PLUGIn: A simple algorithm for inverting generative models with recovery guarantees

We consider the problem of recovering an unknown latent code vector under a known generative model. We introduce a simple novel algorithm, Partially Linearized Update for Generative Inversion (PLUGIn), to estimate x (and thus \mathcal{G}(x)). We prove that, when weights are Gaussian and layer widths n_i \gtrsim 5 i n_0 (up to log factors), the algorithm converges geometrically to a neighbourhood of x with high probability. Note the inequality on layer widths allows n_i n_{i 1} when i\geq 1 . To our knowledge, this is the first such result for networks with some contractive layers.