Neuromorphic Engineering Book
  • Welcome
  • Preliminaries
    • About the author
    • Preface
    • A tale about passion and fear
    • Before we begin
  • I. Introduction
    • 1. Introducing the perspective of the scientist
      • From the neuron doctrine to emergent behavior
      • Brain modeling
      • Take away lessons
    • 2. Introducing the perspective of the computer architect
      • Limits of integrated circuits
      • Emerging computing paradigms
      • Brain-inspired hardware
      • Take away lessons
      • Errata
    • 3. Introducing the perspective of the algorithm designer
      • From artificial to spiking neural networks
      • Neuromorphic software development
      • Take home lessons
  • II. Scientist perspective
    • 4. Biological description of neuronal dynamics
      • Potentials, spikes and power estimation
      • Take away lessons
      • Errata
    • 5. Models of point neuronal dynamic
      • Tutorial - models of point neuronal processes
        • The leaky integrate and fire model
        • The Izhikevich neuron model
        • The Hodgkin-Huxley neuron model
      • Synapse modeling and point neurons
      • Case study: a SNN for perceptual filling-in
      • Take away lessons
    • 6. Models of morphologically detailed neurons
      • Morphologically detailed modeling
      • The cable equation
      • The compartmental model
      • Case study: direction-selective SAC
      • Take away lessons
    • 7. Models of network dynamic and learning
      • Circuit taxonomy, reconstruction, and simulation
      • Case study: SACs' lateral inhibition in direction selectivity
      • Neuromorphic and biological learning
      • Take away lessons
      • Errate
  • III. Architect perspective
    • 8. Neuromorphic Hardware
      • Transistors and micro-power circuitry
      • The silicon neuron
      • Case study: hardware - software co-synthesis
      • Take away lessons
    • 9. Communication and hybrid circuit design
      • Neural architectures
      • Take away lessons
    • 10. In-memory computing with memristors
      • Memristive computing
      • Take away lessons
      • Errata
  • IV. Algorithm designer perspective
    • 11. Introduction to neuromorphic programming
      • Theory and neuromorphic programming
      • Take away lessons
    • 12. The neural engineering framework
      • NEF: Representation
      • NEF: Transformation
      • NEF: Dynamics
      • Case study: motion detection using oscillation interference
      • Take away lessons
      • Errate
    • 13. Learning spiking neural networks
      • Learning with SNN
      • Take away lessons
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  1. IV. Algorithm designer perspective
  2. 12. The neural engineering framework

Take away lessons

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NEF-based representation: Distributed representation of mathematical constructs using nonlinear - spike-based - encoding and linear decoding.

Orthogonal and over-complete basis for representation. In the canonical description of vector representation, the spanning vectors are orthogonal. If we relaxed this constraint, such that these vectors were not necessarily independent, we might end up with an over-complete basis. With an over-complete representation, the number of the basis vectors is larger than the dimensionality of the input and it is, therefore, considered less efficient

NEF-based transformation: The transformation of one representation to another through weighted synaptic connections between two neuron ensembles.

NEF-based dynamics: The manifestation of a dynamical system from recurrently connected neuron ensembles.