Learning in Curved Weight Space:Exponential-Linear Weight Reparameterization for Improved Optimization
Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps. Adaptive optimizers such as Adam normalize updates per coordinate, but update steps remain additive; weights with very different magnitudes receive similarly sized absolute changes, producing very different relative perturbations. We introduce \textbf{\method} (\textbf{\methodshort}), a weight reparameterization for neural networks that combines a sign-aware symmetric-exponential pathway with an identity-like linear pathway. The symmetric-exponential pathway is near-linear for small raw w...
| Authors | Ethan Smith |
|---|---|
| Primary category | cs.LG |
| Published | 10 July 2026 |
| Last updated at source | 3 September 2026 |
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