High Performance Associative

High Performance Associative
Neural Networks:

Overview and Library

Presented at AI’06, Quebec city, Canada, June 7
-
9, 2006


Oleksiy K. Dekhtyarenko
1

and Dmitry O. Gorodnichy
2


1
-

Institute of Mathematical Machines and Systems, Dept. of Neurotechnologies,

42 Glushkov Ave., Kiev, 03187, Ukraine.
olexii@mail.ru

2
-

Institute for Information Technology, National Research Council of Canada,

M
-
50 Montreal Rd, Ottawa, Ontario, K1A 0R6, Canada.
dmitry.gorodnichy@nrc.gc.ca

http://synapse.vit.iit.nrc.ca

2

Associative Neural Network Model

Features:

•
Distributed storage of information


fault tolerance

•
Parallel way of operation


efficient hardware
implementation

•
Non
-
iterative learning rules


fast, deterministic training


Confirms to three main principles of neural processing
:

1.
Non
-
linear processing

2.
Massively distributed collective decision making

3.
Synaptic plasticity

1.
to accumulate learning data in time by adjusting synapses

2.
to associate receptor to effector (using thus computed synaptic values)

The
Associative Neural Network

(AsNN) is a dynamical
nonlinear system capable of processing information via
the evolution of its state in high dimensional state
-
space.

3

Examples of Practical Applications

•
Face recognition from video
*

•
“
Electronic Nose
”
**

*
D. Gorodnichy
–

“Associative Neural Networks as Means for Low
-
Resolution Video
-
Based
Recognition”,
IJCNN’05

**
A. Reznik; Y. Shirshov; B. Snopok; D. Nowicki; O. Dekhtyarenko & I. Kruglenko
–

“Associative Memories for Chemical Sensing”,
ICONIP'02

4

Associative Properties

Convergence Process

Network evolves according to the state update rule:

–

set of memorized patterns

We want the network to be
retrieve data by associative
similarity (to restore noisy or
incomplete input data):

5

Sparse Associative Neural Network

Advantages over Fully
-
Connected Model:

•
Less memory needed for s/w simulation

•
Quicker convergence during s/w simulation

•
Fewer and/or more suitable connections for h/w
implementation

•
Greater biological plausibility

Output of neuron
i

can affect
neuron
j

(
w
ij
≠ 0) if and only if:

Architecture,
or

Connectivity Template
:

Connection Density
:

6

Network Architectures

Random Architecture

1D Cellular Architecture

Small
-
World Architecture

1
–

the worst

5
–

the best

Associative
Performance

Memory
Consumption

Hardware
Friendly

Regular (cellular)

1

5

5

Small
-
World

2

5

4

Scale
-
Free

2

5

3

Random

3

5

2

Adaptive

4

5

2

Fully
-
Connected

5

1

1

7

Compare to
…


Fully connected net with
n
=24x24
neurons obtained by tracking and
memorizing faces (of 24x24 pixel
resolution) from
real
-
life

video
sequences [Gorodnichy
’
05]



•
Notice visible inherent synaptic
structure !

•
This synaptic interdependency is
utilized by Sparse architectures.

8

Some Learning Algorithms

•
Projective

•
Hebbian (Perceptron LR)

•
Delta Rule

•
Pseudo
-
Inverse

–

selection operator

, where

1.
Performance Evaluation Criteria

Error correction capability

(Associativity strength)

Capacity


Training complexity


Memory requirements


Execution time: a) in Learning and b) in Recognition

9

Comparative Performance Analysis

Networks with Fixed Architectures

Associative performance and training complexity as a function of
number of stored patterns

Cellular 1D network with dimension 256 and connection
radius 12, randomly generated data vectors

10

Comparative Performance Analysis

Influence of Architecture

Sparse network with dimension 200, randomly generated
data vectors, various ways of architecture selection

Associative performance as a
function of connection density

•
PI WS

–

PseudoInverse Weight
Select, architecture targeting
maximum informational capacity
per synapse

•
PI Random

–

Randomly set
sparse architecture with
PseudoInverse learning rule

•
PI Cell

–

Cellular architecture
with PseudoInverse learning rule

•
PI WS Reverse

–

architecture
constructed using the opposite
criterion of PI WS

11

Associative Neural Network Library

•
Publicly available

at
http://synapse.vit.iit.nrc.ca/memory/pinn/library.html

•
Effective

C++ implementation of full and sparse associative networks

•

Includes
noniterative Pseudo
-
Inverse LR
with possibility of
addition/removal of selected vectors to/from memory

•
Different learning rules
:

Projective, Hebbian, Delta Rule, Pseudo
-
Inverse

•
Different architectures
: fully
-
connected, cellular (1D and 2D), random,
small
-
world, adaptive

•
Desaturation Technique
: allows to increase memory capacity up to 100%

•
Different update rules
: synchro. vs. asynchro. Detection of cycles

•
Different testing functions
: absolute and normalized radius of attraction,
capacity

•
Associative Classifiers
: Convergence
-
based, Modular

12

Associative Neural Network Library

Hierarchy of Main Classes