Neural Network AlgorithmsReview, Quantum and Glial

Directions

Martin DimkovskiCSE 6111 Presentation

York UniversityMarch 31st, 2011

March 32st, 2011 Neural Network Algorithms 2

Presentation Goals Hope to increase awareness of NNs’ potential

Very general toolkit, applicable to many problems

(<10 min) Overview: Algorithm models Computational power Complexity, limitations

Interesting research directions (<5 min) Quantum (<5 min) Glia

March 32st, 2011 Neural Network Algorithms 3

Presentation Motivation Can’t explain

On a serious note…: ubiquitous (brains, computers, society, space-time fabric), accessible & good inspiration

Fight common over-simplification Backpropagation-only/mostly view Practical applications and solid theoretical

foundations exist for presented alternatives

0.5

March 32st, 2011 Neural Network Algorithms 4

Network Graphs Unidirectional: simple, feed-forward

Backpropagation is here

+ Bidirectional: recurrent, interactive Network dynamics comes up

++ lateral: resonance, competition, pattern completion

0.5

March 32st, 2011 Neural Network Algorithms 5

Learning Approaches Supervised vs Unsupervised Error-driven (ex: backprop)

Straightforward Mature Adaptive basis functions For well defined tasks input>output, functions

Hebbian-Style (more on next slide) More sophisticated, more bio-inspired, self-organizing But not as mature (still weak like error-driven in 1960s) Order and Chaos

Combinations (superior)

1.5

March 32st, 2011 Neural Network Algorithms 6

On Hebbian-Style Network dynamics, more complex graphs

Fire together – wire together Compete Resonate

Build internal models of environ. - Identify principal features

Constraint satisfaction Find energy function minima

Attractors = memorized patterns Deal with corrupt and partial memory

1.5

March 32st, 2011 Neural Network Algorithms 7

More Modeling Aspects Complex (superior) vs real valued

Temporal dynamics

Signal coding: Discreet, analog, pulse averaging, or Superior: detailed pulse/spike pattern modeling

Static vs dynamic weights (in between training) Stay the same for any input/output condition Superior: Adjust to input/output condition

Excitation - inhibition modeling Superior: not on the same weight

1.5

March 32st, 2011 Neural Network Algorithms 8

Use of Probability Bayesian: Solves a BIG problem

Over-fitting When noise and peculiarities become more attended-to than

the general features of interest Problem especially with error-driven, like backprop.

Solves it because it samples from whole posterior and does not depend on a single set of weights

To get a feeling, compare: MAP = argmax P( | data) E[] = P( | data) d

The benefit of noise To avoid local minima/maxima (ketchup)

1.5

March 32st, 2011 Neural Network Algorithms 9

Research Directions NNs have come a long way

Yet, still far below known upper bounds For precision, performance, and usability

What better place to turn for help, than back to our original inspiration? In green are my personal speculations

1.0

March 32st, 2011 Neural Network Algorithms 10

Cues to Quantum Classically unexplained brain features

Simultaneous synchronized stimulations in distant regions for same stimuli

highly structured in phase and amplitude Perception unification – global attractor states

Speculation brain has ingredients for macroscopic quantum state

High metabolic energy; extreme dielectric prop. Microtubules, superconducting waves, gap junctions (anaesthesia)

Interest in just plain quantum computing power

1.5

March 32st, 2011 Neural Network Algorithms 11

A (Qu)bit of Quantum Basics

If left alone – a linear ‘combination’ of basis states (in coherence)

| = ci|i Each |i is a single reality for us classical beings

(ex: |0 or |1) But in quantum world, they all exist at once

|ci|2 giving the probability

If ‘touched’ by anything – decoheres Into one of the basis states, as per probabilities

Entanglement Instantaneous sync link between remote qubits

1.5

March 32st, 2011 Neural Network Algorithms 12

How can Quantum Translate for Artificial

NNs?1. Run existing NN algorithms on quantum

computers …getting there, but will take a long time Extra slide in appendix

2. Could we simulate the quantum ‘spooky’ effects in new NN algorithms?

Using our classical computers

0.5

March 32st, 2011 Neural Network Algorithms 13

Simulating Quantum Effects

Maybe the brain uses certain quantum features for evolutionary reasons.

