Split learning (SL) has been recently proposed as a way to enable resource-constrained devices to train multi-parameter neural networks (NNs) and participate in federated learning (FL). In a nutshell, SL splits the NN model into parts, and allows clients (devices) to offload the largest part as a processing task to a computationally powerful helper. In parallel SL, multiple helpers can process model parts of one or more clients, thus, considerably reducing the maximum training time over all clients (makespan). In this paper, we focus on orchestrating the workflow of this operation, which is critical in highly heterogeneous systems, as our experiments show. In particular, we formulate the joint problem of client-helper assignments and scheduling decisions with the goal of minimizing the training makespan, and we prove that it is NPhard. We propose a solution method based on the decomposition of the problem by leveraging its inherent symmetry, and a second one that is fully scalable. A wealth of numerical evaluations using our testbed’s measurements allow us to build a solution strategy comprising these methods. Moreover, we show that this strategy finds a near-optimal solution, and achieves a shorter makespan than the baseline scheme by up to 52.3%.@en

We have imaged the current noise with atomic resolution in a Josephson scanning tunneling microscope with a Pb-Pb junction. By measuring the current noise as a function of applied bias, we reveal the change from single-electron tunneling above the superconducting gap energy to double-electron charge transfer below the gap energy when Andreev processes become dominant. Our spatially resolved noise maps show that this doubling occurs homogeneously on the surface, and also on impurity locations, demonstrating that indeed the charge pairing is not influenced by disruptions in the superconductor smaller than the superconducting coherence length.

@en