# T-Net: Parametrizing Fully Convolutional Nets with a Single High-Order Tensor

arXiv: https://arxiv.org/abs/1904.02698 · HTML: https://mlsanity.com/paper/1904.02698/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 22 of 22)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Tesseract: Tensorised Actors for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2106.00136/) (2021)
- [Reusing Pretrained Models by Multi-linear Operators for Efficient Training](https://mlsanity.com/paper/2310.10699/) (2023)
- [Geometry-aware training of factorized layers in tensor Tucker format](https://mlsanity.com/paper/2305.19059/) (2023)
- [ELRT: Efficient Low-Rank Training for Compact Convolutional Neural Networks](https://mlsanity.com/paper/2401.10341/) (2024)
- [Model based Multi-agent Reinforcement Learning with Tensor Decompositions](https://mlsanity.com/paper/2110.14524/) (2021)
- [TT-NF: Tensor Train Neural Fields](https://mlsanity.com/paper/2209.15529/) (2022)
- [Reinforcement Learning in Factored Action Spaces using Tensor Decompositions](https://mlsanity.com/paper/2110.14538/) (2021)
- [Update Compression for Deep Neural Networks on the Edge](https://mlsanity.com/paper/2203.04516/) (2022)
- [Quantization Aware Factorization for Deep Neural Network Compression](https://mlsanity.com/paper/2308.04595/) (2023)
- [Semi-tensor Product-based TensorDecomposition for Neural Network Compression](https://mlsanity.com/paper/2109.15200/) (2021)
- [Multi-task Swin Transformer for Motion Artifacts Classification and Cardiac Magnetic Resonance Image Segmentation](https://mlsanity.com/paper/2209.02470/) (2022)
- [How Informative is the Approximation Error from Tensor Decomposition for Neural Network Compression?](https://mlsanity.com/paper/2305.05318/) (2023)
- [Defensive Tensorization](https://mlsanity.com/paper/2110.13859/) (2021)
- [STN: Scalable Tensorizing Networks via Structure-Aware Training and Adaptive Compression](https://mlsanity.com/paper/2205.15198/) (2022)
- [Long Sequence Modeling with Attention Tensorization: From Sequence to Tensor Learning](https://mlsanity.com/paper/2410.20926/) (2024)
- [BackSlash: Rate Constrained Optimized Training of Large Language Models](https://mlsanity.com/paper/2504.16968/) (2025)
- [QR-LoRA: QR-Based Low-Rank Adaptation for Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2508.21810/) (2025)
- [Convolutional Neural Network Compression via Dynamic Parameter Rank Pruning](https://mlsanity.com/paper/2401.08014/) (2024)
- [Explaining Anomalies with Tensor Networks](https://mlsanity.com/paper/2505.03911/) (2025)
- [Data Understanding Survey: Pursuing Improved Dataset Characterization Via Tensor-based Methods](https://mlsanity.com/paper/2510.14161/) (2025)

## Abstract (arXiv)

Recent findings indicate that over-parametrization, while crucial for successfully training deep neural networks, also introduces large amounts of redundancy. Tensor methods have the potential to efficiently parametrize over-complete representations by leveraging this redundancy. In this paper, we propose to fully parametrize Convolutional Neural Networks (CNNs) with a single high-order, low-rank tensor. Previous works on network tensorization have focused on parametrizing individual layers (convolutional or fully connected) only, and perform the tensorization layer-by-layer separately. In contrast, we propose to jointly capture the full structure of a neural network by parametrizing it with a single high-order tensor, the modes of which represent each of the architectural design parameters of the network (e.g. number of convolutional blocks, depth, number of stacks, input features, etc). This parametrization allows to regularize the whole network and drastically reduce the number of parameters. Our model is end-to-end trainable and the low-rank structure imposed on the weight tensor acts as an implicit regularization. We study the case of networks with rich structure, namely Fully Convolutional Networks (FCNs), which we propose to parametrize with a single 8th-order tensor. We show that our approach can achieve superior performance with small compression rates, and attain high compression rates with negligible drop in accuracy for the challenging task of human pose estimation.