Analog Logic and Differential Belief Propagation

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Analog Logic andDifferential Belief Propagation

• Benjamin Vigoda, Ph.D.

MIT Media Laboratory
Physics and Media Group
NSF CCR-0122419
Benjamin Vigoda, November, 2003
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Optimization/Inference (Belief Propagation)
Using Physical Systems (Analog Circuits)
Benjamin Vigoda, November, 2003
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Avogadro-Scale Computing as Optimization
Conjecture 1 Optimization is probably not how
we want to perform all computation.
Benjamin Vigoda, November, 2003
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Avogadro-Scale Computing as Optimization
Conjecture 2 But as the number of gates
becomes large, the majority of gates will be used
to solve inference/optimization
problems. (Thats how we use super-computers
now.)
Benjamin Vigoda, November, 2003
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Implementing Optimization/Inference Natively
with Physical Dynamics

• No clock necessary
• Parallel programming of 1023 transistors by
  saying, optimize this.
• Robustness to noise and fault tolerance arise
  naturally
• Enables smoother design trade-offs between
• Speed, Power, Accuracy, and Complexity
• Implement natively with physical dynamics,
  dLx/dt0

Benjamin Vigoda, November, 2003
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Linear Feedback Shift Register (LFSR)
(000111101011001) or 0
Benjamin Vigoda, November, 2003
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Transmitter LFSR
Transmitter LFSR
Benjamin Vigoda, November, 2003
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Receiver Noise Lock Loop
Transmitter LFSR
Receiver Noise Lock Loop
Low-Complexity LFSR Synchronization by
Forward-Only Message Passing, Vigoda, Dauwels,
Gershenfeld and Loeliger, submitted IEEE
Transactions on Information Theory, 2003
Benjamin Vigoda, November, 2003
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Noise Lock Loop Performs LFSR Synchronization
Benjamin Vigoda, PhD, August, 2003
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Soft-XOR gateCircuit
Translinear circuits A proposed classification.
Barrie Gilbert. Electronics Letters, 1975.
Benjamin Vigoda, November, 2003
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soft-EQUALS Gate Circuit
Benjamin Vigoda, PhD, August, 2003
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Soft-DELAYContinuous-Time Analog Memory
Elements
Benjamin Vigoda, November, 2003
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Noise Lock Loop Circuit
Synchronization of a Chaotic Dynamical System
Using a Soft-Decision Receiver. Justin Dauwels,
Matthias Frey, Tobias Koch, Hans-Andrea Loeliger,
Patrick Merkli, Benjamin Vigoda.
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Design FlowCompile MATLAB to Spice to Circuits
Waveform probing commands .probe .options
probefilename"D probesdbfile"D
probetopmodule"3 softxors" .SUBCKT softxor p_x0
p_x1 p_y0 p_y1 p_z0 p_z1 GND Vdd M4 N5 p_y1 N7
GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M8 N1 p_y0 N7
GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M7 N8 p_y1 N1
GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M3 N8 p_y0 N5
GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M9 GND p_x1
N1 GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M6 N5 p_x0
GND GND NMOS_49 W'48l' L'4l' AS'40ll'
AD'40ll' PS'24l' PD'24l' M1 M12 p_z1 N7
Vdd N6 PMOS_49 W'48l' L'10l' AS'66ll'
AD'66ll' PS'60l' PD'60l' M1 M11 Vdd N7 N7
N2 PMOS_49 W'48l' L'10l' AS'66ll'
AD'66ll' PS'60l' PD'60l' M1 .ENDS Main
circuit 3 softxors .tran 1n 1600n .include
Mami_15.md .options abstol1e-15 .param l0.8u R1
N1 GND 50 TC0.0, 0.0 R2 N7 GND 50 TC0.0,
0.0
SPICE netlist written by Bayes2Gates (c) 2002
Ben Vigoda, MIT Media Lab Written on
28-Jun-2002
Xsoftxor_1 N5 N3 N4 N19 N11 N10 GND Vdd
softxor Xsoftxor_2 N11 N10 N9 N8 N7 N1 GND Vdd
softxor Xsoftxor_3 N2 N16 N15 N14 N9 N8 GND Vdd
softxor
MATLAB Bayes Net Toolbox
Spice Netlist
Benjamin Vigoda, November, 2003
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Fault Tolerant Soft-Logic
Xu Sun, Mehdi Gazor, Bernard Yen, Ben Vigoda
Benjamin Vigoda, November, 2003
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Differential Belief Propagation(advertisement)

• How do algorithmic dynamics of belief propagation
  relate to the physical dynamics of the computing
  substrate?
• Belief Propagation high-frequency electronics
  ?
• Parasitic capacitances in transistors
• Imperfect delay elements
• Belief Propagation molecular dynamics ?
• Use belief propagation to estimate solutions of
  partial differential equations

Benjamin Vigoda, November, 2003