A Probabilistic Approach to Nano-computing

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A Probabilistic Approach to Nano-computing

• J. Chen, J. Mundy, Y. Bai, S.-M. C. Chan,
• P. Petrica and R. I. Bahar
• Division of Engineering
• Brown University
• Acknowledgements NSF

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Motivation

• Silicon-based techniques are approaching
  practical limits

http//www.intel.com/research/silicon/mooreslaw.ht
m
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Nanotechnology

• Quantum transistors
• Computing with molecules, carbon nanotube
  arrays,
• pure quantum computing
• DNA-based computation,

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Carbon-Nanotube Devices

• We use carbon nanotubes as the basis for our
  initial study, which provides good transistor
  behaviors
• (However, our approach is not specific to
  these devices !!)

http//www.ibm.com
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Why DNA for Self-assembling?

• Are there other ways and other molecules that
  can do it too? Yes, there are.
• But, DNA is the best understood, plentiful, easy
  to handle, robust, near-perfect and near-infinite
  specificity

Cee Dekar, Nature 2002
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Non-silicon Approaches

• Nano-scale devices are attractive but have high
  probability of failure
• Defects may fluctuate in time

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Nano-architecture Approaches

• Nanofabrics Goldstein-Budiu
• Architecture detects faults and reconfigures
• using redundant components
• Array-based approach DeHon
• PLA logic arrays connected by
• conventional logic
• Neural Nets Likharev
• Builds neural networks from single-electron
• switches
• Needs a training stage for proper operation

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Our Probabilistic-based Approach

• Device failure should not cause computing
  systems to malfunction if they have been designed
  from the beginning to tolerate faults ---
  Von Neumann

• Our Probabilistic-based Design
• Dynamically defects tolerant
• Adapts to errors as a natural consequence of
  probability maximization
• Removes need to actually detect faults

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Why Markov Random Fields?

• MRF has been widely used in pattern recognition
  comm.
• Its operation does not depend on perfect devices
  or perfect connections.
• MRF can express arbitrary circuits and logic
  operation is achieved by maximizing state
  probability.
• or
• Minimizing a form of energy that depends on
  neighboring nodes in the network ? low-power
  design

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A Half-adder Example
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Rules to Formulate Clique Energy

• Clique energy is the negative sum of all valid
  states
• We use Boolean ring conversion to express each
  minterm representing a valid state (i.e. 000)

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Clique Energy for the Summation

• Sum over the valid states (000, 011, 101, 110)
• Lemma The energy of correct
• logic state is always less than
• that of invalid logic state by a
• constant.

x0 x1 x2 U
0 0 0 -1
0 0 1 0
0 1 0 0
0 1 1 -1
1 0 0 0
1 0 1 -1
1 1 0 -1
1 1 1 0
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Structural and Signal Errors

• Our implementation does not distinguish between
  devices and connections.
• Instead, we have structural-based and
  signal-based faults.
• -- Structural-based error Nano-scale devices
  contain a large number of defects or structural
  errors, which fluctuate on time scales
  comparable to the computation cycle.
• The error will result in variation in the
  clique
• energy coefficients.
• -- The second type of error is directly
  accounted for process noise that affects the
  signals.

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Take Device Errors into Design

• Sum over the valid states (000, 011, 101, 110)
• If we take the device error into consideration,
  the energy can be rewritten as
• In the error-free case, ABCDEFG1

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Take Structural Error into Design
x0 x1 x2 U
0 0 0 -1
0 0 1 0
0 1 0 0
0 1 1 -1
1 0 0 0
1 0 1 -1
1 1 0 -1
1 1 1 0
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The Inequalities for Correct Logic
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Constraints on Clique Coefficients

• We obtain the following constraints on the
  coefficients
• 2GgtD 2FgtC 2EgtA 2DgtB
• 2GgtF 2FgtB 2EgtC 2DgtA
• 2GgtE

Constraints form a polytope

• High order coefficients constraints the lower
  order ones

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Take Signal Errors into Design

• Gibbs distribution for an inverter is
• The conditional probability is

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Continuous Errors in Signal

• We model signal noise using Gaussian process

Design choice 1 -- Inputs around 0 1
Design choice 2 -- Inputs around -1 1
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Tolerance to Temperature Variation

• By taking input around 1, we get marginalized
  probability

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Error Rate Calculation
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Signal Error in NAND Design

• Gibbs distribution for a NAND is
• The marginalized probability P(xc) is

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Tolerance to Temperature Variation

• Apply inputs 01

• Apply inputs 11

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Error Rate Calculation
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Conclusions

• Proposed design doesnt depends on specific
  techniques!!
• Propose a probabilistic approach based on MRF
• Dynamically defect tolerant
• Adapts to errors as a natural consequence of
  probability maximization
• Removes need to actually detect fault
• For correct operation, energy of valid states
  must be less than invalid states
• The proposed design favors for lower power
  operation

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Future Works

• We are currently investigating how this approach
  can be extended to more complex logic
• Implement design using different Nanotechnologies

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Thank you Jie_Chen_at_Brown.Eduhttp//binary.engin
.brown.edu
Device failure should not cause computing
systems to malfunction if they have been designed
from the beginning to tolerate faults ---
Von Neumann