1. of 30 10/31/2013Cornell: Uncertainty in Communication1 Communication amid Uncertainty Madhu Sudan Microsoft, Cambridge, USA Based on: -Universal Semantic Communication – Juba & S. (STOC 2008) -Goal-Oriented Communication – Goldreich, Juba & S. (JACM 2012) -Compression without a common prior … – Kalai, Khanna, Juba & S. (ICS 2011) -Efficient Semantic Communication with Compatible Beliefs – Juba & S. (ICS 2011) -Deterministic Compression with uncertain priors – Haramaty & S. (ITCS 2014)

2. of 30 Classical theory of communication Clean architecture for reliable communication. Clean architecture for reliable communication. Remarkable mathematical discoveries: Prob. Method, Entropy, (Mutual) Information Remarkable mathematical discoveries: Prob. Method, Entropy, (Mutual) Information Needs reliable encoder + decoder (two reliable computers). Needs reliable encoder + decoder (two reliable computers). 10/31/2013Cornell: Uncertainty in Communication2 Shannon (1948) AliceAlice BobBob EncoderEncoder DecoderDecoder

3. of 30 Uncertainty in Communication? Always has been a central problem: Always has been a central problem: But usually focusses on uncertainty introduced by the channel But usually focusses on uncertainty introduced by the channel Standard Solution: Standard Solution: Use error-correcting codes Use error-correcting codes Significantly: Significantly: Design Encoder/Decoder jointly Design Encoder/Decoder jointly Deploy Encoder at Sender, Decoder at Receiver Deploy Encoder at Sender, Decoder at Receiver 10/31/2013Cornell: Uncertainty in Communication3

4. of 30 New Era, New Challenges: Interacting entities not jointly designed. Interacting entities not jointly designed. Can’t design encoder+decoder jointly. Can’t design encoder+decoder jointly. Can they be build independently? Can they be build independently? Can we have a theory about such? Can we have a theory about such? Where we prove that they will work? Where we prove that they will work? Hopefully: Hopefully: YES YES And the world of practice will adopt principles. And the world of practice will adopt principles. 10/31/2013Cornell: Uncertainty in Communication4

5. of 30 Example 1 10/31/2013Cornell: Uncertainty in Communication5

6. of 30 Example 2 Heterogenous data? Heterogenous data? Amazon-marketplace spends N programmer hours converting data from mom-n-pop store catalogs to uniform searchable format. Amazon-marketplace spends N programmer hours converting data from mom-n-pop store catalogs to uniform searchable format. Healthcare analysts spend enormous #hours unifying data from multiple sources. Healthcare analysts spend enormous #hours unifying data from multiple sources. Problem: Interface of software with data: Problem: Interface of software with data: Challenge: Challenge: Software designer uncertain of data format. Software designer uncertain of data format. Data designer uncertain of software. Data designer uncertain of software. 10/31/2013Cornell: Uncertainty in Communication6

7. of 30 Example 3 Archiving data Archiving data Physical libraries have survived for 100s of years. Physical libraries have survived for 100s of years. Digital books have survived for five years. Digital books have survived for five years. Can we be sure they will survive for the next five hundred? Can we be sure they will survive for the next five hundred? Problem: Uncertainty of the future. Problem: Uncertainty of the future. What systems will prevail? What systems will prevail? Why aren’t software systems ever constant? Why aren’t software systems ever constant? Problem: Problem: When designing one system, it is uncertain what the other’s design is (or will be in the future)! When designing one system, it is uncertain what the other’s design is (or will be in the future)! 10/31/2013Cornell: Uncertainty in Communication7

8. of 30 Modelling uncertainty Classical Shannon Model 10/31/2013Cornell: Uncertainty in Communication8 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Semantic Communication Model New Class of Problems New challenges Needs more attention!

9. of 30 Nature of uncertainty 10/31/2013Cornell: Uncertainty in Communication9

10. of 30 10/31/2013Cornell: Uncertainty in Communication10 II: Compression under uncertain beliefs/priors

11. of 30 Motivation 10/31/2013Cornell: Uncertainty in Communication11

12. of 30 Role of Dictionary (/Grammar/Language) 10/31/2013Cornell: Uncertainty in Communication12

13. of 30 Context? In general complex notion … In general complex notion … What does sender know/believe What does sender know/believe What does receiver know/believe What does receiver know/believe Modifies as conversation progresses. Modifies as conversation progresses. Our abstraction: Our abstraction: Context = Probability distribution on potential “meanings”. Context = Probability distribution on potential “meanings”. Certainly part of what the context provides; and sufficient abstraction to highlight the problem. Certainly part of what the context provides; and sufficient abstraction to highlight the problem. 10/31/2013Cornell: Uncertainty in Communication13

14. of 30 The problem 10/31/2013Cornell: Uncertainty in Communication14

15. of 30 Closeness of distributions: 10/31/2013Cornell: Uncertainty in Communication15

16. of 30 Dictionary = Shared Randomness? 10/31/2013Cornell: Uncertainty in Communication16

17. of 30 Solution (variant of Arith. Coding) 10/31/2013Cornell: Uncertainty in Communication17

18. of 30 Performance 10/31/2013Cornell: Uncertainty in Communication18

19. of 30 Implications 10/31/2013Cornell: Uncertainty in Communication19

20. of 30 10/31/2013Cornell: Uncertainty in Communication20 III: Deterministic Communication Amid Uncertainty

21. of 30 A challenging special case 10/31/2013Cornell: Uncertainty in Communication21

22. of 30 Model as a graph coloring problem 10/31/2013Cornell: Uncertainty in Communication22X

23. of 30 Main Results [w. Elad Haramaty] 10/31/2013Cornell: Uncertainty in Communication23

24. of 30 Restricted Uncertainty Graphs 10/31/2013Cornell: Uncertainty in Communication24X

25. of 30 Homomorphisms 10/31/2013Cornell: Uncertainty in Communication25

26. of 30 10/31/2013Cornell: Uncertainty in Communication26

27. of 30 Better upper bounds: 10/31/2013Cornell: Uncertainty in Communication27

28. of 30 10/31/2013Cornell: Uncertainty in Communication28 Better upper bounds:

29. of 30 Future work? 10/31/2013Cornell: Uncertainty in Communication29

30. of 30 Thank You 10/31/2013Cornell: Uncertainty in Communication30