The Anytime Automaton Joshua San Miguel Natalie Enright Jerger - - PowerPoint PPT Presentation

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The Anytime Automaton Joshua San Miguel Natalie Enright Jerger - - PowerPoint PPT Presentation

Feb 14, 2023 1.99k likes •3.55k views

The Anytime Automaton Joshua San Miguel Natalie Enright Jerger Summary We propose the Anytime Automaton : A new computation model for approximate computing. 2 Summary We propose the Anytime Automaton : A new computation model for

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SLIDE 1

The Anytime Automaton

Joshua San Miguel Natalie Enright Jerger

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SLIDE 2

Summary

2

We propose the Anytime Automaton:

  • A new computation model for approximate computing.
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SLIDE 3

Summary

3

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality final

  • utput
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SLIDE 4

Summary

4

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality final

  • utput
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SLIDE 5

Approximate Computing

Many applications are inherently noisy and imprecise.

5

http://www.zentut.com/ http://www.businessweek.com/ http://www.cc.gatech.edu/~cnieto6/ http://www.analyticbridge.com/ http://themusicparlour.blogspot.ca/ http://www.scientific-computing.com/

Data mining Computer vision Audio and video processing Gaming Machine learning Dynamical simulation

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Approximate Computing

Many applications are inherently noisy and imprecise.

6

http://www.zentut.com/ http://www.businessweek.com/ http://www.cc.gatech.edu/~cnieto6/ http://www.analyticbridge.com/ http://themusicparlour.blogspot.ca/ http://www.scientific-computing.com/

Data mining Computer vision Audio and video processing Gaming Machine learning Dynamical simulation

But how can we apply approximate computing techniques and still ensure acceptability in final output?

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SLIDE 7

Approximate Computing

program () { foos_on_first(); bars_on_second(); hello_worlds_on_third(); }

7

time foos_on_first bars_on_second hello_worlds_on_third

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SLIDE 8

Approximate Computing

program () { approx_foos_on_first(); bars_on_second(); hello_worlds_on_third(); }

8

time foos_on_first bars_on_second hello_worlds_on_third tune quality (runtime-quality tradeoff)

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Approximate Computing

program () { approx_foos_on_first(); bars_on_second(); hello_worlds_on_third(); }

9

time foos_on_first bars_on_second hello_worlds_on_third tune quality (runtime-quality tradeoff)

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Approximate Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time bars_on_second hello_worlds_on_third tune quality foos_on_first

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SLIDE 11

Approximate Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time bars_on_second hello_worlds_on_third tune quality foos_on_first

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Approximate Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time bars_on_second hello_worlds_on_third foos_on_first But final output may not be acceptable!

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Approximate Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time bars_on_second hello_worlds_on_third foos_on_first But final output may not be acceptable!

Difficult to ensure acceptability of final output

  • n-the-fly, since quality control limited to local

approximations and not their composition. (Challenge #1: Holistic Quality Control)

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SLIDE 14

Approximate Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

14

time bars_on_second hello_worlds_on_third foos_on_first But final output may not be acceptable!

Difficult to ensure acceptability of final output

  • n-the-fly, since quality control limited to local

approximations and not their composition. (Challenge #1: Holistic Quality Control)

tune local quality tune local quality

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SLIDE 15

Real-Time Computing

Real-time systems impose strict runtime constraints; loss in output quality more tolerable than not finishing in time.

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http://www.streamingvideoprovider.co.uk/ http://www.beaudaniels-illustration.com/ http://m.exed.hec.edu/

Streaming multimedia Automotive systems Telecommunications

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Real-Time Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time foos_on_first bars_on_second hello_worlds_on_third strict target runtime

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Real-Time Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

17

time foos_on_first bars_on_second hello_worlds_on_third tune quality tune quality strict target runtime

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SLIDE 18

Real-Time Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time foos_on_first bars_on_second hello_worlds_on_third tune quality tune quality strict target runtime

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SLIDE 19

Real-Time Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

19

time foos_on_first bars_on_second hello_worlds_on_third But actual runtimes variable! strict target runtime

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SLIDE 20

Real-Time Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

20

time foos_on_first bars_on_second hello_worlds_on_third

Difficult to ensure strict real-time constraints are met (i.e., interrupt the application), since runtime-quality tradeoffs vary dynamically. (Challenge #2: Interruptibility)

But actual runtimes variable! strict target runtime

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User-Interactive Computing

In user-interactive environments, users dictate quality requirements on-the-fly.

