February Semantic CMU1 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

Disclaimer Work in progress (for ever) … Work in progress (for ever) … Comments/Criticisms/Collaboration/Competition welcome. Comments/Criticisms/Collaboration/Competition welcome. February Semantic CMU2

February Semantic CMU3 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 Bob Freeze!

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 February Semantic CMU 4

February Semantic CMU5 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?

Part I: Computational Motivation February Semantic CMU

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? February Semantic CMU7

qkqkqkqk February Semantic CMU8 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.

February Semantic CMU9 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)

February Semantic CMU10 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)

February Semantic CMU11 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).

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 …) February Semantic CMU12

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? February Semantic CMU13

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? February Semantic CMU14 Next part of talk

February Semantic CMU15 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.: AAAA Read the TexPoint manual before you delete this box.: AAAA

February Semantic CMU16 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

Communication: Example 1 (Printing) February Semantic CMU17

Communication: Ex. 2 (Computation) February Semantic CMU18 X f(X)

Communication: Ex. 3 (Web search) February Semantic CMU19 Q(WWW(P)) = ? WWW Q Q P

Communication: Ex. 4 (Intelligence?) February Semantic CMU20 Yes No

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? What is the mathematical model of a communicating computer? What is universality? What is universality? Aside: Modelling Computing February Semantic CMU21

Communication: Ex. 2 (Computation) February Semantic CMU22 X f(X)

Generic communication problem? February Semantic CMU23 Yes No X f(X) Q(WWW(P)) = ? WWWQ Q P Should model All 4 examples!

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? February Semantic CMU24

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. February Semantic CMU25User

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? February Semantic CMU26 User Server X X X

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. February Semantic CMU27UserServer Referee/Environment

Generic Goals Pure Control Pure Control Pure Informational Pure Informational February Semantic CMU28UserServer Referee/Environment UserServer Referee/Environment

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: Sensing is necessary (in one-shot goals) Sensing is necessary (in one-shot goals) (In infinite goals, If non-trivial generic goal is achieved with sufficiently rich class of helpful servers, then it is safely achieved with every server.) (In infinite goals, If non-trivial generic goal is achieved with sufficiently rich class of helpful servers, then it is safely achieved with every server.) February Semantic CMU29

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? February Semantic CMU30

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! February Semantic CMU31

References Juba & S. Juba & S. ECCC TR07-084: ECCC TR07-084: Goldreich, Juba & S. Goldreich, Juba & S. ECCC TR09-075: ECCC TR09-075: February Semantic CMU32

Thank You! February Semantic CMU33

February Semantic CMU34 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