text: It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.
  @cite_4: In this work we compute lower Lipschitz bounds of @math pooling operators for @math as well as @math pooling 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.
summary: As a consequence, the input of Parseval networks can be recovered if but only if the built-in non-linearities are invertible as well, which is typically not the case. @cite_4 derive conditions under which pooling representations are, but our method directly overcomes this issue. The Scattering transform is an example of predefined deep representation, approximately invariant to translations, that can be reconstructed when the degree of invariance specified is small. Yet, it requires a gradient descent optimization and no guarantee of convergences are known. In summary, the references make clear that invertibility requires special care in designing the architecture or special care in designing the optimization procedure. In this paper, we introduce a network, that overcomes these issues and has an exact inverse by construction.