An Algorithmic Theory of Brain Networks
summary
A formal stochastic spiking neural network model uses synchronized discrete rounds, sigmoid noisy thresholds and signed weights to prove concrete algorithmic claims: a winner-take-all with two inhibitors converges to one active output with probability at least 1 − δ in time O((log n)(log 1/δ)), uses weights (inputs→outputs 3, self-loop 2, outputs→inhibitors 1, inhibitors→outputs −1) scaled by γ, and remains stable for long TS; one inhibitor is provably insufficient, additional inhibitors speed convergence toward the k‑th root of log n. Similarity testing implements random sampling with an indexing module (≈√n resources).
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chapters (13)
- 0:00Start
- 1:30Biological Distributed Algorithms
- 4:19Our Work on Brain Algorithms
- 5:57Guiding Questions
- 7:482. Stochastic Spiking Neural Networks
- 10:09Neural Network Model
- 11:35Network Dynamics
- 30:43Stability Proof
- 33:19Convergence Proof
- 37:03Lower Bounds
- 41:31Algorithm Idea
- 42:47Similarity Testing with Neuro-RAM
- 43:12Composing Spiking Neural Networks
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