1. 2/2/2009Semantic Communication: MIT TOC Colloquium1 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.: AAAA Read the TexPoint manual before you delete this box.: AAAA

2. Disclaimer Work in progress (for ever) … Work in progress (for ever) … Comments/Criticisms/Collaboration/Competition welcome. Comments/Criticisms/Collaboration/Competition welcome. 2/2/2009Semantic Communication: MIT TOC Colloquium2

3. 2/2/2009Semantic Communication: MIT TOC Colloquium3 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. 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 2/2/2009Semantic Communication: MIT TOC Colloquium 4

5. 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? What is the mathematical model? Do we still have universality? Do we still have universality? Modelling Computing 2/2/2009Semantic Communication: MIT TOC Colloquium5

6. 2/2/2009Semantic Communication: MIT TOC Colloquium6 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?

7. 2/2/2009Semantic Communication: MIT TOC Colloquium7 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 “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

8. 2/2/2009Semantic Communication: MIT TOC Colloquium8 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

9. Part II: Computational Motivation 2/2/20099Semantic Communication: MIT TOC Colloquium

10. Computational Goal for Bob Why does User want to learn algorithm? Why does User 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: 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? 2/2/2009Semantic Communication: MIT TOC Colloquium10

11. qkqkqkqk 2/2/2009Semantic Communication: MIT TOC Colloquium11 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.

12. 2/2/2009Semantic Communication: MIT TOC Colloquium12 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)

13. 2/2/2009Semantic Communication: MIT TOC Colloquium13 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 universal, if U is 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)

14. 2/2/2009Semantic Communication: MIT TOC Colloquium14 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).

15. 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. User can make hypothesis about what the Server is saying, and use membership proof to be convinced answer is right, or hypothesis is wrong. 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 …) 2/2/2009Semantic Communication: MIT TOC Colloquium15

16. 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? 2/2/2009Semantic Communication: MIT TOC Colloquium16

17. 2/2/2009Semantic Communication: MIT TOC Colloquium17 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.

18. 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. 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? 2/2/2009Semantic Communication: MIT TOC Colloquium18 Next part of talk

19. 2/2/2009 Semantic Communication: MIT TOC Colloquium19 Part III: Generic Goals

20. Generic Communication [ Goldreich, J., S. ] Not every goal is computational! Not every goal is computational! Even if it is, is Semantic Communication only possible is Server is “much better” than User? Even if it is, is Semantic Communication only possible is Server is “much better” than User? What are generic goals? What are generic goals? Why do we send emails? Why do we send emails? Why do I browse on Amazon? Why do I browse on Amazon? Why do we listen to boring lectures? Why do we listen to boring lectures? (or give inspirational ones ) (or give inspirational ones ) Seemingly rich diversity Seemingly rich diversity 2/2/2009Semantic Communication: MIT TOC Colloquium20

21. Universal Semantics for such Goals? 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? 2/2/2009Semantic Communication: MIT TOC Colloquium21

22. 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. 2/2/2009Semantic Communication: MIT TOC Colloquium22User

23. 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? 2/2/2009Semantic Communication: MIT TOC Colloquium23 User Server X X X

24. 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. 2/2/2009Semantic Communication: MIT TOC Colloquium24UserServer Referee/Environment

25. Generic Goals Pure Control Pure Control Pure Informational Pure Informational 2/2/2009Semantic Communication: MIT TOC Colloquium25UserServer Referee/Environment UserServer Referee/Environment

26. Sensing & Universality (Theorems) 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. “User simulates Referee” “User simulates Referee” 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. 2/2/2009Semantic Communication: MIT TOC Colloquium26

27. Why is the paper so long? To capture fully general models … To capture fully general models … User/Server live for ever and Goal achievement is a function of infinite sequence of states. User/Server live for ever and Goal achievement is a function of infinite sequence of states. User/Server should be allowed to be probabilistic. User/Server should be allowed to be probabilistic. Referee should be allowed to be non- deterministic. Referee should be allowed to be non- deterministic. (Getting quantifiers right non-trivial.) (Getting quantifiers right non-trivial.) 2/2/2009Semantic Communication: MIT TOC Colloquium27

