Deep Tree Tensor Networks

Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful application in natural image recognition. When employed, they primarily serve to compress parameters within pre-existing networks, thereby losing their distinctive capability to capture exponential-order feature interactions. This paper introduces a novel architecture named Deep Tree Tensor Network (DTTN), which captures 2L-order multiplicative interactions across features through multilinear operations, while essentially unfolding into a tree-like TN topology with the parameter-sharing property. DTTN is stacked with multiple antisymmetric interaction modules (AIMs), and this design facilitates efficient implementation. Furthermore, our theoretical analysis demonstrates the equivalence between quantum-inspired TN models and polynomial/multilinear networks under specific conditions.