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Optimization problems with group sparse regularization are ubiquitous in various popular downstream applications, such as feature selection and compression for Deep Neural Networks (DNNs). Nonetheless, the existing methods in the literature do not perform particularly well when such regularization is used in combination with a stochastic loss function. In particular, it is challenging to design a computationally efficient algorithm with a convergence guarantee and can compute group-sparse solutions. Recently, a half-space stochastic projected gradient ({\tt HSPG}) method was proposed that partly addressed these challenges. This paper presents a substantially enhanced version of {\tt HSPG} that we call~{\tt AdaHSPG+} that makes two noticeable advances. First, {\tt AdaHSPG+} is shown to have a stronger convergence result under significantly looser assumptions than those required by {\tt HSPG}. This improvement in convergence is achieved by integrating variance reduction techniques with a new adaptive strategy for iteratively predicting the support of a solution. Second, {\tt AdaHSPG+} requires significantly less parameter tuning compared to {\tt HSPG}, thus making it more practical and user-friendly. This advance is achieved by designing automatic and adaptive strategies for choosing the type of step employed at each iteration and for updating key hyperparameters. The numerical effectiveness of our proposed {\tt AdaHSPG+} algorithm is demonstrated on both convex and non-convex benchmark problems. The source code is available at \url{https://github.com/tianyic/adahspg}. 

Abstract Following significant advances in image acquisition, synapse detection, and neuronal segmentation in connectomics, researchers have extracted an increasingly diverse set of wiring diagrams from brain tissue. Neuroscientists frequently represent these wiring diagrams as graphs with nodes corresponding to a single neuron and edges indicating synaptic connectivity. The edges can contain “colors” or “labels”, indicating excitatory versus inhibitory connections, among other things. By representing the wiring diagram as a graph, we can begin to identify motifs, the frequently occurring subgraphs that correspond to specific biological functions. Most analyses on these wiring diagrams have focused on hypothesized motifs—those we expect to find. However, one of the goals of connectomics is to identify biologically-significant motifs that we did not previously hypothesize. To identify these structures, we need large-scale subgraph enumeration to find the frequencies of all unique motifs. Exact subgraph enumeration is a computationally expensive task, particularly in the edge-dense wiring diagrams. Furthermore, most existing methods do not differentiate between types of edges which can significantly affect the function of a motif. We propose a parallel, general-purpose subgraph enumeration strategy to count motifs in the connectome. Next, we introduce a divide-and-conquer community-based subgraph enumeration strategy that allows for enumeration per brain region. Lastly, we allow for differentiation of edges by types to better reflect the underlying biological properties of the graph. We demonstrate our results on eleven connectomes and publish for future analyses extensive overviews for the 26 trillion subgraphs enumerated that required approximately 9.25 years of computation time. 

This work presents a stable and reliable turnkey continuous-wave laser system for a Yb/Ba multi-species trapped-ion quantum computer. The compact and rack-mountable optics system exhibits high robustness, operating over a year without realignment, regardless of temperature changes in the laboratory. The overall optical system is divided into a few isolated modules interconnected by optical fibers for easy maintenance. The light sources are frequency-stabilized by comparing their frequency with two complementary references, a commercial Fizeau wavelength meter and a high-finesse optical cavity. This scheme enables automatic frequency-stabilization for days with a sub-MHz precision.