4 papers
Structured Preconditioning in Affine-Invariant Geometry: Projection, Certificates, and Kronecker Separation
Zavier Li
Nearest structured approximation and best structured preconditioning solve different matrix optimization problems. We determine their exact relation for Kronecker positive-definite…
Restricted Dynamic Geometric Complexity: Path-Space Reduction and Möbius--Jacobi Response
Zavier Li
Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to…
Optimization Geometrodynamics: Variational Reduction and Interaction Curvature
Zavier Li
Adaptive optimizers carry hidden states that change how visible gradients become parameter motion. We develop optimization geometrodynamics as a variational theory of this hidden g…
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions
Zavier Li
Optimizer experiments observe responses to algorithmic configurations without uniquely revealing hidden mechanisms. We develop a causal optimizer interaction calculus that separate…