Could we program/simulate?: Synchronization and unification of distant physically

unconnected neurons?

Coherence and decoherence of macroscopic quantum states

even though we would have to use many more bits

Interference and quantum functions in discretized approximations?

1.0

March 32st, 2011 Neural Network Algorithms 14

Old View on Glia Myelinate for insulation only

Clean-up and recycle neurotransmitters

Feed and heal neurons

…But, Einstein’s brain Double the glia

0.5

March 32st, 2011 Neural Network Algorithms 15

Recent FindingsGlia-Neuron and Glia-Glia Information Processing

Listen to all neurotransmitters, and uses them to communicate with both glia and neurons

Control synapse formation and operations As many as 100,000 synapses per glia

Connect neurons which have no synapses between them, and correlate them

Run separate network in parallel to NNs

Control speed of neuron’s output (axon)

Most regulated genes during REM are in glia (integration/consolidation)

It’s a whole new brain out there… And there’s more:

2.0

March 32st, 2011 Neural Network Algorithms 16

Glia Quantum Correlates Brain-wide calcium broadcast network

Connect through gap junctions

Calcium messaging affects neural circuits Drive global broadcast waves

Glia Quantum Correlates Calcium stores related to microtubules Gap junctions as hypothesized

Quantum aspects might play a big function in glia networks

1.0

March 32st, 2011 Neural Network Algorithms 17

Glia as Biological Bayesian?

Accumulated effect from previous inputs (old posterior) serves as baseline for new input (new prior).

Glia excitations last second to minutes, compared to ms for neurons, and it span much wider

This could produce something alike cumulative data likelihood during the period t of glia excitation

Glia could then adjust/sample weights for neurons as per latest posterior (weight factors coupled to posterior)

Would need a mechanism for normalization to 1

)(*)1(*)(_)( tDatatPosteriortConstNormtPosterior

2.0

March 32st, 2011 Neural Network Algorithms 18

Conclusion Existing NN algorithms offer a rich toolkit for

computing Much more beyond plain backpropagation Take advantage of combinations and complex graphs Use as many of the superior modeling aspects as

affordable Use probability theory

Glia networks and interactions with neurons can be modeled in new algorithms

Might be possible to simulate quantum effects for more enhancements

1.0

March 32st, 2011 Neural Network Algorithms 19

The End Questions?

March 32st, 2011 Neural Network Algorithms 20

References O’Reilly, Y. Munakata, “Computational Explorations in Cognitive Neuroscience, The MIT

Press, 2000

V. Ivancevic, T. Ivancevic, “Quantum Neural Computation”, Springer, 2010

U. Ramacher, C. v.d. Malsburg, “On the Construction of Artificial Brains”, Springer, 2010

(Ed.) A. Volterra, P. Magistretti, P. Haydon, “The Tripartite Synapse”, Oxford University Press 2002

R. M. Neal, “Bayesian Learning for Neural Networks”, Springer, 1996

R. D. Fields, “The Other Brain”, Simon & Schuster 2009 S. Gupta, R. Zia, “Quantum Neural Networks”, Journal of Computer and Systems

Sciences 63, 355-383, 2001 A. A. Ezhov, D. Ventura, “Quantum Neural Networks”, Future Directions for Intelligent

Systems and Information Science. Physica-Verlang, 2000 J. J. Hopfield, “Neural networks and physical systems with emergent collective

computational abilities”, Proc. Natl. Acad. Sci. USA Vol 79, pp. 2554-2558, April 1982

Additional Slides

March 32st, 2011 Neural Network Algorithms 22

Existing NNs on Quantum Computers

Quantum Computing1. N-qubit register can contain all 2N

values at once2. You can have a quantum ‘circuit’

‘computing’ on all of them at once3. But when you ‘touch it’, you will get

one value only. 4. Goal – how to touch it, to get the

value you want, with high probability