# TensLoRA: Tensor Alternatives for Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2509.19391 · HTML: https://mlsanity.com/paper/2509.19391/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [FacT: Factor-Tuning for Lightweight Adaptation on Vision Transformer](https://mlsanity.com/paper/2212.03145/) (2022)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [LoTR: Low Tensor Rank Weight Adaptation](https://mlsanity.com/paper/2402.01376/) (2024)
- [A Novel Benchmark for Few-Shot Semantic Segmentation in the Era of Foundation Models](https://mlsanity.com/paper/2401.11311/) (2024)
- [LoRTA: Low Rank Tensor Adaptation of Large Language Models](https://mlsanity.com/paper/2410.04060/) (2024)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) is widely used to efficiently adapt Transformers by adding trainable low-rank matrices to attention projections. While effective, these matrices are considered independent for each attention projection (Query, Key, and Value) and each layer. Recent extensions have considered joint, tensor-based adaptations, but only in limited forms and without a systematic framework. We introduce TensLoRA, a unified framework that aggregates LoRA updates into higher-order tensors and models a broad family of tensor-based low-rank adaptations. Our formulation generalizes existing tensor-based methods and enables mode-specific compression rates, allowing parameter budgets to be tailored according to the modality and task. Experiments on vision and language benchmarks reveal that the tensor construction directly impacts performance, sometimes better than standard LoRA under similar parameter counts.