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http://www.businessweek.com/ http://www.pcadvisor.co.uk/ http://www.expressvpn.com/

Gaming Mobile vision Search/recommendation

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User-Interactive Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

22

time foos_on_first bars_on_second hello_worlds_on_third

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SLIDE 23

User-Interactive Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

23

time bars_on_second hello_worlds_on_third foos_on_first tune quality?

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SLIDE 24

User-Interactive Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

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time bars_on_second hello_worlds_on_third But target quality unknown! foos_on_first tune quality?

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User-Interactive Computing

program () { approx_foos_on_first(); approx_bars_on_second(); hello_worlds_on_third(); }

25

time bars_on_second hello_worlds_on_third But target quality unknown! foos_on_first tune quality?

Difficult to ensure acceptability for a given user at a given context, since acceptable quality cannot be determined a priori. (Challenge #3: User Flexibility)

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Anytime Automaton

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We propose the Anytime Automaton:

  • A new computation model for approximate computing.
  • Revisits and generalizes concepts from anytime (or iterative)

algorithms, originally studied for real-time decision problems.

  • A recipe for applying approximate computing techniques such

that the final output is available early and improves in quality

  • ver time.
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Anytime Automaton

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application execution quality

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Anytime Automaton

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application execution quality final

  • utput

conventionally, single output

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Anytime Automaton

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application execution quality precise

  • utput
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SLIDE 30

Anytime Automaton

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application execution quality precise

  • utput

holistic quality control: final output available early

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SLIDE 31

Anytime Automaton

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application execution quality precise

  • utput

strict target runtime

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Anytime Automaton

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application execution quality precise

  • utput

interruptibility: use current output if needed strict target runtime

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Anytime Automaton

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application execution quality precise

  • utput
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Anytime Automaton

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application execution quality precise

  • utput
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Anytime Automaton

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application execution quality precise

  • utput
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Anytime Automaton

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application execution quality precise

  • utput

user flexibility: wait longer for better quality

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Outline

Anytime Automaton

  • The Model
  • The Approximations

Evaluation

  • Methodology
  • Experimental Results

Conclusion

37

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Anytime Automaton

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program:

data dependence computation

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Anytime Automaton

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inst A;

program:

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Anytime Automaton

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inst A; inst B; inst C;

program:

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Anytime Automaton

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func (...);

program:

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Anytime Automaton

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kernel () { ... }

program:

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Dataflow Model

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program:

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Dataflow Model

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i n p u t

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Anytime Automaton

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Anytime Automaton

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produce a single result

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Anytime Automaton

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produce multiple approx versions of result (i.e., anytime) precise version

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Anytime Automaton

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Data Diffusion Model

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t child works on parent’s approx result

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Anytime Automaton

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i n p u t child works on parent’s approx result parent works on producing better approx result

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t final output available early

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SLIDE 64

Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t

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SLIDE 66

Anytime Automaton

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i n p u t

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SLIDE 67

Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t

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Anytime Automaton

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i n p u t precise output

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Anytime Automaton – The Model

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  • 1. Ensure precise output is always produced eventually.
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Anytime Automaton – The Model

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  • 1. Ensure precise output is always produced eventually.
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Anytime Automaton – The Model

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  • 1. Ensure precise output is always produced eventually.

kernel () { ... }

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Anytime Automaton – The Model

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  • 1. Ensure precise output is always produced eventually.

kernel () { ... } pure function

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Anytime Automaton – The Model

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  • 1. Ensure precise output is always produced eventually.

kernel () { ... } pure function single-writer, updates isolated

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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.
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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.

Anytime (or iterative) algorithms have been studied before but are traditionally built into the coarse-grained derivation of an application. Approximate computing techniques have proliferated recently and have been shown to have general fine-grained applicability.

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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.
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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.

anytime algorithm?

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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.

kernel () { ... }

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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.

kernel () { ... } approx computing techniques

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Anytime Automaton – The Model

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  • 2. Create the effect of improving accuracy over time.

approx computing techniques

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.
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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation A computation B computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation B computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation C final output not ready!

