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  1. Free, publicly-accessible full text available January 1, 2023
  2. Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulomore »folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance.« less
    Free, publicly-accessible full text available December 1, 2022
  3. Free, publicly-accessible full text available December 1, 2022
  4. Free, publicly-accessible full text available December 1, 2022
  5. Free, publicly-accessible full text available November 13, 2022
  6. In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality . In this paper, we build on recent algorithmic progresses in distributed deep learning to explore various consensus-optimality trade-offs over a fixed communication topology. First, we propose the incremental consensus -based distributed stochastic gradient descent (i-CDSGD) algorithm, which involves multiple consensus steps (where each agent communicates information with its neighbors) within each SGD iteration. Second, we propose the generalized consensus -based distributed SGD (g-CDSGD) algorithm that enables us to navigate the full spectrum from complete consensus (all agentsmore »agree) to complete disagreement (each agent converges to individual model parameters). We analytically establish convergence of the proposed algorithms for strongly convex and nonconvex objective functions; we also analyze the momentum variants of the algorithms for the strongly convex case. We support our algorithms via numerical experiments, and demonstrate significant improvements over existing methods for collaborative deep learning.« less
    Free, publicly-accessible full text available September 14, 2022