![Page 1: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/1.jpg)
of 37 10/18/2012 Uncertainty in Communication @ NU 1
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)
![Page 2: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/2.jpg)
of 37 05/30/2012 CSOI-Summer: Uncertainty in Communication 2
The Meaning of Bits
Is this perfect communication?
What if Alice is trying to send instructions? In other words … an algorithm Does Bob understand the correct algorithm? What if Alice and Bob speak in different
(programming) languages? Root Cause: Uncertainty …
Channel Alice Bob 01001011 01001011
Bob Freeze!
![Page 3: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/3.jpg)
of 37
Importance of semantics
Why is semantics (relatively) important today? Factor 1: Success of the Shannon program:
Reliability, in syntactic sense, has been achieved.
Factor 2: Communication vs. Computing.
05/30/2012 CSOI-Summer: Uncertainty in Communication 3
![Page 4: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/4.jpg)
of 37
Communication vs. Computation Interdependent technologies: Neither can exist without other
Technologies/Products/Commerce developed (mostly) independently. Early products based on clean abstractions of the other. Later versions added other capability as afterthought. Today products … deeply integrated.
Deep theories:
05/30/2012 CSOI-Summer: Uncertainty in Communication 4
Time for the theoretical wall to come down?
Well separated … and have stayed that way
Turing ‘36 Shannon ‘48
![Page 5: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/5.jpg)
of 37
Consequences of the wall
Computing theory: Fundamental principle = Universality You can program your computer to do whatever you want.
Communication principle: Centralized design (Encoder, Decoder, Compression, IPv4, TCP/IP). You can NOT program your device!
Contradiction! But does it matter? Aren’t communicating+computing systems just working
fine? Theory matters!
05/30/2012 CSOI-Summer: Uncertainty in Communication 5
![Page 6: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/6.jpg)
of 37
Role of theory?
Ideally: Foundations of practice!
05/30/2012 CSOI-Summer: Uncertainty in Communication 6
Theory layer
Application
![Page 7: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/7.jpg)
of 37
Option 1
Communication vs. Computing
05/30/2012 CSOI-Summer: Uncertainty in Communication 7
Communication
Computing
![Page 8: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/8.jpg)
of 37
Option 2
Communication vs. Computing
05/30/2012 CSOI-Summer: Uncertainty in Communication 8
Communication
Computing
![Page 9: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/9.jpg)
of 37
Option 3
Communication vs. Computing
05/30/2012 CSOI-Summer: Uncertainty in Communication 9
Communication
Computing
![Page 10: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/10.jpg)
of 37
Good News/ Bad News
Good: We are mostly practicing option 2 or 3!
Bad: Lost opportunities. Vulnerabilities. Inefficiency. Incompatibilities.
05/30/2012 CSOI-Summer: Uncertainty in Communication 10
![Page 11: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/11.jpg)
of 37
Uncertainty in Communication?
Always has been a central problem: But usually focusses on uncertainty introduced
by the channel Standard Solution:
Use error-correcting codes Significantly:
Design Encoder/Decoder jointly Deploy Encoder at Sender, Decoder at Receiver
10/18/2012 Uncertainty in Communication @ NU 11
![Page 12: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/12.jpg)
of 37
New Era, New Challenges:
Interacting entities not jointly designed. Can’t design encoder+decoder jointly. Can they be build independently? Can we have a theory about such?
Where we prove that they will work?
Hopefully: YES And the world of practice will adopt principles.
10/18/2012 Uncertainty in Communication @ NU 12
![Page 13: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/13.jpg)
of 37
Example 1
Intersystem communication? Google+ ↔ Facebook friendship ? Skype ↔ Facetime chat?
Problem:
When designing one system, it is uncertain what the other’s design is (or will be in the future)!
10/18/2012 Uncertainty in Communication @ NU 13
![Page 14: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/14.jpg)
of 37
Example 2
Heterogenous data? 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.
Problem: Interface of software with data: Challenge:
Software designer uncertain of data format. Data designer uncertain of software.
10/18/2012 Uncertainty in Communication @ NU 14
![Page 15: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/15.jpg)
of 37
Example 3
Archiving data Physical libraries have survived for 100s of
years. Digital books have survived for five years. Can we be sure they will survive for the next
five hundred?
Problem: Uncertainty of the future. What systems will prevail? Why aren’t software systems ever constant?
10/18/2012 Uncertainty in Communication @ NU 15
![Page 16: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/16.jpg)
of 37
Modelling uncertainty
Classical Shannon Model
10/18/2012 Uncertainty in Communication @ NU 16
A B Channel
B2
Ak
A3
A2
A1 B1
B3
Bj
Semantic Communication Model
New Class of Problems New challenges
Needs more attention!
