The training of deep and/or convolutional neural networks (DNNs/CNNs) is traditionally done on servers with powerful CPUs and GPUs. Recent efforts have emerged to localize machine learning tasks fully on the edge. This brings advantages in reduced latency and increased privacy, but necessitates working with resource-constrained devices. Approaches for inference and training in mobile and edge devices based on pruning, quantization or incremental and transfer learning require trading off accuracy. Several works have explored distributing inference operations on mobile and edge clusters instead. However, there is limited literature on distributed training on the edge. Existing approaches all require a central, potentially powerful edge or cloud server for coordination or offloading. In this paper, we describe an approach for distributed CNN training exclusively on mobile and edge devices. Our approach is beneficial for the initial CNN layers that are feature map dominated. It is based on partitioning forward inference and back-propagation operations among devices through tiling and fusing to maximize locality and expose communication and memory-aware parallelism. We also introduce the concept of layer grouping to further fine-tune performance based on computation and communication trade-off. Results show that for a cluster of 2-6 quad-core Raspberry Pi3 devices, training of an object-detection CNN provides a 2x-15x speedup with respect to a single core and up to 8x reduction in memory usage per device, all without sacrificing accuracy. Grouping offers up to 1.5x speedup depending on the reference profile and batch size.

Using information theoretic concepts to understand and explore the inner organization of deep neural networks (DNNs) remains a big challenge. Recently, the concept of an information plane began to shed light on the analysis of multilayer perceptrons (MLPs). We provided an in-depth insight into stacked autoencoders (SAEs) using a novel matrix-based Rényi's α-entropy functional, enabling for the first time the analysis of the dynamics of learning using information flow in real-world scenario involving complex network architecture and large data. Despite the great potential of these past works, there are several open questions when it comes to applying information theoretic concepts to understand convolutional neural networks (CNNs). These include for instance the accurate estimation of information quantities among multiple variables, and the many different training methodologies.