28. Some Examples [JS2] 2/2/2009Semantic Communication: MIT TOC Colloquium28

29. When Server is less powerful than User What should the goal be? What should the goal be? Can’t expect server to solve (computational) problems user can’t. Can’t expect server to solve (computational) problems user can’t. So what can user try to do? Why? So what can user try to do? Why? Ask Server: Repeat after me … Ask Server: Repeat after me … Test if Server has some computational power … solves simple (linear/quadratic time) problems. Test if Server has some computational power … solves simple (linear/quadratic time) problems. Has memory … can store/recall. Has memory … can store/recall. Can act (pseudo-)independently – is not deterministic, produces incompressible strings. Can act (pseudo-)independently – is not deterministic, produces incompressible strings. Can challenge me with puzzles. Can challenge me with puzzles. Each Goal/combo can be cast in our framework. Each Goal/combo can be cast in our framework. (Sensing functions do exist; communication is essential to achieving Goals; problems are more about control …) (Sensing functions do exist; communication is essential to achieving Goals; problems are more about control …) 2/2/2009Semantic Communication: MIT TOC Colloquium29

30. (Generalized) Turing tests Distinguish between “Intelligent”/”Not” Distinguish between “Intelligent”/”Not” Distinguish between “Humans”/”Bots” Distinguish between “Humans”/”Bots” Generically: Generically: Class of servers = H union N: Class of servers = H union N: H = { (1,i) | i } H = { (1,i) | i } N = { (0,i) | i } N = { (0,i) | i } Referee: gets identity of server from server (b,s),; and after interaction between user and server, gets User’s guess b’. Accepts if b = b’. Referee: gets identity of server from server (b,s),; and after interaction between user and server, gets User’s guess b’. Accepts if b = b’. Sensing function exists? Depends on H vs. N. Sensing function exists? Depends on H vs. N. 2/2/2009Semantic Communication: MIT TOC Colloquium30

31. Conclusions - 1 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: What is your goal? What is your goal? Server = Helpful? Server = Helpful? User = Sensing? User = Sensing? 2/2/2009Semantic Communication: MIT TOC Colloquium31

32. References Juba & S. (computational) Juba & S. (computational) 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. (generic) Goldreich, Juba & S. (generic) 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. – 2. (examples) Juba & S. – 2. (examples) ECCC TR08-095: http://eccc.uni-trier.de/report/2008/095/ ECCC TR08-095: http://eccc.uni-trier.de/report/2008/095/ http://eccc.uni-trier.de/report/2008/095/ 2/2/2009Semantic Communication: MIT TOC Colloquium32

33. Thank You! 2/2/2009Semantic Communication: MIT TOC Colloquium33

34. 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! 2/2/2009Semantic Communication: MIT TOC Colloquium34

35. Open challenges What is a model that reflects language learning? What is a model that reflects language learning? Has slow phase (we may be enumerating) and fast phase (we are enhancing our vocabulary). Has slow phase (we may be enumerating) and fast phase (we are enhancing our vocabulary). Build Semantics into Multiparty Computation? Build Semantics into Multiparty Computation? More symmetric language learning? More symmetric language learning? What is a more symmetric Goal? What is a more symmetric Goal? Model collaboration among humans? … Model collaboration among humans? … 2/2/2009Semantic Communication: MIT TOC Colloquium35

36. Part I: Context/Motivation 2/2/2009Semantic Communication: MIT TOC Colloquium36

37. 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! 2/2/200937Semantic Communication: MIT TOC Colloquium

38. 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. 2/2/200938Semantic Communication: MIT TOC Colloquium

39. 2/2/2009Semantic Communication: MIT TOC Colloquium39 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?

40. 2/2/2009Semantic Communication: MIT TOC Colloquium40 Classical Paradigm for interaction Object 1 Object 2 Designer

41. 2/2/2009Semantic Communication: MIT TOC Colloquium41 Object 2 New paradigm Object 1 Designer

42. 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. 2/2/2009Semantic Communication: MIT TOC Colloquium42 Few words about the proof: Positive result Server Prover User Interpreter