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Inverting Deep Generative models, One layer at a time
Qi Lei · Ajil Jalal · Inderjit Dhillon · Alex Dimakis

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #48

We study the problem of inverting a deep generative model with ReLU activations. Inversion corresponds to finding a latent code vector that explains observed measurements as much as possible. In most prior works this is performed by attempting to solve a non-convex optimization problem involving the generator. In this paper we obtain several novel theoretical results for the inversion problem.

We show that for the realizable case, single layer inversion can be performed exactly in polynomial time, by solving a linear program. Further, we show that for two layers, inversion is NP-hard to recover binary latent code (even for the realizable case) and the pre-image set can be non-convex.

For generative models of arbitrary depth, we show that exact recovery is possible in polynomial time with high probability, if the layers are expanding and the weights are randomly selected. Very recent work analyzed the same problem for gradient descent inversion. Their analysis requires significantly higher expansion (logarithmic in the latent dimension) while our proposed algorithm can provably reconstruct even with constant factor expansion. We also provide provable error bounds for different norms for reconstructing noisy observations. Our empirical validation demonstrates that we obtain better reconstructions when the latent dimension is large.

Author Information

Qi Lei (University of Texas at Austin)
Ajil Jalal (University of Texas at Austin)
Inderjit Dhillon (UT Austin & Amazon)
Alex Dimakis (University of Texas, Austin)

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