CSNNs: Unsupervised, Backpropagationfree Convolutional Neural Networks for Representation Learning. This work combines Convolutional Neural Networks (CNNs), clustering via SelfOrganizing Maps (SOMs) and Hebbian Learning to propose the building blocks of Convolutional SelfOrganizing Neural Networks (CSNNs), which learn representations in an unsupervised and Backpropagationfree manner. Our approach replaces the learning of traditional convolutional layers from CNNs with the competitive learning procedure of SOMs and simultaneously learns local masks between those layers with separate Hebbianlike learning rules to overcome the problem of disentangling factors of variation when filters are learned through clustering. We investigate the learned representation by designing two simple models with our building blocks, achieving comparable performance to many methods which use Backpropagation, while we reach comparable performance on Cifar10 and give baseline performances on Cifar100, Tiny ImageNet and a small subset of ImageNet for Backpropagationfree methods.

Variations on the Convolutional Sparse Coding Model Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and highdimensional signals by local, patchbased, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same   ell _1  ell _2   problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.