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Theory

Theory

The Start and Build sections describe the API. This section specifies what the library computes: the exact update equations, which index is zero, which direction the target shift points, and what is and is not centered. Each formula is cross-referenced with the code that implements it, so the implementation can be checked against your own derivations or a published result.

Each page is self-contained, equations cite their implementing code, and conventions are stated explicitly rather than assumed.

Page What it covers
Reservoir dynamics The leaky-ESN update, spectral radius scaling, the echo state property, bias and symmetry, the NG-RC feature map
Readout solvers The ridge objective, centered vs. uncentered normal equations, conjugate gradient on the Gram system, the dtype strategy
Timing conventions The one-step-ahead contract, the target shift, forecast index maps, driver alignment, statefulness across calls
Design of the library The package map, the cell/layer split, frozen weights as parameters, the hook-based trainer

See also

  • The mental model — a prose introduction to the concepts these equations formalize
  • Build — composing models from the layers these equations describe