User guide¶
These pages explain the concepts behind the library and the choices that the API reference does not spell out. Start with How the library fits together, the map of the package; the other pages can be read in any order.
The three levels (functions, layers, models), the shapes flowing through a network, and the conventions: float64, two gradient paths, parametrizations.
BiMap, ReEig, LogEig and their equations; static vs dynamic parametrization of the orthonormal and SPD parameters.
Which model to use, the constructor arguments grouped by role, and the configurations of published experiments.
The Riemannian geometries on the SPD manifold, their means and dispersions, and how to pick one.
How the SPD batch normalization layers centre, rescale and re-bias a batch, and their training/evaluation behaviour.
RResNet residual blocks: spectral vector field, affine-invariant (unit step) or log-Euclidean exponential map.
Daleckii–Krein backwards, Sylvester equations, means as iterations, implicit differentiation, parametrizations, batch normalization and residual-step mechanics, precision — with their equations.