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We demonstrate the application of recent theoretical results on the stability of linear threshold (LT) networks to the competitive layer model architecture (CLM). LT networks can be efficiently built in silicon and exhibit the interesting behavior of coexistence of digital selection and analogue amplification in a single circuit. The CLM provides a large-scale network based on LT units, which was successfully applied to complex perceptual grouping tasks. We show that recent results on LT networks can be employed to operate the CLM with maximal recurrence close to its stability limits, causing strong contextual integration and improved grouping quality.