Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection

• URL: http://arxiv.org/abs/2605.19122v1
• Date: Mon, 18 May 2026 21:16:37 GMT
• Title: Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection
• Abstract summary: We propose a *Dual-Channel Neural Network* (DC-TNN) that decomposes each tensor into a low-rank core and a sparse, and processes the two neural channels.<n>For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms.<n>For inference, we develop a *linear-aware ROC* procedure that calibrates within the core-refinement latent space and produces AUC and AUC confidence bands with finite-, distribution-free coverage.
• Score: 6.699424706776662
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a *Dual-Channel Tensor Neural Network* (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a *structure-aware conformal ROC* procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a *conformal structure selector* that, to our knowledge, is the *first distribution-free procedure* for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

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