1. of 32 October 19, 2010Semantic Communication @ U.Penn. 1 Semantic Goal-Oriented Communication Madhu Sudan Microsoft Research + MIT 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 33 Disclaimer Work in progress (for ever) … Work in progress (for ever) … Comments/Criticisms welcome. Comments/Criticisms welcome. October 19, 2010Semantic Communication @ U.Penn.2

3. of 33 October 19, 2010Semantic Communication @ U.Penn.3 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? Channel Alice Bob Bob 01001011 01001011 Bob Freeze!

4. of 33 Miscommunication (in practice) Exchanging (powerpoint) slides. Exchanging (powerpoint) slides. Don’t render identically on different laptops. Don’t render identically on different laptops. Printing on new printer. Printing on new printer. User needs to “learn” the new printer, even though printer is quite “intelligent”. User needs to “learn” the new printer, even though printer is quite “intelligent”. Many such examples … Many such examples … In all cases, sending bits is insufficient. In all cases, sending bits is insufficient. Notion of meaning … intuitively clear. Notion of meaning … intuitively clear. But can it be formalized? But can it be formalized? Specifically? Generically? Specifically? Generically? While conforming to our intuition While conforming to our intuition October 19, 2010Semantic Communication @ U.Penn. 4

5. of 33 Modelling Miscommunication Classical Shannon Model October 19, 2010Semantic Communication @ U.Penn.5 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Semantic Communication Model

6. of 33 Basic issues Source of Miscommunication: Source of Miscommunication: A i doesn’t know j A i doesn’t know j B j doesn’t know i B j doesn’t know i But what do they wish to achieve? But what do they wish to achieve? Distinguish B j from B k ? Distinguish B j from B k ? What if they are indistinguishable? What if they are indistinguishable? Thesis: Communication ought to have Goal!!! Thesis: Communication ought to have Goal!!! Alice/Bob should strive to achieve Goal. Alice/Bob should strive to achieve Goal. What is the Goal of communication? (or what are the Goals?) What is the Goal of communication? (or what are the Goals?) Goal specifies problem, but what is a solution? Goal specifies problem, but what is a solution? October 19, 2010Semantic Communication @ U.Penn.6

7. of 33 Examples of Goals In future slides: In future slides: User communicates/interacts with Server. User communicates/interacts with Server. Will try to look at User’s goal. Will try to look at User’s goal. October 19, 2010Semantic Communication @ U.Penn.7

8. of 33 Communication: Example 1 (Printing) October 19, 2010Semantic Communication @ U.Penn.8

9. of 33 Communication: Ex. 2 (Computation) October 19, 2010Semantic Communication @ U.Penn.9 X f(X)

10. of 33 Communication: Ex. 3 (Web search) October 19, 2010Semantic Communication @ U.Penn.10 Q(WWW(P)) = ? WWW Q Q P

11. of 33 Communication: Ex. 4 (Intelligence?) October 19, 2010Semantic Communication @ U.Penn.11 Yes No

12. of 33 Classically: Turing Machine/(von Neumann) RAM. Classically: Turing Machine/(von Neumann) RAM. Described most computers being built? Described most computers being built? Modern computers: more into communication than computing. Modern computers: more into communication than computing. What is the mathematical model of a communicating computer? Why do they communicate? What are all the “communication problems”? What is universality? What is the mathematical model of a communicating computer? Why do they communicate? What are all the “communication problems”? What is universality? Aside: Modelling Computing October 19, 2010Semantic Communication @ U.Penn.12

13. of 33 Theory? or Practice? Problems: Motivated by practice. Problems: Motivated by practice. But to address them: But to address them: Need a deeper theory. Need a deeper theory. One that understands misunderstanding. One that understands misunderstanding. In the limit … should be able to learn languages, assign meaning etc. – to achieve goals (of communication). In the limit … should be able to learn languages, assign meaning etc. – to achieve goals (of communication). Ad-hoc solutions unacceptable. Ad-hoc solutions unacceptable. This talk: A starting point for the theory. This talk: A starting point for the theory. October 19, 2010Semantic Communication @ U.Penn.13

14. of 33 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. October 19, 2010Semantic Communication @ U.Penn.14User

15. of 33 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? October 19, 2010Semantic Communication @ U.Penn.15 User Server X X X

16. of 33 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. October 19, 2010Semantic Communication @ U.Penn.16UserServer Referee/Environment

17. of 33 Referee for Computation (Ex. 2) October 19, 2010Semantic Communication @ U.Penn.17 X Y=f(X)? Referee/Environment Y

18. of 33 Broad subclasses of Goals Pure Control Pure Control Pure Informational Pure Informational October 19, 2010Semantic Communication @ U.Penn.18UserServer Referee/Environment UserServer Referee/Environment

19. of 33 Sensing & Universality To achieve goal: To achieve goal: Server should be “helpful” Server should be “helpful” User should be able to “sense progress”. User should be able to “sense progress”. I.e., user should be compute a function that mimics referee’s verdict. I.e., user should be compute a function that mimics referee’s verdict. General positive result [GJS ’09]: General positive result [GJS ’09]: Generic goals ( with appropriate definitions ) universally achievable if 9 sensing function. Generic goals ( with appropriate definitions ) universally achievable if 9 sensing function. General negative result [GJS ’09]: General negative result [GJS ’09]: Sensing is necessary (in sufficiently general classes of users/servers). Sensing is necessary (in sufficiently general classes of users/servers). October 19, 2010Semantic Communication @ U.Penn.19

20. of 33 Concrete Example: Computation October 19, 201020Semantic Communication @ U.Penn.

