1. of 30 September 22, 2010Semantic Communication @ Berkeley 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 30 Disclaimer Work in progress (for ever) … Work in progress (for ever) … Comments/Criticisms welcome. Comments/Criticisms welcome. September 22, 2010Semantic Communication @ Berkeley2

3. of 30 September 22, 2010Semantic Communication @ Berkeley3 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 30 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 September 22, 2010Semantic Communication @ Berkeley 4

5. of 30 Modelling Miscommunication Classical Shannon Model September 22, 2010Semantic Communication @ Berkeley5 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Semantic Communication Model

6. of 30 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. Is there a specific Goal to all communication? Is there a specific Goal to all communication? Are there many possible Goals? Are there many possible Goals? Goal specifies problem, but what is a solution? Goal specifies problem, but what is a solution? September 22, 2010Semantic Communication @ Berkeley6

7. of 30 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. September 22, 2010Semantic Communication @ Berkeley7

8. of 30 Communication: Example 1 (Printing) September 22, 2010Semantic Communication @ Berkeley8

9. of 30 Communication: Ex. 2 (Computation) September 22, 2010Semantic Communication @ Berkeley9 X f(X)

10. of 30 Communication: Ex. 3 (Web search) September 22, 2010Semantic Communication @ Berkeley10 Q(WWW(P)) = ? WWW Q Q P

11. of 30 Communication: Ex. 4 (Intelligence?) September 22, 2010Semantic Communication @ Berkeley11 Yes No

12. of 30 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 September 22, 2010Semantic Communication @ Berkeley12

13. of 30 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. September 22, 2010Semantic Communication @ Berkeley13User

14. of 30 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? September 22, 2010Semantic Communication @ Berkeley14 User Server X X X

15. of 30 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. September 22, 2010Semantic Communication @ Berkeley15UserServer Referee/Environment

16. of 30 Generic Goals Pure Control Pure Control Pure Informational Pure Informational September 22, 2010Semantic Communication @ Berkeley16UserServer Referee/Environment UserServer Referee/Environment

17. of 30 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). September 22, 2010Semantic Communication @ Berkeley17

18. of 30 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. September 22, 2010Semantic Communication @ Berkeley18

19. of 30 Concrete Example: Computation September 22, 201019Semantic Communication @ Berkeley

20. of 30 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? September 22, 2010Semantic Communication @ Berkeley20

21. of 30 qkqkqkqk September 22, 2010Semantic Communication @ Berkeley21 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.

22. of 30 September 22, 2010Semantic Communication @ Berkeley22 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 f-helpful if Server S is f-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)

23. of 30 September 22, 2010Semantic Communication @ Berkeley23 Successful universal communication Universality: Universal User U should be able to talk to any (every) f-helpful server S to compute f. Universality: Universal User U should be able to talk to any (every) f-helpful server S to compute f. Formally: Formally: U is f-universal, if U is f-universal, if 8 f-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)

24. of 30 September 22, 2010Semantic Communication @ Berkeley24 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 (“compIP”) problems Extends to checkable (“compIP”) 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 (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).

25. of 30 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 …) September 22, 2010Semantic Communication @ Berkeley25

26. of 30 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? September 22, 2010Semantic Communication @ Berkeley26

27. of 30 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! September 22, 2010Semantic Communication @ Berkeley27

28. of 30 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] September 22, 2010Semantic Communication @ Berkeley28

29. of 30 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). September 22, 2010Semantic Communication @ Berkeley29

30. of 30 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] September 22, 2010Semantic Communication @ Berkeley30

31. of 30 Thank You! September 22, 2010Semantic Communication @ Berkeley31

32. of 30 September 22, 2010Semantic Communication @ Berkeley32 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?

33. of 30 Classical Shannon Model Classical Shannon Model Modelling Miscommunication September 22, 2010Semantic Communication @ Berkeley33 Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj

34. of 30 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? September 22, 2010Semantic Communication @ Berkeley34 Next part of talk

35. of 30 September 22, 2010Semantic Communication @ Berkeley 35 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

36. of 30 September 22, 2010Semantic Communication @ Berkeley36 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

37. of 30 Communication: Ex. 2 (Computation) September 22, 2010Semantic Communication @ Berkeley37 X f(X)

38. of 30 Generic communication problem? September 22, 2010Semantic Communication @ Berkeley38 Yes No X f(X) Q(WWW(P)) = ? WWWQ Q P Should model All 4 examples!

39. of 30 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? September 22, 2010Semantic Communication @ Berkeley39

40. of 30 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? September 22, 2010Semantic Communication @ Berkeley40

41. of 30 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! September 22, 2010Semantic Communication @ Berkeley41

42. of 30 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/ September 22, 2010Semantic Communication @ Berkeley42

43. of 30 September 22, 2010Semantic Communication @ Berkeley43 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