We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use knownsymmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use knownsymmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use known symmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.

CatBoost is a popular machine learning library. CatBoost models are based on oblivious decision trees, making training and evaluation rapid. CatBoost has many applications, and some require low latency and high throughput evaluation. This paper investigates the possibilities for improving CatBoost's performance in single-core CPU computations. We explore the new features provided by the AVX instruction sets to optimize evaluation. We increase performance by 20-40% using AVX2 instructions without quality impact. We also introduce a new trade-off between speed and quality. Using float16 for leaf values and AVX-512 instructions, we achieve 50-70% speed-up.