1. of 33 March 1, 2011 Semantic Communication @ UCLA1 Universal Semantic 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 March 1, 2011Semantic Communication @ UCLA 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? Channel Alice Bob Bob 01001011 01001011 Bob Freeze!

3. of 33 Part I: Context/Motivation March 1, 2011Semantic Communication @ UCLA 3

4. of 33 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! March 1, 2011 4 Semantic Communication @ UCLA

5. of 33 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. March 1, 2011 5 Semantic Communication @ UCLA

6. of 33 March 1, 2011Semantic Communication @ UCLA 6 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?

7. of 33 March 1, 2011Semantic Communication @ UCLA 7 Classical Paradigm for interaction Object 1 Object 2 Designer

8. of 33 March 1, 2011Semantic Communication @ UCLA 8 Object 2 New paradigm Object 1 Designer

9. of 33 March 1, 2011Semantic Communication @ UCLA 9 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?

10. of 33 March 1, 2011Semantic Communication @ UCLA 10 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

11. of 33 March 1, 2011Semantic Communication @ UCLA 11 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

12. of 33 Part II: Computational Motivation March 1, 2011 12 Semantic Communication @ UCLA

13. of 33 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? March 1, 2011Semantic Communication @ UCLA 13

14. of 33 qkqkqkqk March 1, 2011Semantic Communication @ UCLA 14 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.

15. of 33 March 1, 2011Semantic Communication @ UCLA 15 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)

16. of 33 March 1, 2011Semantic Communication @ UCLA 16 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)

17. of 33 March 1, 2011Semantic Communication @ UCLA 17 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).

18. of 33 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? March 1, 2011Semantic Communication @ UCLA 18

19. of 33 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. March 1, 2011Semantic Communication @ UCLA 19 Few words about the proof: Positive result Server Prover User Interpreter

20. of 33 March 1, 2011Semantic Communication @ UCLA 20 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.

21. of 33 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? March 1, 2011Semantic Communication @ UCLA 21 Next part of talk

22. of 33 March 1, 2011 Semantic Communication @ UCLA22 Part III: Generic Goals

23. of 33 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. March 1, 2011Semantic Communication @ UCLA 23

24. of 33 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? March 1, 2011Semantic Communication @ UCLA 24

25. 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. March 1, 2011Semantic Communication @ UCLA 25User

26. 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? March 1, 2011Semantic Communication @ UCLA 26 User Server X X X

27. 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. Results generalize, assuming “sensing” Results generalize, assuming “sensing” March 1, 2011Semantic Communication @ UCLA 27UserServer Referee/Environment

28. 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! March 1, 2011Semantic Communication @ UCLA 28

29. of 33 March 1, 2011 Semantic Communication @ UCLA29 Part IV: Some recent works

30. of 33 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. March 1, 2011Semantic Communication @ UCLA 30

31. of 33 Compression in natural settings 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: Reveals same phenomena: Novel redundancy (increases with uncertainty), still ambiguous, but robust. Novel redundancy (increases with uncertainty), still ambiguous, but robust. March 1, 2011Semantic Communication @ UCLA 31

32. of 33 Conclusion: A new model Classical Shannon Model March 1, 2011Semantic Communication @ UCLA 32 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Semantic Communication Model New Class of Problems New challenges Needs more attention!

33. 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/ 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 March 1, 2011Semantic Communication @ UCLA 33 Thank You!

34. of 33 Thank You! March 1, 2011Semantic Communication @ UCLA 34

35. of 33 Generic Goals Pure Control Pure Control Pure Informational Pure Informational March 1, 2011Semantic Communication @ UCLA 35UserServer Referee/Environment UserServer Referee/Environment

36. of 33 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. March 1, 2011Semantic Communication @ UCLA 36