Semiconductors
Carver Mead
Gordon and Betty Moore Professor of
Engineering and Applied Science, California
Institute of Technology
ACM
ACM 97
THE NEXT 50 YEARS OF COMPUTING
ACM
ACM 97
THE NEXT 50 YEARS OF COMPUTING
Copyright  1997 ACM, Association for Computing
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CARVER MEAD
ACM
Computation


Church-Turing Thesis: Any computable
function can be computed on a Turing
machine.
Mead's Thesis: The Class of Computable
Functions is defined by Algorithms that
Execute Efficiently on Commercial
Machines.
ACM
Computation


Complexity Theory:
Time: The number of steps required to
execute a program
Space: The number of memory
locations required by a program.
Assumption:
The computation done by different
machines (per step or per unit hardware
complexity) differs by at most a
polynomial factor.
ACM
What if

We Could Build a Computing Structure
With a Computational Capability
That Increased Exponentially with Its Size
It Would Completely Change the Game!
 Candidate Structures:
– Ultra-Parallel Digital VLSI Structures
– Neural Computing Structures
– Quantum Computing Structures
ACM
Ultra-Parallel Digital VLSI
Structures


The Good News:
Remarkable Speedup Can De Achieved
for Many Functions
The Bad News:
Speedup is No More than Polynomial
ACM
What is Going On ?

Digital Systems:
Represent information by a finite set of Discrete
Symbols
Digital Representation Permits Information to be
– Transmitted through Space
– Stored through Time without Loss
 Signal Representing the Symbol is Restored to the
Nearest Symbol by a Contractive Mapping
 Precision of the Representation is exponential in
the Number of Symbols per Value
ACM
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Digital System Limitations




Have No Natural Representation for
Time
All Continuous Variables Must Be
Represented by Finite Strings of
Discrete Symbols
Process Information in Discrete Chunks
Have No Notion of Locality or Continuity
ACM
Digital System Limitations

When Used to Simulate Continuous Non-Linear
Systems
 No General Criterion is Known for Numerical
Stability
 Most Computations Dominated by Aliasing
Artifacts
 Alternative Hypotheses Have Only Discrete
Representation
 Exponential Alternatives Require Exponential
Resources
 Quantizes After Every (Very Simple) Operation
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ACM
Neural Computation

Signals Transmitted over Distance:
 Represented as Events
– Discrete in Amplitude
– Discrete in Time
– Continuous Arrival Time Variable
 Local Signals:
Electrical Potential
Continuous in
Amplitude
Chemical Concentration Continuous in Time
 Information is encoded in Spatio-Temporal
Structure of Signals
}-{
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Neural Computation

Signals are Decoded in Highly Branched Dendrite
Structure
– Arrival Time Aligned by Propagation Delay
– Temporal Integrity Maintained
– Continuous Amplitude
– Active Amplification
– NonLinear Interaction
– Adaptive Control keeps Structure Stable
– Positive and Negative Feedback
 Keeps Many Combinatorial Possibilities Active in
Same Structure Avoids Pre-Quantization
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Neuromorphic VLSI Systems

Silicon and Wetware Have Similar Physics
 Basic Continuous Representation
– Continuous Time
– Limited Precision
– Many Operations Come Free From Physics
Interconnection Limits Complexity
– Energy is Precious
– Stability is a major Concern
 Natural World as Source of Information
– Real-Time Systems
– Adaptation to Environment
– Learning vs programming
– Time Evolution as Source of Learning
ACM
Many Functional Sub-Systems Have
Been Built

Vision Systems
–
–
–

Auditory Systems
–
–
–

Retinas
Motion Perception
Stereo Matching
Cochleas
Auditory Feature Extraction
Stereo Localization
In Situ Learning
–
Floating Silicon Gates
– Autonomous On-Chip Operation
– Weight Modification when In Use

Has Not Yet All Come Together
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Quantum Computation

Information Encoded in Spatio- Temporal
Structure of Many-Body Wave Function
 Phase Space for Coupled Many-Body System is
Cartesian Product of Individual Phase Spaces
– Greatly Enlarged Dimensionality
 Time Evolution of Coupled Many-Body System
Explores Volume in Phase Space that is
Exponential in the Number of Dimensions
– All in Parallel
 Physical Size of System is
Linear in the Number of Dimensions
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Quantum Computation


Theory: New Model of Computation
Experiment:
–
Many Delightful Model Systems
– Working Understanding of Quantum
Mechanics

Problems: Unwanted Coupling to rest of
Universe
–
DePhasing of the Wave Function
– Limits Computational Possibilities
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