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation A computation B computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation A computation B computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time computation A computation B computation C

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Anytime Automaton – The Model

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  • 3. Enable interruptibility via pipelining.

time approx output ready! computation A computation B computation C

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Anytime Automaton – The Approximations

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  • 1. General case: apply approximations iteratively.
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Anytime Automaton – The Approximations

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  • 1. General case: apply approximations iteratively.

quality knob

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Anytime Automaton – The Approximations

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loop perforation smaller perforation stride load value approximation lower approximation degree neural acceleration higher neural network complexity SRAM bit upsets higher supply voltage floating-point precision more mantissa bits

  • 1. General case: apply approximations iteratively.
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Anytime Automaton – The Approximations

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  • 1. General case: apply approximations iteratively.
  • Loop perforation
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Anytime Automaton – The Approximations

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perforation stride 20: for i = 0, 20, 40, 60, 80, 100, ...., N-1

  • 1. General case: apply approximations iteratively.
  • Loop perforation
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Anytime Automaton – The Approximations

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  • 1. General case: apply approximations iteratively.
  • Loop perforation

perforation stride 20: for i = 0, 20, 40, 60, 80, 100, ...., N-1 perforation stride 15: for i = 0, 15, 30, 45, 60, 75, ....., N-1 perforation stride 10: for i = 0, 10, 20, 30, 40, 50, ....., N-1 perforation stride 5: for i = 0, 5, 10, 15, 20, 25, ......, N-1 perforation stride 1: for i = 0, 1, 2, 3, 4, 5, 6, 7, ...., N-1

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Anytime Automaton – The Approximations

97

  • 1. General case: apply approximations iteratively.
  • Loop perforation

perforation stride 20: for i = 0, 20, 40, 60, 80, 100, ...., N-1 perforation stride 15: for i = 0, 15, 30, 45, 60, 75, ....., N-1 perforation stride 10: for i = 0, 10, 20, 30, 40, 50, ....., N-1 perforation stride 5: for i = 0, 5, 10, 15, 20, 25, ......, N-1 perforation stride 1: for i = 0, 1, 2, 3, 4, 5, 6, 7, ...., N-1

Achieves desired effect of improving quality over time, but can yield redundant work.

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Anytime Automaton – The Approximations

98

  • 1. General case: apply approximations iteratively.
  • Loop perforation

perforation stride 20: for i = 0, 20, 40, 60, 80, 100, ...., N-1 perforation stride 15: for i = 0, 15, 30, 45, 60, 75, ....., N-1 perforation stride 10: for i = 0, 10, 20, 30, 40, 50, ....., N-1 perforation stride 5: for i = 0, 5, 10, 15, 20, 25, ......, N-1 perforation stride 1: for i = 0, 1, 2, 3, 4, 5, 6, 7, ...., N-1

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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Each approximation builds on the previous one.
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Each approximation builds on the previous one.

data dependences (each approximate result contributes usefully to precise result)

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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Each approximation builds on the previous one.

data dependences (each approximate result contributes usefully to precise result) data sampling more samples integer/fixed-point precision more bits

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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)

commutative

  • peration
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)

To improve quality, no need to reiterate from beginning; therefore, diffusive. (e.g., just add more samples to current result)

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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Input sampling (e.g., generating a distribution)

Minimal redundant work since each element processed exactly once.

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Anytime Automaton – The Approximations

111

  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)

sequential permutation

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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)

tree permutation

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Anytime Automaton – The Approximations

119

  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Output sampling (e.g., generating an image)
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Anytime Automaton – The Approximations

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  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 123

X * 10.1101 Y * 01.0010 Z * 11.0110

Anytime Automaton – The Approximations

123

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 124

X * 10.1101 Y * 01.0010 Z * 11.0110

Anytime Automaton – The Approximations

124

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time final result not ready!

