Invariant polynomials and machine learning

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We present an application of invariant polynomials in machine learning.

• Using the methods developed in previous work, we obtain two types of generators of the Lorentz- and permutation-invariant polynomials in particle momenta; minimal algebra generators and Hironaka decompositions.
• We discuss and prove some approximation theorems to make use of these invariant generators in machine learning algorithms in general and in neural networks specifically.
• By implementing these generators in neural networks applied to regression tasks, we test the improvements in performance under a wide range of hyperparameter choices and find a reduction of the loss on training data and a significant reduction of the loss on validation data.