Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks
A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable. We build DDC, a Dead-Direction Conditioner that lifts a base optimizer into a $G$-equivariant one: it conditions the optimizer's state in the orbit decomposition of a $G$-invariant metric, so the trajectory stays a preconditioned gradient flow on the quotient $\barΘ= Θ/G$. The construction carries four arch...
| Authors | Tejas Pradeep Shirodkar |
|---|---|
| Primary category | cs.LG |
| Published | 28 June 2026 |
| Last updated at source | 28 June 2026 |
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