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 algorithm converges inexactly when applied to model training on non-ideal devices. This paper puts forth a theoretical foundation for gradient-based training on analog devices. We begin by characterizing the non-convergent issue of SGD%2C which is caused by the asymmetric updates on the analog devices. We then provide a lower bound of the asymptotic error to show that there is a fundamental performance limit of SGD-based analog training rather than an artifact of our analysis. To address this issue%2C we study a heuristic analog algorithm called Tiki-Taka that has recently exhibited superior empirical performance compared to SGD and rigorously show its ability to exactly converge to a critical point and hence eliminates the asymptotic error. The simulations verify the correctness of the analyses.?quality=80&w=800)
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