Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is always tractable. Those properties follow from some conditions (i.e., completeness and decomposability) that must be respected by the structure of the network. As a result, it is not easy to specify a valid sum-product network by hand and therefore structure learning techniques are typically used in practice. This paper describes the first online structure learning technique for continuous SPNs with Gaussian leaves. We also introduce an accompanying new parameter learning technique.
Integrated metrology in the lithography cluster is a promising solution to tighten process control. It is shown that optical CD metrology using YieldStar, an angular resolved scatterometer, meets all requirements in terms of precision, process robustness, throughput and matching to CD-SEM, the current tool-of-reference. The same metrology tool supports also diffraction-based overlay metrology. Using an appropriate sampling plan and the full scanner correction capabilities, overlay control can be improved. The throughput of the integrated tool is sufficient to support high volume sampling plans for combined CD and overlay monitoring and control, with 100% lot coverage.
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