mlsanityData to 14 Oct 2026

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

arXiv 2605.19122 ↗First posted 18 May 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 41 of its 57 references that are in the map. First posted on arXiv 18 May 2026.

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References · 41

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29 more
  1. 2014Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-1 Updatescited by 21
  2. 2015Bayesian Tensor Regressioncited by 21
  3. 2015Parsimonious Tensor Response Regressioncited by 20
  4. 2015Provable Sparse Tensor Decompositioncited by 16
  5. 2017Constrained Factor Models for High-Dimensional Matrix-Variate Time Seriescited by 13
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  9. 2020Statistical Inference for High-Dimensional Matrix-Variate Factor Modelcited by 10
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  26. 2025Statistical Inference for Low-Rank Tensor Modelscited by 1
  27. 2025Bridging Domain Adaptation and Graph Neural Networks: A Tensor-Based Framework for Effective Label Propagationcited by 1
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  29. 2025High-Dimensional Tensor Discriminant Analysis: Low-Rank Discriminant Structure, Representation Synergy, and Theoretical Guaranteescited by 1

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