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 125

X * 10.1101 Y * 01.0010 Z * 11.0110

Anytime Automaton – The Approximations

125

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 126

Y * 01.0010 Z * 11.0110

Anytime Automaton – The Approximations

126

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

X * 10 X * 11 X * 01

MSb LSb

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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Anytime Automaton – The Approximations

127

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

X * 10 Y * 01 Z * 11 X * 11 Y * 00 Z * 01 X * 01 Y * 10 Z * 10

MSb LSb

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 128

Anytime Automaton – The Approximations

128

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

X * 10 Y * 01 Z * 11 X * 11 Y * 00 Z * 01 X * 01 Y * 10 Z * 10

MSb LSb

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 129

Anytime Automaton – The Approximations

129

  • 2. Better case: apply diffusive approximations.
  • Integer/fixed-point precision (e.g., dot product)

time

X * 10 Y * 01 Z * 11 X * 11 Y * 00 Z * 01 X * 01 Y * 10 Z * 10

approx result ready! MSb LSb

[ X Y Z ] ● [ 10.1101 01.0010 11.0110 ]

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SLIDE 130

Anytime Automaton

130

More details in paper:

  • Asynchronous/synchronous pipelining
  • Data locality with sampling
  • Approximate storage techniques
  • Thread scheduling
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Evaluation – Methodology

131

Experiments:

  • IBM Power 780 system
  • 4 POWER7+ cores
  • 32 total hardware threads

Applications:

  • PERFECT and AxBench suites
  • 2D convolution (output sampling, reduced precision†, SRAM bit upsets†)
  • debayer (output sampling)
  • discrete wavelet transform (loop perforation)
  • histogram equalization (input and output sampling)
  • k-means clustering (output sampling)

†see paper

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Evaluation – 2D Convolution

132 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

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Evaluation – 2D Convolution

133 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

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Evaluation – 2D Convolution

134 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

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Evaluation – 2D Convolution

135 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

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SLIDE 136

Evaluation – 2D Convolution

136 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

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SLIDE 137

Evaluation – 2D Convolution

137 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

slide-138
SLIDE 138

Evaluation – 2D Convolution

138 10 20 30 40 0.5 1 1.5 2 SNR (dB) runtime (normalized to baseline) inf

better

slide-139
SLIDE 139

Evaluation – Debayer

139 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 SNR (dB) runtime (normalized to baseline) inf

better

slide-140
SLIDE 140

Evaluation – Debayer

140 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 SNR (dB) runtime (normalized to baseline) inf

better

slide-141
SLIDE 141

Evaluation – Debayer

141 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 SNR (dB) runtime (normalized to baseline) inf

better

slide-142
SLIDE 142

Evaluation – Debayer

142 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 SNR (dB) runtime (normalized to baseline) inf

better

slide-143
SLIDE 143

Evaluation – Debayer

143 5 10 15 20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 SNR (dB) runtime (normalized to baseline) inf

better

slide-144
SLIDE 144

Evaluation – Discrete Wavelet Transform

144 5 10 15 20 25 30 0.5 1 1.5 2 2.5 SNR (dB) runtime (normalized to baseline) inf

better

slide-145
SLIDE 145

Evaluation – Discrete Wavelet Transform

145 5 10 15 20 25 30 0.5 1 1.5 2 2.5 SNR (dB) runtime (normalized to baseline) inf

better

slide-146
SLIDE 146

Evaluation – Discrete Wavelet Transform

146 5 10 15 20 25 30 0.5 1 1.5 2 2.5 SNR (dB) runtime (normalized to baseline) inf

better

slide-147
SLIDE 147

Evaluation – Discrete Wavelet Transform

147 5 10 15 20 25 30 0.5 1 1.5 2 2.5 SNR (dB) runtime (normalized to baseline) inf

better

slide-148
SLIDE 148

Evaluation – Discrete Wavelet Transform

148 5 10 15 20 25 30 0.5 1 1.5 2 2.5 SNR (dB) runtime (normalized to baseline) inf

better

slide-149
SLIDE 149

Evaluation – Summary

149

how acceptable the output is how much time is expended

slide-150
SLIDE 150

Conclusion

150

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality precise

  • utput
slide-151
SLIDE 151

Conclusion

151

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality holistic quality control: final output available early precise

  • utput
slide-152
SLIDE 152

Conclusion

152

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality interruptibility: use current output if needed precise

  • utput
slide-153
SLIDE 153

Conclusion

153

We propose the Anytime Automaton:

  • A new computation model for approximate computing.

application execution quality precise

  • utput

user flexibility: wait longer for better quality

slide-154
SLIDE 154

Thank you

The Anytime Automaton

Joshua San Miguel Natalie Enright Jerger Special thanks to IBM collaborators: Viji Srinivasan, Ravi Nair, Dan Prener