The Liquid Brain Chrisantha Fernando & Sampsa Sojakka

Motivations

• Only 30,000 genes, ≈1011 neurons• Attractor neural networks, Turing machines• Problems with classical models

– Often depend on synchronization by a central clock– Particular recurrent circuits need to be constructed for each task– Recurrent circuits often unstable and difficult to regulate– Lack parallelism– Real organisms cannot wait for convergence to an attractor

• Wolfgang Maass’ invented the Liquid State Machine (a model of the cortical microcircuit) in which he viewed the network as a liquid (or liquid-like dynamical system).

Liquid State Machine (LSM)• Maass’ LSM is a spiking recurrent

neural network which satisfies two properties– Separation property (liquid)– Approximation property (readout)

• LSM features– Only attractor is rest– Temporal integration– Memoryless linear readout map– Universal computational power: can

approximate any time invariant filter with fading memory

– It also does not require any a-priori decision regarding the ``neural code'' by which information is represented within the circuit.

Maass’ Definition of the Separation Property

The current state x(t) of the microcircuit at time t has to hold all information about preceding inputs.

Approximation Property

Readout can approximate any continuous function f that maps current liquid states x(t) to outputs v(t).

• We took the metaphor seriously and made the real liquid brain shown below. WHY?

BECAUSE.

• Real water is computationally efficient.Maass et al. used a small recurrent network of leaky integrate-and-

fire neurons– But it was computationally expensive to model. – And I had to do quite a bit of parameter tweaking.

• Exploits real physical properties of water.• Simple local rules, complex dynamics. • Potential for parallel computation applications. • Educational aid, demonstration of a physical

representation that does computation. • Contributes to current work on computation in non-linear

media, e.g. Adamatsky, Database search.

Pattern Recognition in a Bucket

• 8 motors, glass tray, overhead projector

• Web cam to record footage at 320x240, 5fps

• Frames Sobel filtered to find edges and averaged to produce 700 outputs

• 50 perceptrons in parallel trained using the p-delta rule

Experiment 1: The XOR Problem.

2 motors, 1 minute footage of each case, 3400 framesReadouts could utilize wave interference patterns

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BOTH MOTORS MOTOR A MOTOR B

STILL WATER

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BOTH MOTORS MOTOR A MOTOR B STILL WATER

Can Anyone Guess How it Works?

Experiment 2 : Speech Recognition

• Objective: Robust spatiotemporal pattern recognition in a noisy environment• 20+20 samples of 12kHz pulse-code modulated wave files (“zero” and “one”),

1.5-2 seconds in length• Short-Time Fourier transform on active frequency range (1-3000Hz) to create

a 8x8 matrix of inputs from each sample (8 motors, 8 time slices)• Each sample to drive motors for 4 seconds, one after the other

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4 Presentations of the Word "One"

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Zero One

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Epochs

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Perceptrons trained on dataset NOT passed through water.

Final error rates correspond to 25% Mistakes in Classification

Analysis

Conclusion

• Properties of a natural dynamical system (water) can be harnessed to solve non-linear pattern recognition problems.

• Set of simple linear readouts suffice. • No tweaking of parameters required. • Further work will explore neural networks

which exploit the epigenetic self-organising physical properties of materials.

Acknowledgements

• Inman Harvey• Phil Husbands• Ezequiel Di Paolo• Emmet Spier• Bill Bigge• Aisha Thorn, Hanneke De Jaegher, Mike Beaton. • Sally Milwidsky