Sharp Approximation Rates for Neural Networks with Affine Latent Parameterizations

Original description

Many parameter-efficient methods generate the parameters of a large neural network from a low-dimensional latent representation. Given an architecture $Φ$ with $P_Φ$ parameter slots, we write $\boldsymbolθ_f=\mathcal{G}(\boldsymbolξ_f)$, where $\mathcal{G}\colon\mathbb{R}^M\to\mathbb{R}^{P_Φ}$ is a parameter generator and $\boldsymbolξ_f\in\mathbb{R}^M$ is a latent representation of the target function $f$. The architecture $Φ$ and the generator $\mathcal{G}$ are shared across the entire target class, while each target $f$ is represented by its own latent vector $\boldsymbolξ_f$, with $Φ_{\mat...