21. of 33 Computational Goal for User User wants to compute function f on input x. User wants to compute function f on input x. Setting: Setting: User is prob. poly time bounded. User is prob. poly time bounded. Server is computationally unbounded, does not speak same language as User, but is “helpful”. Server is computationally unbounded, does not speak same language as User, 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? October 19, 2010Semantic Communication @ U.Penn.21

22. of 33 qkqkqkqk October 19, 2010Semantic Communication @ U.Penn.22 Setup 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.

23. of 33 October 19, 2010Semantic Communication @ U.Penn.23 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 if Server S is helpful 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)

24. of 33 October 19, 2010Semantic Communication @ U.Penn.24 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? Benign view ) Don’t care (everyone is helpful) Benign view ) Don’t care (everyone is helpful)

25. of 33 October 19, 2010Semantic Communication @ U.Penn.25 Main Theorems [Juba & S. ‘08] If f is in PSPACE, then there exists a f-universal user who runs in probabilistic polynomial time. If f is in PSPACE, then there exists a f-universal user who runs in probabilistic polynomial time. If we require server to only solve f, then hold for every checkable (“compIP”) problem. If we require server to only solve f, then hold for every checkable (“compIP”) problem. Still includes NP Å co-NP, breaking crypto Still includes NP Å co-NP, breaking crypto 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 (in “compIP”) Conversely, if there exists a f-universal user, then f is PSPACE-computable (in “compIP”) Scope of computation by communication is limited by misunderstanding (alone). Scope of computation by communication is limited by misunderstanding (alone).

26. of 33 Proofs? Positive result: Positive result: f Є PSPACE ) membership is verifiable. f Є PSPACE ) membership is verifiable. User can make hypothesis about what the Server is saying, and use membership proof to be convinced answer is right, or hypothesis is wrong. Enumerate, till hypothesis is right. User can make hypothesis about what the Server is saying, and use membership proof to be convinced answer is right, or hypothesis is wrong. Enumerate, till hypothesis is right. Negative result: Negative result: In the absence of proofs, sufficiently rich class of users allow arbitrary initial behavior, including erroneous ones. In the absence of proofs, sufficiently rich class of users allow arbitrary initial behavior, including erroneous ones. (Only leads to finitely many errors …) (Only leads to finitely many errors …) October 19, 2010Semantic Communication @ U.Penn.26

27. of 33 Implications Communication is not unboundedly helpful  Communication is not unboundedly helpful  If it were, should have been able to solve every problem (not just (PSPACE) computable ones). If it 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? October 19, 2010Semantic Communication @ U.Penn.27

28. of 33 Implications for Language Learning Standard question in linguistics, cognition … Standard question in linguistics, cognition … What is a precondition for two entities to come to some “common understanding/language”? What is a precondition for two entities to come to some “common understanding/language”? Standard answers: Standard answers: Humans seem to need little commonality (a child can learn any language) Humans seem to need little commonality (a child can learn any language) But humans share enormous common physical needs and have large common genetic code? But humans share enormous common physical needs and have large common genetic code? Is all this necessary? “POS debate” Is all this necessary? “POS debate” Our Answer: No. Compatible goals suffice. Our Answer: No. Compatible goals suffice. October 19, 2010Semantic Communication @ U.Penn.28

29. of 33 Implications for Language Learning Well-explored theme in “linguistics” Well-explored theme in “linguistics” Semantics learned by functional relevance. Semantics learned by functional relevance. But how does one have “common” grounding? Is this a purely a function of having common physical environment + needs? But how does one have “common” grounding? Is this a purely a function of having common physical environment + needs? Is there a purely intellectual basis for common grounding? Is there a purely intellectual basis for common grounding? Our answer: YES! Our answer: YES! October 19, 2010Semantic Communication @ U.Penn.29

30. of 33 Towards Efficiency Learning of language is not efficient Learning of language is not efficient User takes at least k steps to enumerate k possible servers (k possible languages). User takes at least k steps to enumerate k possible servers (k possible languages). Can this be made faster? Can this be made faster? Answers: Answers: No! Not without assumptions on language … No! Not without assumptions on language … Yes! If server and user are “broadminded”, and have “compatible beliefs” [JS ‘10] Yes! If server and user are “broadminded”, and have “compatible beliefs” [JS ‘10] October 19, 2010Semantic Communication @ U.Penn.30

