Server more powerful than User (asymmetric). Communication (presumably) serves many other goals Communication (presumably) serves many other goals What are they? What are they? Can we capture them all in single definition? Can we capture them all in single definition? Usual definitions (via transcript of interaction) inadequate in “semantic” setting. Usual definitions (via transcript of interaction) inadequate in “semantic” setting. May 2, 2011Semantic Communication @ Northwestern 16

17. of 29 Modelling User/Interacting agents (standard AI model) (standard AI model) User has state and input/output wires. User has state and input/output wires. Defined by the map from current state and input signals to new state and output signals. Defined by the map from current state and input signals to new state and output signals. May 2, 2011Semantic Communication @ Northwestern 17User

18. of 29 Generic Goal? Goal = function of ? Goal = function of ? User? – But user wishes to change actions to achieve universality! User? – But user wishes to change actions to achieve universality! Server? – But server also may change behaviour to be helpful! Server? – But server also may change behaviour to be helpful! Transcript of interaction? – How do we account for the many different languages? Transcript of interaction? – How do we account for the many different languages? May 2, 2011Semantic Communication @ Northwestern 18 User Server X X X

19. of 29 Generic Goals Key Idea: Introduce 3rd entity: Referee Key Idea: Introduce 3rd entity: Referee Poses tasks to user. Poses tasks to user. Judges success. Judges success. Generic Goal specified by Generic Goal specified by Referee (just another agent) Referee (just another agent) Boolean Function determining if the state evolution of the referee reflects successful achievement of goal. Boolean Function determining if the state evolution of the referee reflects successful achievement of goal. Class of users/servers. Class of users/servers. May 2, 2011Semantic Communication @ Northwestern 19UserServer Referee/Environment

20. of 29 Results in “General Setting” New concept: “Sensing” New concept: “Sensing” Ability of User to predict Referee’s verdict. Ability of User to predict Referee’s verdict. Computational example shows this can be achieved in non-trivial ways. Computational example shows this can be achieved in non-trivial ways. Relatively straightforward generalization of computational example: Relatively straightforward generalization of computational example: Sensing (is necessary and) sufficient for achieving goals in semantic setting. Sensing (is necessary and) sufficient for achieving goals in semantic setting. May 2, 2011Semantic Communication @ Northwestern 20

21. of 29 Part III: Beyond Example III.2: Efficient Learning? May 2, 2011Semantic Communication @ Northwestern 21

22. of 29 The Enumeration Bottleneck Enumeration of users seems inefficient, can we get around it? Enumeration of users seems inefficient, can we get around it? Formally, in k time, User can only explore O(k) other users. Formally, in k time, User can only explore O(k) other users. Bad News: Bad News: Provable bottleneck: Server could use passwords (of length log k). Provable bottleneck: Server could use passwords (of length log k). Good News: Good News: Can formalize this as only bottleneck … Can formalize this as only bottleneck … using “Beliefs, Compatibility” using “Beliefs, Compatibility” May 2, 2011Semantic Communication @ Northwestern 22

23. of 29 Broadmindedness, Compatible beliefs: Beliefs of server S: Beliefs of server S: Expects users chosen from distribution X. Expects users chosen from distribution X. Allows “typical” user to reach goal in time T. Allows “typical” user to reach goal in time T. # such users may be exponential # such users may be exponential Beliefs of user U: Beliefs of user U: Anticipates some distribution Y on users that the server is trying to serve. Anticipates some distribution Y on users that the server is trying to serve. Compatibility: K = (1 - |X – Y| TV ) Compatibility: K = (1 - |X – Y| TV ) Theorem[JS]: U can achieve goal in time poly(T/K). Theorem[JS]: U can achieve goal in time poly(T/K). October 14, 2010Semantic Communication @ Waterloo 23

24. of 29 Part III: Beyond Example III.3: Semantics? May 2, 2011Semantic Communication @ Northwestern 24

25. of 29 Semantic Communication Origins: The Gap between Turing and Shannon Origins: The Gap between Turing and Shannon Turing counts on reliable communication Turing counts on reliable communication Shannon counts on general computation Shannon counts on general computation Separating theories was essential to initial progress. Separating theories was essential to initial progress. Modern technology: Modern technology: Communication & Computation deeply intertwined. Communication & Computation deeply intertwined. Unreasonable to separate the two. Unreasonable to separate the two. Semantic Communication: Prime example Semantic Communication: Prime example May 2, 2011Semantic Communication @ Northwestern 25

26. of 29 A new model Classical Shannon Model May 2, 2011Semantic Communication @ Northwestern 26 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Semantic Communication Model New Class of Problems New challenges Needs more attention!

