IdentityRegularizer

class t3toolbox.backend.regularization.IdentityRegularizer

Bases: Regularizer

Identity (Tikhonov) regularization ρ(X) = ½·strength·‖X‖² in the geometry’s own tangent metric.

On the manifold this is the Hilbert-Schmidt ridge ½λ‖X‖²_HS – H_R = λ·Π (= λp on a gauged tangent), which is the exact Riemannian Hessian (∇ρ = X is fully tangent, so the curvature term vanishes). On corewise it is core weight-decay ½λ Σ‖core_i‖², which also makes the gauge-singular corewise Gauss-Newton Hessian strictly positive-definite – a better-conditioned Newton system (though CG already converges on the singular H since the gradient g = 𝒥ᵀr lies in range(H)). X_ref = 0. The point_tangent = v_X construction (the attachment point as a single gauged tangent term) is in dev/regularization_design.md §4.

strength: float

Methods

value(geom, x_cores)
gradient(geom, frame)
hessian(geom, frame, p)
quadratic(geom, frame, p)