Multi-socket machines with 1-100 TBs of physical memory are becoming prevalent. Applications running on multi-socket machines suffer non-uniform bandwidth and latency when accessing physical memory. Decades of research have focused on data allocation and placement policies in NUMA settings, but there have been no studies on the question of how to place page-tables amongst sockets. We make the case for explicit page-table allocation policies and show that pagetable placement is becoming crucial to overall performance.We propose Mitosis to mitigate NUMA effects on page-table walks by transparently replicating and migrating page-tables across sockets without application changes. This reduces the frequency of accesses to remote NUMA nodes when performing page-table walks. Mitosis uses two components: (i) a mechanism to enable efficient page-table replication and migration; and (ii) policies for processes to efficiently manage and control page-table replication and migration.We implement Mitosis in Linux and evaluate its benefits on real hardware. Mitosis improves performance for large-scale multi-socket workloads by up to 1.34x by replicating pagetables across sockets. Moreover, it improves performance by up to 3.24x in cases when the OS migrates a process across sockets by enabling cross-socket page-table migration.

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Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and despite steady effort since the 1960's, breakthroughs have been made on the problem only within the past few years, primarily on the problem of finding optimal sparse decision trees. However, current state-of-the-art algorithms often require impractical amounts of computation time and memory to find optimal or near-optimal trees for some real-world datasets, particularly those having several continuous-valued features. Given that the search spaces of these decision tree optimization problems are massive, can we practically hope to find a sparse decision tree that competes in accuracy with a black box machine learning model? We address this problem via smart guessing strategies that can be applied to any optimal branch-and-bound-based decision tree algorithm. The guesses come from knowledge gleaned from black box models. We show that by using these guesses, we can reduce the run time by multiple orders of magnitude while providing bounds on how far the resulting trees can deviate from the black box's accuracy and expressive power. Our approach enables guesses about how to bin continuous features, the size of the tree, and lower bounds on the error for the optimal decision tree. Our experiments show that in many cases we can rapidly construct sparse decision trees that match the accuracy of black box models. To summarize: when you are having trouble optimizing, just guess.