We give a 3-universal property for the Karoubi envelope of 2-category. Using this, we show that 3-categories finite semisimple 2-categories (as introduced in arXiv:1812.11933) and multifusion categories are equivalent.

In computer image processing, traditional object classification methods focus on visual objects such as cars, dogs, and airplanes. However, these objects are not easy to scale, require extensive training for all classes, and are susceptible to unseen object classification failure. Recently, a new object classification approach called attribute-based object classification has been introduced by ...

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores...

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to number evaluations. An analogous nonsmooth is challenging. Even when objective smooth at every iterate, corresponding local models unstable, and cutting planes invoked by traditional remedies difficult bound, leading guarantees sublinear cumulative We instead propose a...