Deep Tree Tensor Networks for Image Recognition

Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful application in natural image processing. When employed, they primarily serve to compress parameters within off-the-shelf networks, thus losing their distinctive capability to enhance exponential-order feature interactions. This paper introduces a novel architecture named \textit{\textbf{D}eep \textbf{T}ree \textbf{T}ensor \textbf{N}etwork} (DTTN), which captures $2^L$-order multiplicative interactions across features through multilinear operations, while essentially unfolding into a \emph{tree}-like TN topology with the parameter-sharing property. DTTN is stacked with multiple antisymmetric interacting modules (AIMs), and this design facilitates efficient implementation. Moreover, we theoretically reveal the equivalency among quantum-inspired TN models and polynomial and multilinear networks under certain conditions, and we believe that DTTN can inspire more interpretable studies in this field. We evaluate the proposed model against a series of benchmarks and achieve excellent performance compared to its peers and cutting-edge architectures. Our code will soon be publicly available.