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We revisit two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), with multiple local updates. We consider two settings and demonstrate that incorporating $K > 1$ local update steps can reduce communication complexity. Specifically, for $\mu$-strongly convex and $L$-smooth loss functions, we proved that local DGT achieves communication complexity $\tilde{\mathcal{O}} \Big(\frac{L}{\mu K} + \frac{\delta}{\mu (1 - \rho)} + \frac{\rho }{(1 - \rho)^2} \cdot \frac{L+ \delta}{\mu}\Big)$, where $\rho$ measures the network connectivity and $\delta$ measures the second-order heterogeneity of the local loss. Our result reveals the tradeoff between communication and computation and shows increasing $K$ can effectively reduce communication costs when the data heterogeneity is low and the network is well-connected. We then consider the over-parameterization regime where the local losses share the same minimums, we proved that employing local updates in DGD, even without gradient correction, can yield a similar effect as DGT in reducing communication complexity. Numerical experiments validate our theoretical results.

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Defect detection plays a crucial role in infrared non-destructive testing systems, offering non-contact, safe, and efficient inspection capabilities. However, challenges such as low resolution, high noise, and uneven heating in infrared thermal images hinder comprehensive and accurate defect detection. In this study, we propose DefectSAM, a novel approach for segmenting defects on highly noisy thermal images based on the widely adopted model, Segment Anything (SAM)\cite{kirillov2023segany}. Harnessing the power of a meticulously curated dataset generated through labor-intensive lab experiments and valuable prompts from experienced experts, DefectSAM surpasses existing state-of-the-art segmentation algorithms and achieves significant improvements in defect detection rates. Notably, DefectSAM excels in detecting weaker and smaller defects on complex and irregular surfaces, reducing the occurrence of missed detections and providing more accurate defect size estimations. Experimental studies conducted on various materials have validated the effectiveness of our solutions in defect detection, which hold significant potential to expedite the evolution of defect detection tools, enabling enhanced inspection capabilities and accuracy in defect identification.

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