# Tensor-on-tensor Regression Neural Networks for Process Modeling with High-dimensional Data

arXiv: https://arxiv.org/abs/2510.05329 · HTML: https://mlsanity.com/paper/2510.05329/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 51 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [A novel approach for fusion of heterogeneous sources of data](https://mlsanity.com/paper/1803.00138/) (2018)
- [Structured Point Cloud Data Analysis via Regularized Tensor Regression for Process Modeling and Optimization](https://mlsanity.com/paper/1807.10278/) (2018)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Tensor Decomposition via Variational Auto-Encoder](https://mlsanity.com/paper/1611.00866/) (2016)

## Built on by (most cited first, 2 of 2)

- [Low-Rank and Structured Sparse Tensor Decomposition for Anomaly Detection in Multivariate Functional Data](https://mlsanity.com/paper/2610.06930/) (2026)
- [A Data-Driven Framework for Unsupervised Monitoring of Transmission Systems Using End-of-Line Testing Data: A Case Study at Ford Motor Company](https://mlsanity.com/paper/2610.06980/) (2026)

## Abstract (arXiv)

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression models that preserve tensor geometry, yet remain expressive enough to capture the pronounced nonlinear interactions that dominate many industrial and mechanical processes. Existing tensor-based regressors meet the first requirement but remain essentially linear. Conversely, conventional neural networks offer nonlinearity only after flattening, thereby discarding spatial structure and incurring prohibitive parameter counts. This paper introduces a Tensor-on-Tensor Regression Neural Network (TRNN) that unifies these two paradigms.