![Page 17: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/17.jpg)
of 37
Nature of uncertainty
𝐴𝑖’𝑠,𝐵𝑗 ’𝑠 differ in beliefs, but can be centrally programmed/designed. [Juba,Kalai,Khanna,S.’11] : Compression in this context
has graceful degradation as beliefs diverge. 𝐴𝑖’𝑠,𝐵𝑗 ’𝑠 differ in behavior:
Nothing to design any more. Best hope: Can highlight certain 𝐴𝑖’s (universalists) that
can interact successfully with many 𝐵𝑗’s [Juba,S’08; Goldreich,J,S’12; J,S’11]: “All is not lost, if
we keep goal of communication in mind” Details don’t fit in margin …
10/18/2012 Uncertainty in Communication @ NU 17
![Page 18: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/18.jpg)
of 37 10/18/2012 Uncertainty in Communication @ NU 18
II: Compression under uncertain beliefs/priors
![Page 19: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/19.jpg)
of 37
Motivation: Human Communication
Human communication (dictated by languages, grammars) very different. Grammar: Rules, often violated. Dictionary: Often multiple meanings to a word. Redundant: But not as in any predefined way
(not an error-correcting code). Our thesis: Emerges from uncertainty:
Sender of message uncertain about receiver’s background/context/prior.
Will try to explain in the context of Redundancy
10/18/2012 Uncertainty in Communication @ NU 19
![Page 20: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/20.jpg)
of 37
Natural Communication
To send a “message” Humans have a repertoire of choices of
words/phrases (from dictionary/language). Some are shorter than others.
Why the variation? How are options used? If sender understands receiver well … then use
short message. Compression is a natural instinct
If not, use longer, redundant choice. But understanding is never perfect!
Can we formalize use of such redundancy?
10/18/2012 Uncertainty in Communication @ NU 20
![Page 21: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/21.jpg)
of 37
Model: Communication amid uncertainty
Wish to design encoding/decoding schemes (E/D) to be used as follows: Sender has distribution P on M = {1,2,…,N} Receiver has distribution Q on M = {1,2,…,N} Sender gets 𝑋 ∈ 𝑀 Sends E(P,X) to receiver. Receiver receives Y = E(P,X) Decodes to 𝑋� = D(Q,Y)
Want: X = 𝑋� (provided P,Q close),
While minimizing 𝐸𝐸𝑝𝑋←𝑃 |𝐸(𝑃,𝑋)|
10/18/2012 Uncertainty in Communication @ NU 21
![Page 22: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/22.jpg)
of 37
Contrast with some previous models
Universal compression? Doesn’t apply: P,Q are not finitely specified. Don’t have a sequence of samples from P; just
one! K-L divergence?
Measures inefficiency of compressing for Q if real distribution is P.
But assumes encoding/decoding according to same distribution Q.
Semantic Communication: Uncertainty of sender/receiver; but no special
goal. 10/18/2012 Uncertainty in Communication @ NU 22
![Page 23: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/23.jpg)
of 37
Closeness of distributions:
P is 𝛼-close to Q if for all 𝑋 ∈ 𝑀,
1𝛼≤ 𝑃 𝑋
𝑄 𝑋≤ 𝛼
P 𝛼-close to Q ⇒ 𝐷(𝑃||𝑄),𝐷(𝑄| 𝑃 ≤ log𝛼 .
10/18/2012 Uncertainty in Communication @ NU 23
![Page 24: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/24.jpg)
of 37
Dictionary = Shared Randomness?
Modelling the dictionary: What should it be?
Simplifying assumption – it is shared randomness, so …
Assume sender and receiver have some shared randomness R and X is independent of R. Y = E(P,X,R) 𝑋� = D(Q,Y,R)
Want ∀𝑋, Pr
𝑅𝑋� = 𝑋 ≥ 1 − 𝜖
10/18/2012 Uncertainty in Communication @ NU 24
![Page 25: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/25.jpg)
of 37
Solution (variant of Arith. Coding)
Use R (randomness/dictionary) to define sequences 𝑅1 1 ,𝑅1 2 ,𝑅1 3 , … (encoding of message 1) 𝑅2 1 ,𝑅2 2 ,𝑅2 3 , … (encoding of message 2) … 𝑅𝑁 1 ,𝑅𝑁 2 ,𝑅𝑁 3 , … (encoding of message N)
𝐸𝛼 𝑃, 𝐸,𝑅 = 𝑅𝑥 1 … 𝐿 , where 𝐿 chosen s.t. ∀𝑧 ≠ 𝐸 Either 𝑅𝑧 1 … 𝐿 ≠ 𝑅𝑥 1 … 𝐿
Or 𝑃 𝑧 < 𝑃 𝑥𝛼2
𝐷𝛼 𝑄,𝑦,𝑅 = Max. Likelihood Decoding = argmax𝑥� {𝑄 𝐸� } among 𝐸� ∈ 𝑧 𝑅𝑧[1 … 𝐿] = 𝑦
10/18/2012 Uncertainty in Communication @ NU 25
![Page 26: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/26.jpg)
of 37
Performance
Obviously decoding always correct.
Easy exercise:
Exp𝑋 𝐸 𝑃,𝑋 = 𝐻 𝑃 + 2 log 𝛼
Limits: No scheme can achieve 1 − 𝜖 ⋅ [𝐻 𝑃 + log 𝛼] Can reduce randomness needed.