27. of 29 Compression in semantic setting Human-Human communication: Human-Human communication: Robust, ambiguous, redundant. Robust, ambiguous, redundant. Explored in [Juba,Kalai,Khanna,S. ICS ‘11] Explored in [Juba,Kalai,Khanna,S. ICS ‘11] Thesis: Reason is diversity of audiences/their priors. Thesis: Reason is diversity of audiences/their priors. Leads to compression for “uncertain” priors. Leads to compression for “uncertain” priors. Reveals same phenomena as natural languages: Reveals same phenomena as natural languages: Novel redundancy (increases with uncertainty), still ambiguous, but robust. Novel redundancy (increases with uncertainty), still ambiguous, but robust. May 2, 2011Semantic Communication @ Northwestern 27

28. of 29 References Juba & S. Juba & S. ECCC TR07-084: http://eccc.uni-trier.de/report/2007/084/ ECCC TR07-084: http://eccc.uni-trier.de/report/2007/084/ http://eccc.uni-trier.de/report/2007/084/ Goldreich, Juba & S. Goldreich, Juba & S. ECCC TR09-075: http://eccc.uni-trier.de/report/2009/075/ ECCC TR09-075: http://eccc.uni-trier.de/report/2009/075/ http://eccc.uni-trier.de/report/2009/075/ Juba & S. Juba & S. ICS ‘11: http://people.csail.mit.edu/madhu/papers/beliefs.pdf ICS ‘11: http://people.csail.mit.edu/madhu/papers/beliefs.pdf http://people.csail.mit.edu/madhu/papers/beliefs.pdf Juba, Kalai, Khanna & S. Juba, Kalai, Khanna & S. ICS ‘11: http://people.csail.mit.edu/madhu/papers/ambiguity.pdf ICS ‘11: http://people.csail.mit.edu/madhu/papers/ambiguity.pdf http://people.csail.mit.edu/madhu/papers/ambiguity.pdf May 2, 2011Semantic Communication @ Northwestern 28

29. of 29 Thank You! May 2, 2011Semantic Communication @ Northwestern 29

30. of 29 Efficient Learning & Compatible Beliefs Generically: Generically: Efficient learning of server not possible. Efficient learning of server not possible. E.g., Password protected server. E.g., Password protected server. However, if: However, if: Server is “broad-minded” Server is “broad-minded” User & Server’s beliefs about each other are “compatible” User & Server’s beliefs about each other are “compatible” Then efficient learning is possible. Then efficient learning is possible. [Juba+S., ICS ‘11]: [Juba+S., ICS ‘11]: Provide definitions of broad-minded, compatible, prove efficiency. Provide definitions of broad-minded, compatible, prove efficiency. May 2, 2011Semantic Communication @ Northwestern 30

31. of 29 What? Why? Example 1: I have a presentation that used to work well on my last laptop. Example 1: I have a presentation that used to work well on my last laptop. I transferred the file to my new laptop and it looks like this. I transferred the file to my new laptop and it looks like this. … but the bits are intact! … but the bits are intact! May 2, 2011 31 Semantic Communication @ Northwestern

32. of 29 What? Why? Example 2: I would like to print some document on some printer. Example 2: I would like to print some document on some printer. You can do it. You can do it. I have same permissions as you. I have same permissions as you. But I don’t have the printer installed. But I don’t have the printer installed. I have the information … I don’t know how to translate to printer’s language. I have the information … I don’t know how to translate to printer’s language. May 2, 2011 32 Semantic Communication @ Northwestern

33. of 29 May 2, 2011Semantic Communication @ Northwestern 33 Motivation: Better Computing Computers are constantly communicating. Computers are constantly communicating. Networked computers use common languages: Networked computers use common languages: Interaction between computers (getting your computer onto internet). Interaction between computers (getting your computer onto internet). Interaction between pieces of software. Interaction between pieces of software. Interaction between software, data and devices. Interaction between software, data and devices. Getting two computing environments to “talk” to each other is getting problematic: Getting two computing environments to “talk” to each other is getting problematic: time consuming, unreliable, insecure. time consuming, unreliable, insecure. Can we communicate more like humans do? Can we communicate more like humans do?

34. of 29 May 2, 2011Semantic Communication @ Northwestern 34 Classical Paradigm for interaction Object 1 Object 2 Designer

35. of 29 May 2, 2011Semantic Communication @ Northwestern 35 Object 2 New paradigm Object 1 Designer

36. of 29 May 2, 2011Semantic Communication @ Northwestern 36 Bits vs. their meaning Say, Alice and Bob know different programming languages. Alice wishes to send an algorithm A to Bob. Say, Alice and Bob know different programming languages. Alice wishes to send an algorithm A to Bob. A = sequence of bits … (relative to prog. language) A = sequence of bits … (relative to prog. language) Bad News: Can’t be done Bad News: Can’t be done For every Bob, there exist algorithms A and A’, and Alices, Alice and Alice’, such that Alice sending A is indistinguishable (to Bob) from Alice’ sending A’ For every Bob, there exist algorithms A and A’, and Alices, Alice and Alice’, such that Alice sending A is indistinguishable (to Bob) from Alice’ sending A’ Good News: Need not be done. Good News: Need not be done. From Bob’s perspective, if A and A’ are indistinguishable, then they are equally useful to him. From Bob’s perspective, if A and A’ are indistinguishable, then they are equally useful to him. What should be communicated? Why? What should be communicated? Why?

