The Liquid Brain

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The Liquid Brain

• Chrisantha Fernando Sampsa Sojakka

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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).

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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.

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

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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.

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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

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Experiment 1 The XOR Problem.
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2 motors, 1 minute footage of each case, 3400
frames Readouts could utilize wave interference
patterns
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Can Anyone Guess How it Works?
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Experiment 2 Speech Recognition
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• Objective Robust spatiotemporal pattern
  recognition in a noisy environment
• 2020 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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One
Zero
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Analysis
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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.

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Acknowledgements

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