10/18/2012 Uncertainty in Communication @ NU 26
![Page 27: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/27.jpg)
of 37
Implications
Reflects the tension between ambiguity resolution and compression. Larger the 𝛼 ((estimated) gap in context),
larger the encoding length. Coding scheme reflects the nature of human
process (extend messages till they feel unambiguous).
The “shared randomness’’ is a convenient starting point for discussion Dictionaries do have more structure. But have plenty of entropy too. Still … should try to do without it.
10/18/2012 Uncertainty in Communication @ NU 27
![Page 28: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/28.jpg)
of 37
A teaser:
Can we do this deterministically? Suppose you and I have a ranking of N players.
Rankings 𝜋,𝜎 ∶ 𝑁 → [𝑁] Further suppose we know the rankings are close.
∀ 𝑖 ∈ 𝑁 : 𝜋 𝑖 − 𝜎 𝑖 ≤ 2. You want to know: Is 𝜋−1 1 = 𝜎−1 1 How many bits do I need to send to you (non-
interactively). 𝑂(1)? 𝑂(log𝑁)? 𝑂(log log log𝑁)?
10/18/2012 Uncertainty in Communication @ NU 28
![Page 29: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/29.jpg)
of 37 10/18/2012 Uncertainty in Communication @ NU 29
III: Uncertainty on Action: Goal-Oriented Communication
![Page 30: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/30.jpg)
of 37
Back to meaning
What if sender is sending instructions? Sender and receiver are uncertain about each
other’s “instruction ↔ bits” association? Can we ensure receiver decodes the right
instructions? Translation of bits to instructions?
Well studied in language/computer science. (Many) “Complete” languages/codebooks exist.
Each translates bits to meaning. All equivalent (upto “Kolmogorov constant”) But not same.
10/18/2012 Uncertainty in Communication @ NU 30
![Page 31: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/31.jpg)
of 37
Goal of communication Easy negative result:
(Due to plethora of languages/codebooks): In finite time, can’t guarantee “receiver understands instructions.”
Is this bad? If receiver can not distinguish correct instructions
from incorrect ones, why should it try to do so? Goals of communication:
Communication is not an end in itself, it a means to achieving some end.
Hopefully receiver wishes to achieve a goal and using information from sender to achieve this goal.
Semantic communication: Help communication achieve its goal. Use progress towards goal to understand meaning.
10/18/2012 Uncertainty in Communication @ NU 31
![Page 32: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/32.jpg)
of 37
Utility of Communication?
The lens of computational complexity: To prove some resource is useful:
Step 1: Identify hardest problems one can solve without the resource.
Step 2: Show presence of resource can help solve even harder problems.
Classical resources: CPU speed, Memory, Non-determinism, Randomness …
In our case: Communication in presence of understanding. Communication w/o understanding.
10/18/2012 Uncertainty in Communication @ NU 32
![Page 33: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/33.jpg)
of 37
Computation as a goal [ Juba & S. ’08]
Model: Simple user talking to powerful server. Class of problems user can solve on its own:
~ probabilistic polynomial time (P). Class of problems user can solve with perfect
understanding of server: ~ Any problem. (Even uncomputable!)
Class of problems user can solve without understanding of server: ~ Polynomial space.
Roughly: If you are solving problems and can verify solutions, then this helps. If you have a solution, you are done. If not, you’ve found some error in communication.
Moral: Communication helps, even with misunderstanding, but misunderstanding introduces limits.
10/18/2012 Uncertainty in Communication @ NU 33
![Page 34: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/34.jpg)
of 37
Summarizing results of [GJS 2012]
But not all goals are computational. We use communication mostly for (remote) control. Intellectual/informational goals are rare(r).
Modelling general goals, in the presence of misunderstanding: Non-trivial, but can be done. Results extend those from computational setting:
Goals can be achieved if user can sense progress towards goal, servers are “forgiving” and “helpful”
10/18/2012 Uncertainty in Communication @ NU 34
![Page 35: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/35.jpg)
of 37
Useful lessons
User/Server can be designed separately.
Each should attempt to model its “uncertainty” about the other.
Each should plan for uncertainty: Server: By assuming some short “interrupt”
sequence. User: By always checking its progress.
10/18/2012 Uncertainty in Communication @ NU 35
![Page 36: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/36.jpg)
of 37
Future goals
Broadly: Information-theoretic study of human
communication, with uncertainty as an ingredient. Should exploit natural restrictions of
humans: Limited ability to learn/infer/decode. Limited bandwidth.
Conversely, use human interactions to create alternate paradigms for “designed communications. Place semantics on solid foundations.
10/18/2012 Uncertainty in Communication @ NU 36
![Page 37: Communication amid Uncertaintymadhu.seas.harvard.edu/talks/2012/NU-Uncertain.pdf · 10/18/2012 Uncertainty in Communication @ NU 1 of 37 Communication amid Uncertainty Madhu Sudan](https://reader033.vdocuments.site/reader033/viewer/2022041521/5e2e554f68b9b50715589586/html5/thumbnails/37.jpg)
of 37 10/18/2012 Uncertainty in Communication @ NU 37
Thank You!