One key question when using an abstraction framework is how close its performance comes to the "native", i.e. architecture-specific programming models. In our case, we compared the performance of our batched least-squares-regression algorithm (for ℓ0 regularization) to a native CUDA implementation co-developed with Nvidia engineers. This new CUDA code is about twice as fast as the Kokkos version. However, it is worth noting that Kokkos' continuous development is promising. For instance, during our development, transitioning from Kokkos version 3 to version 4 resulted in a 10% speedup without requiring any code modifications from us in the application code.