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

arXiv: https://arxiv.org/abs/2605.19122 · HTML: https://mlsanity.com/paper/2605.19122/

## 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.

## Builds on (most cited first, 30 of 41)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization](https://mlsanity.com/paper/2103.08895/) (2021)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-1 Updates](https://mlsanity.com/paper/1402.5180/) (2014)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [Provable Sparse Tensor Decomposition](https://mlsanity.com/paper/1502.01425/) (2015)
- [Constrained Factor Models for High-Dimensional Matrix-Variate Time Series](https://mlsanity.com/paper/1710.06075/) (2017)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [Sparse and Low-rank Tensor Estimation via Cubic Sketchings](https://mlsanity.com/paper/1801.09326/) (2018)
- [Tensor Regression Using Low-rank and Sparse Tucker Decompositions](https://mlsanity.com/paper/1911.03725/) (2019)
- [Statistical Inference for High-Dimensional Matrix-Variate Factor Model](https://mlsanity.com/paper/2001.01890/) (2020)
- [Boosted Sparse and Low-Rank Tensor Regression](https://mlsanity.com/paper/1811.01158/) (2018)
- [Semi-parametric TEnsor Factor Analysis by Iteratively Projected Singular Value Decomposition](https://mlsanity.com/paper/2007.02404/) (2020)
- [Modeling Dynamic Transport Network with Matrix Factor Models: with an Application to International Trade Flow](https://mlsanity.com/paper/1901.00769/) (2019)
- [Modeling Multivariate Spatial-Temporal Data with Latent Low-Dimensional Dynamics](https://mlsanity.com/paper/2002.01305/) (2020)
- [Factor Augmented Matrix Regression](https://mlsanity.com/paper/2405.17744/) (2024)
- [High-Dimensional Tensor Classification with CP Low-Rank Discriminant Structure](https://mlsanity.com/paper/2409.14397/) (2024)
- [High-Dimensional Tensor Discriminant Analysis with Incomplete Tensors](https://mlsanity.com/paper/2410.14783/) (2024)
- [Time-Varying Matrix Factor Models](https://mlsanity.com/paper/2404.01546/) (2024)
- [Conditional Prediction ROC Bands for Graph Classification](https://mlsanity.com/paper/2410.15239/) (2024)

## 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.