We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that
end, we first establish a global bound for the Lipschitz constant of neural networks. Based on the obtained bound, we then formulate a variational problem for learning activation functions. Our variational problem is infinite-dimensional and is not computationally tractable. However, we prove that there always exists a solution that has continuous and piecewise-linear (linear-spline) activations. This reduces the original problem to a finite-dimensional minimization where an l1 penalty on the parameters of the activations favors the learning of sparse nonlinearities. We numerically compare our scheme with standard ReLU network and its variations, PReLU and LeakyReLU and we empirically demonstrate the practical aspects of our framework.
The field of neural image compression has witnessed exciting progress as recently proposed architectures already surpass the established transform coding based approaches. While, so far, research has mainly focused on architecture and model improveme
nts, in this work we explore content adaptive optimization. To this end, we introduce an iterative procedure which adapts the latent representation to the specific content we wish to compress while keeping the parameters of the network and the predictive model fixed. Our experiments show that this allows for an overall increase in rate-distortion performance, independently of the specific architecture used. Furthermore, we also evaluate this strategy in the context of adapting a pretrained network to other content that is different in visual appearance or resolution. Here, our experiments show that our adaptation strategy can largely close the gap as compared to models specifically trained for the given content while having the benefit that no additional data in the form of model parameter updates has to be transmitted.
