Tutorials
Neuroscience
Mean Field Approximation
Explore the relationship between neural mean field methods and variational inference through interactive POMDP and binary-neuron demonstrations.
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AdEx Mean Field (Zerlaut)
Move from adaptive exponential neurons and transfer functions to semi-analytical mean field models and whole-brain dynamics.
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Wilson-Cowan Tutorial
Develop the mathematical progression from binary neurons through Wilson-Cowan dynamics to stochastic criticality.
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Neural Criticality Tutorial
Learn phase transitions, E/I balance, avalanches, power laws, Gillespie simulation, and scaling relations.
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Wilson-Cowan with Co-Transmission
Compare mono-transmitting and co-transmitting Wilson-Cowan networks and their effects on neural criticality.
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The Widom Line: Quasi-Criticality and Robustness
Build susceptibility from perturbations, trace response maxima into a non-equilibrium Widom line, and connect the ridge to Fisher geometry.
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Measuring Criticality Robustness
Quantify critical-window robustness with parameter perturbations and finite-size scaling.
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Probability Theory
Probability Theory: Expectation to Cumulants
A first-principles guide to random variables, expectations, variance, signal-to-noise ratios, moments, generating functions, and cumulants.
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From Binomial to Dirichlet
Build the mathematics of learning from Bernoulli trials and conjugate priors through Beta, Gamma, and Dirichlet distributions.
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Information Theory
From Information Theory to Information Geometry
Follow excess bits through KL divergence, Fisher information, statistical manifolds, geodesics, and dual probability geometry.
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Scale-Free Active Inference
Study POMDPs, variational free energy, Dirichlet learning, coarse-graining, renormalization, and hierarchical planning across scales.
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