31. of 33 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. 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 19, 2010Semantic Communication @ U.Penn.31

32. of 33 Conclusions Basis of semantic communucation: Model “miscommunication” Basis of semantic communucation: Model “miscommunication” Can be done by allowing users/servers to be variable (members of a set). Can be done by allowing users/servers to be variable (members of a set). Such settings seem commonplace, especially in “natural communication”, but no prior attempts to model them theoretically (in the context of information transmission). Such settings seem commonplace, especially in “natural communication”, but no prior attempts to model them theoretically (in the context of information transmission). Can also look at the “compression” problem. Can also look at the “compression” problem. Unveils phenomena reflective of natural communication [Juba,Kalai,Khanna,S. ’10] Unveils phenomena reflective of natural communication [Juba,Kalai,Khanna,S. ’10] October 19, 2010Semantic Communication @ U.Penn.32

33. of 33 Thank You! October 19, 2010Semantic Communication @ U.Penn.33

34. of 33 October 19, 2010Semantic Communication @ U.Penn.34 Bits vs. their meaning Say, User and Server know different programming languages. Server wishes to send an algorithm A to User. Say, User and Server know different programming languages. Server wishes to send an algorithm A to User. 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 User, there exist algorithms A and A’, and Servers S and S’ such that S sending A is indistinguishable (to User) from S’ sending A’ For every User, there exist algorithms A and A’, and Servers S and S’ such that S sending A is indistinguishable (to User) from S’ 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?

35. of 33 Classical Shannon Model Classical Shannon Model Modelling Miscommunication October 19, 2010Semantic Communication @ U.Penn.35 Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj

36. of 33 Principal Criticisms Solution is no good. Solution is no good. Enumerating hypotheses is too slow. Enumerating hypotheses 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. 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? October 19, 2010Semantic Communication @ U.Penn.36 Next part of talk

37. of 32 October 19, 2010Semantic Communication @ U.Penn. 37 Part II: Generic Goals of Communication 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

38. of 33 October 19, 2010Semantic Communication @ U.Penn.38 Aside: Communication? 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 “Just say NO!”? If communication is so problematic, then why not “Just say NO!”? F XF(X) Alice Bob Charlie Dick Alice Bob Charlie Dick

39. of 33 Communication: Ex. 2 (Computation) October 19, 2010Semantic Communication @ U.Penn.39 X f(X)

40. of 33 Generic communication problem? October 19, 2010Semantic Communication @ U.Penn.40 Yes No X f(X) Q(WWW(P)) = ? WWWQ Q P Should model All 4 examples!

41. of 33 Universal Semantics for Generic Goal? Can we still achieve goal without prior common language? Can we still achieve goal without prior common language? Seems feasible … Seems feasible … If user can detect whether goal is being achieved. If user can detect whether goal is being achieved. Seems true in all four examples. Seems true in all four examples. Just need to define Just need to define Sensing Goal Achievement? Sensing Goal Achievement? Helpful/Universal? Helpful/Universal? Goal? Goal? User? User? October 19, 2010Semantic Communication @ U.Penn.41

42. of 33 Conclusions Is there a universal communication protocol? Is there a universal communication protocol? No! ( All functions vs. PSPACE-computable functions ). No! ( All functions vs. PSPACE-computable functions ). But can achieve “sensible” goals universally. But can achieve “sensible” goals universally. But … diversity of goals may be the barrier to universality. But … diversity of goals may be the barrier to universality. Goals of communication. Goals of communication. Should be studied more. Should be studied more. Suggests good heuristics for protocol design: Suggests good heuristics for protocol design: Server = Helpful? Server = Helpful? User = Sensing? User = Sensing? October 19, 2010Semantic Communication @ U.Penn.42

43. of 33 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! October 19, 2010Semantic Communication @ U.Penn.43

44. of 33 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/ October 19, 2010Semantic Communication @ U.Penn.44

45. of 33 October 19, 2010Semantic Communication @ U.Penn.45 Communicating is painful. There must be some compensating gain. Communicating is painful. There must be some compensating gain. What is User’s Goal? What is User’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). Thesis: By studying the goals, can enable User to overcome linguistic differences (and achieve goal). Thesis: By studying the goals, can enable User to overcome linguistic differences (and achieve goal). Motivations for Communication

46. of 33 Implications of “Universality” Standard question in linguistics, cognition … Standard question in linguistics, cognition … What is a precondition for two entities to come to some “common language”? What is a precondition for two entities to come to some “common language”? Standard answers: Standard answers: Humans seem to need little commonality (a child can learn any language) Humans seem to need little commonality (a child can learn any language) But humans share enormous common physical needs and have large common genetic code? But humans share enormous common physical needs and have large common genetic code? Is all this necessary? Is all this necessary? Our Answer: No. Compatible goals suffice. Our Answer: No. Compatible goals suffice. October 19, 2010Semantic Communication @ U.Penn.46