Spiking networks, from the neuron up

The course

Spiking networks, from the neuron up

After a short opening on when spiking networks are worth using, 14 chapters go from one neuron to a network that drives a car from events. Each starts with the idea, builds the math, gives you a live model to change in your browser, and ends with the sparx code that runs the same model.

Where to start

• New to neural networksRead in order from chapter 1. The math uses sums and exponentials, and each chapter builds what it needs.Start with chapter 1
• You train deep networksRead chapter 0 for when spiking networks pay off. Skim 1 to 3, then read 4 to 8, where the training differs from what you know.Start with chapter 0
• You study or simulate brainsSkim 1 to 3 for this course's notation, then read 9 to 11 for circuits in physical units and how sparx checks itself against NEST and Brian2.Start with chapter 9

Before you start

1. 0Why spikes?Where spiking networks beat conventional ones today, where they lose, and how to choose.

Neurons

1. 1What a neuron doesSynapses, a membrane that keeps charge, and the all-or-none spike.
2. 2Membranes and time constantsThe RC circuit, the exact solution, and what a step of dt does to it.
3. 3Spikes and thresholdsThreshold, reset, refractoriness, the f-I curve and adaptation.
4. 4CodingRate, timing and change: three ways to put a number into spikes.

Learning

1. 5Surrogate gradientsWhy a spike has no gradient, and the stand-in that lets gradient descent through.
2. 6Backpropagation through timeUnrolling a network over time, what it costs, and why gradients explode.
3. 7Local learning rulesSTDP, three-factor rules and e-prop: learning from what each synapse can see.
4. 8DelaysSpikes take time to travel. Learning how long turns sequences into coincidences.

Circuits

1. 9Networks and dynamicsBalanced excitation and inhibition, irregular firing, and chaos.
2. 10Physical units and biologyMillivolts and nanosiemens: conductances, receptors and real neurons.
3. 11Simulators and fidelityHow a simulator steps time, and how to tell whether two of them agree.

Machines

1. 12Hardware and eventsEvent cameras, neuromorphic chips, and NIR, the format that moves a network between them.
2. 13Case study: the droneA spiking network that learned to fly by gradients through its physics.
3. 14Case study: the racerDriving from events alone, trained end to end through the camera.