Layerwise LQR for Geometry-Aware Optimization of Deep Networks
Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often discarding cross-layer interactions induced by the network computation. We introduce Layerwise LQR (LLQR), a framework for learning structured inverse preconditioners under a global layerwise optimal-control objective. The starting point is an exact equivalence: the steepest-descent step under a broad class of divergence-induced quadratic models--including Newton, Gauss-Newton, Fisher/natural-gradient, and intermediate-layer metrics--can be written as a finite...
| Authors | Simon Dufort-Labbé, Pierre-Luc Bacon, Razvan Pascanu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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