Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

The paper presents a formal analysis of the quotient geometry of tree tensor networks (TTNs) and introduces efficient first- and second-order optimization algorithms that leverage this geometry. It also develops a backpropagation method for training TTNs in a kernel learning context. Numerical experiments on a digit classification task demonstrate a tradeoff between two horizontal distributions: one provides clearer geometric insights, while the other yields more efficient algorithms.

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