37. of 29 May 2, 2011Semantic Communication @ Northwestern 37 Aside: Why communicate? Classical “Theory of Computing” Classical “Theory of Computing” Issues: Time/Space on DFA? Turing machines? Issues: Time/Space on DFA? Turing machines? Modern theory: Modern theory: Issues: Reliability, Security, Privacy, Agreement? Issues: Reliability, Security, Privacy, Agreement? If communication is so problematic, then why not “Not do it”? If communication is so problematic, then why not “Not do it”? F XF(X) Alice Bob Charlie Dick Alice Bob Charlie Dick

38. of 29 May 2, 2011Semantic Communication @ Northwestern 38 Communicating is painful. There must be some compensating gain. Communicating is painful. There must be some compensating gain. What is Bob’s Goal? What is Bob’s Goal? “Control”: Wants to alter the state of the environment. “Control”: Wants to alter the state of the environment. “Intellectual”: Wants to glean knowledge (about universe/environment). “Intellectual”: Wants to glean knowledge (about universe/environment). Claim: By studying the goals, can enable Bob to overcome linguistic differences (and achieve goal). Claim: By studying the goals, can enable Bob to overcome linguistic differences (and achieve goal). Motivations for Communication

39. of 29 Principal Criticisms Solution is no good. Solution is no good. Enumerating interpreters is too slow. Enumerating interpreters is too slow. Approach distinguishes right/wrong; does not solve search problem. Approach distinguishes right/wrong; does not solve search problem. Search problem needs new definitions to allow better efficiency. Search problem needs new definitions to allow better efficiency. Can find better definitions [Juba+S, ICS‘11] Can find better definitions [Juba+S, ICS‘11] Problem is not the right one. Problem is not the right one. Computation is not the goal of communication. Who wants to talk to a PSPACE-complete server? Computation is not the goal of communication. Who wants to talk to a PSPACE-complete server? May 2, 2011Semantic Communication @ Northwestern 39 Next part of talk

40. of 29 May 2, 2011 Semantic Communication @ Northwestern40 Part III: Generic Goals

41. of 29 Generic Communication [ Goldreich, J., S. ] Still has goals. Goals more diverse. Still has goals. Goals more diverse. Should be studied; defined formally. Should be studied; defined formally. Major types: Major types: Control, e.g. Control, e.g. Laptop wants to print on printer. Laptop wants to print on printer. Buy something on Amazon. Buy something on Amazon. Sensing/Informational: Sensing/Informational: Computing some (hard) function. Computing some (hard) function. Learning/Teaching. Learning/Teaching. Coming to this talk. Coming to this talk. Mix of the two. Mix of the two. May 2, 2011Semantic Communication @ Northwestern 41

42. of 29 Universal Semantics in Generic Setting? Can we still achieve goal without knowing common language? Can we still achieve goal without knowing common language? Seems feasible … Seems feasible … If user can detect whether goal is being achieved (or progress is being made). If user can detect whether goal is being achieved (or progress is being made). Just need to define Just need to define Sensing Progress? Sensing Progress? Helpful + Universal? Helpful + Universal? … Goal? Goal? User? User? May 2, 2011Semantic Communication @ Northwestern 42

43. of 29 Language Learning Meaning = end effect of communication. Meaning = end effect of communication. [Dewey 1920s, Wittgenstein 1950s] [Dewey 1920s, Wittgenstein 1950s] What would make learning more efficient? What would make learning more efficient? What assumptions about “language”? What assumptions about “language”? How to do encapsulate it as “class” restrictions on users/servers. How to do encapsulate it as “class” restrictions on users/servers. What learning procedures are efficient? What learning procedures are efficient? Time to get back to meaningful conversation! Time to get back to meaningful conversation! May 2, 2011Semantic Communication @ Northwestern 43

44. of 29 May 2, 2011 Semantic Communication @ Northwestern44 Part IV: Some recent works

45. of 29 Generic Goals Pure Control Pure Control Pure Informational Pure Informational May 2, 2011Semantic Communication @ Northwestern 45UserServer Referee/Environment UserServer Referee/Environment

46. of 29 Sensing & Universality To achieve goal, User should be able to sense progress. To achieve goal, User should be able to sense progress. I.e., user should be compute a function that (possibly with some delay, errors) reflects achievement of goals. I.e., user should be compute a function that (possibly with some delay, errors) reflects achievement of goals. Generalization of positive result: Generalization of positive result: Generic goals ( with technical conditions ) universally achievable if 9 sensing function. Generic goals ( with technical conditions ) universally achievable if 9 sensing function. Generalization of negative result: Generalization of negative result: If non-trivial generic goal is achieved with sufficiently rich class of helpful servers, then it is safely achieved with every server. If non-trivial generic goal is achieved with sufficiently rich class of helpful servers, then it is safely achieved with every server. May 2, 2011Semantic Communication @ Northwestern 46