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math.OC2026
Backpropagation from KL Projections: Differential and Exact I-Projection Correspondences
Manish Krishan Lal
We establish two correspondences between reverse-mode automatic differentiation (backpropagation at a given forward-pass point) and compositions of projection maps in Kullback--Lei…
math.OC2025
The Flow-Limit of Reflect-Reflect-Relax: Existence, Stability, and Discrete-Time Behavior
Manish Krishan Lal
We study the Reflect-Reflect-Relax (RRR) algorithm in its small-step (flow-limit) regime. In the smooth transversal setting, we show that the transverse dynamics form a hyperbolic…
math.OC2024
Projecting onto rectangular hyperbolic paraboloids in Hilbert space
Heinz H. Bauschke, Manish Krishan Lal, Xianfu Wang
In , a hyperbolic paraboloid is a classical saddle-shaped quadric surface. Recently, Elser has modeled problems arising in Deep Learning using rectangular hyperbolic…