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Efficient Semantic Communication via Compatible Beliefs Efficient Semantic Communication via Compatible Beliefs

Efficient Semantic Communication via Compatible Beliefs - PowerPoint Presentation

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Uploaded On 2015-11-11

Efficient Semantic Communication via Compatible Beliefs - PPT Presentation

Brendan Juba MIT CSAIL amp Harvard w ith Madhu Sudan MSR amp MIT Motivation Beliefs model Sketch of result 2 Miscommunication happens Got that Q CAN COMPUTERS COPE WITH MISCOMMUNICATION AUTOMATICALLY ID: 189780

benchmark time overhead beliefs time benchmark beliefs overhead server user universal communication running natural distribution amp password pspace servers

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Slide1

Efficient Semantic Communication via Compatible Beliefs

Brendan Juba

(MIT CSAIL & Harvard)

w

ith

Madhu

Sudan (MSR & MIT)Slide2

Motivation

Beliefs model

Sketch of result

2Slide3

Miscommunication happens…

Got that?

Q:

CAN COMPUTERS COPE

WITH MISCOMMUNICATION AUTOMATICALLY??

3Slide4

Printer

Defining (

mis

)communication

Printer driver

Printer firmware

ENVIRONMENT

INTERFACE FIXED IN ADVANCE

4Slide5

ENVIRONMENT

Goal of computation (function

f

)

x

f(x

)

user returns

f(x)

?”

“user”

“server”

This talk: f

will be PSPACE-complete

5Slide6

ENVIRONMENT

S

-universal user (for computing

f

)

x

f(x

)

user returns

f(x)

?”

S

6Slide7

Formally,U is a

S

-universal user for computing f ifservers S

S

$

poly.

r

unning time for U inputs x, initial states of U & S Pr[ ] ≥ ⅔

S

-universal user (for computing

f

)

On input x with S, U runs poly(|x|)

steps and

U’s final output is f(x)

[JS’08]: can construct universal users for computing PSPACE-complete

f for maximally large class S

7Slide8

110

0110

11110

Problem:

Password-protected servers

ENVIRONMENT

11110

x

f(x

)

8Slide9

Theorem

[JS08,GJS09]

. S-Universal users for classes S containing password-protected servers and goals that require the server to act must run for Ω(2

l

) rounds with servers with passwords of length

l

.

PROMISES MORE THAN WE WANTED!

CAN WE REFINE AWAY PASSWORDS??

9Slide10

Motivation

Beliefs model

Sketch of result

10Slide11

Server’s Beliefs

Q

x

f(x

)

t

U,S

(|x|)

Def’n

:

Q

-Benchmark running time

T

Q

,S

(n) =

E

U

Q

[

tU,S(n)]

I’VE CHOSEN AN

S

WITH POLYNOMIAL Q-BENCHMARK RUNNING TIME

SO,

NO PASSWORD!!

11Slide12

Q

WHY

DOESN’T IT WORK??

PREFIXING A MESSAGE WITH

%!PS-

Adobe

IS THE

MOST

NATURAL THING IN THE

WORLD

.

x

MORAL:

NEED “SIMILAR” BELIEFS…

THAT

ISN’T A

PASSWORD.”

12Slide13

Compatibility

P

Q

a

(

P

,

Q

) =

S

w

min

{P(

w

),Q(

w

)} = 1-|P-Q|

TV

13Slide14

Compatibility controls overhead of universal communication

Theorem.

Let P

be a

sampleable

distribution, suppose every server S

S has a belief distribution QS. For PSPACE-complete P, there exist polys r & w such that if strategies from

Q

S

decide

P

with S,

there is a user strategy U

P that computes P

with any SS on x of length n in time

w(1/

a(P, Q )

,n) × (TQ,S o r)(n)

RECALL: “benchmark time” T

Q,S(n) = EU

Q[tU,S

(n)], “compatibility” a(

P, Q ) =

Sw min{P(

w),Q(w)}

Can recover [JS’08] by taking

P

= length-weighted uniform

Q

S

=

δ

U

(S)

(for U(S) helped by S)

DEPENDENCE ON SERVER?

DEPENDENCE ON BENCHMARK TIME W.R.T SERVER BELIEFS

DEPENDENCE ON COMPATIBILE BELIEFS

14Slide15

Key points

Server designers can evaluate benchmark time

w.r.t. their beliefs

Compatible beliefs lead to low overhead (beyond benchmark time)

Beliefs capture natural approaches

15Slide16

Motivation

Beliefs model

Sketch of result

16Slide17

Starting point: [JS’08]

Enumerate algorithms U’:

give each constant share of running time, repeatedly double running time (cf. Levin’73)

Use U’ with S to simulate interactive proof system for

P

, return answer if successful

(exploits efficient

prover strategy using P)

SAMPLE

FROM

P

REPEATEDLY DOUBLE # OF SAMPLES PER TIME BOUND,

INTRODUCE DOUBLED MAXIMUM

TIME

BOUND

High weight in

P

corresponds to short programs in enumeration

17Slide18

Analysis in three easy steps

Markov’s inequality: For poly. r from proof system, U’

Q

S

, see success

w.p

. 1-γif we use U’ run for (1/γ)(TQ,S o

r)(n

) steps

See success

w.p

. 1-γ-

|P-Q|

TV = a(P,

QS

)-γ for U’

P insteadSo, if we run 2/a(

P, QS ) samples from P

for (2/

a(P,

Q ) )(T

Q,S o r)(n) steps each, see success with constant probability

So, try using

γ =

a(P,

QS )/2

w also contains:

overhead from simulating proof system, logarithmic

overhead

in 1/

a

(

P

,

Q

S

)

(

i

distinct bounds in phase

i

)

18Slide19

Compatibility controls overhead of universal communication

Theorem.

Let P

be a

sampleable

distribution, suppose every server S

S has a belief distribution QS. For PSPACE-complete P, there exist polys r & w such that if strategies from

Q

S

decide

P

with S,

there is a user strategy U

P that computes P

with any SS on x of length n in time

w(1/

a(P, Q )

,n) × (TQ,S o r)(n)

RECALL: “benchmark time” T

Q,S(n) = EU

Q[tU,S

(n)], “compatibility” a(

P, Q ) =

Sw min{P(

w),Q(w)}

Actual dependence:Õ

(

1

/

a

(

P

,

Q

)

2

)

19Slide20

RECAP:

We refined the

semantic communication model to capture natural settings in which flexible communication is possible

with low overhead

.

20Slide21

Open problem

Construct

a server with low benchmark running time for a natural goal and belief distribution!

21Slide22

Key points

Server designers can evaluate benchmark time

w.r.t. their beliefs

Compatible beliefs lead to low overhead (beyond benchmark time)

Beliefs capture natural approaches

RECALL:

“benchmark time”

T

Q

,S

(n) =

E

U

Q[tU,S(n)]

RECALL:

“compatibility” a(

P, Q ) = Sw

min{P(w),Q(w)},

overhead is

Õ(1/

a(P

, Q )2

)

FIN.

22