# Property Inheritance for Subtensors in Tensor Train Decompositions

arXiv: https://arxiv.org/abs/2504.11396 · HTML: https://mlsanity.com/paper/2504.11396/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework](https://mlsanity.com/paper/2107.12422/) (2021)
- [Robust CUR Decomposition: Theory and Imaging Applications](https://mlsanity.com/paper/2101.05231/) (2021)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions](https://mlsanity.com/paper/2103.11037/) (2021)
- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition](https://mlsanity.com/paper/2108.10448/) (2021)
- [Sparseness-constrained Nonnegative Tensor Factorization for Detecting Topics at Different Time Scales](https://mlsanity.com/paper/2010.01600/) (2020)
- [Guaranteed Sampling Flexibility for Low-tubal-rank Tensor Completion](https://mlsanity.com/paper/2406.11092/) (2024)
- [Correlating Time Series with Interpretable Convolutional Kernels](https://mlsanity.com/paper/2409.01362/) (2024)
- [Three-dimensional signal processing: a new approach in dynamical sampling via tensor products](https://mlsanity.com/paper/2502.02684/) (2025)
- [Non-convex approaches for low-rank tensor completion under tubal sampling](https://mlsanity.com/paper/2303.12721/) (2023)
- [Coseparable Nonnegative Tensor Factorization With T-CUR Decomposition](https://mlsanity.com/paper/2401.16836/) (2024)

## Abstract (arXiv)

Tensor dimensionality reduction is one of the fundamental tools for modern data science. To address the high computational overhead, fiber-wise sampled subtensors that preserve the original tensor rank are often used in designing efficient and scalable tensor dimensionality reduction. However, the theory of property inheritance for subtensors is still underdevelopment, that is, how the essential properties of the original tensor will be passed to its subtensors. This paper theoretically studies the property inheritance of the two key tensor properties, namely incoherence and condition number, under the tensor train setting. We also show how tensor train rank is preserved through fiber-wise sampling. The key parameters introduced in theorems are numerically evaluated under various settings. The results show that the properties of interest can be well preserved to the subtensors formed via fiber-wise sampling. Overall, this paper provides several handy analytic tools for developing efficient tensor analysis methods.