New DC-TNN Network Splits Tensors into Core and Refinement for Better Predictions

Tensor data from neuroimaging, genomics, and climate science often loses multilinear structure when vectorized. Existing methods either impose a single low-rank structure (missing localized signals) or flatten tensors into vectors (discarding multiway geometry). To address this, Elynn Chen, Jiayu Li, Zheshi Zheng, and Jian Pei propose Dual-Channel Tensor Neural Network (DC-TNN). The architecture decomposes each input tensor into a low-rank core and a sparse refinement, then feeds both components through coupled neural channels. It is structure-agnostic, accommodating CP, Tucker, and tensor-train decompositions in one framework. The theoretical contribution includes non-asymptotic risk bounds that decompose into network approximation, core estimation, and refinement-selection terms—showing that effective dimension depends on core rank and refinement sparsity, not ambient tensor size.

For inference, the authors develop a structure-aware conformal ROC procedure that calibrates predictions within the core-refinement latent space and produces ROC curves and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, they propose what they call the first distribution-free procedure for choosing among candidate tensor decompositions with finite-sample validity—a conformal structure selector. Experiments on synthetic data and a real protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the true tensor structure. This work bridges deep learning with rigorous statistical guarantees for high-dimensional tensor data, offering a principled approach for applications where both prediction and trustworthy confidence intervals are critical.