Continuing on Nonlinear Compressive Sensing and related matter, we mentioned it recently in Some thoughts on invertibility: Signal recovery from Pooling Representations, Determination of Nonlinear Genetic Architecture using Compressed Sensing but today we have an implementation of the algorithm featured in that important. Arthur actually made good on his promise :-). Thanks Arthur! Here is the paper: Signal Recovery from Pooling Representations by Joan Bruna, Arthur Szlam, Yann LeCun

In this work we compute lower Lipschitz bounds of ℓp pooling operators for p=1,2,∞ as well as ℓppooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

The code is on Arthur Szlam's publication page

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