# LoRTA: Low Rank Tensor Adaptation of Large Language Models

arXiv: https://arxiv.org/abs/2410.04060 · HTML: https://mlsanity.com/paper/2410.04060/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 72 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 30 of 51)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [A Survey of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2312.14925/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)

## Built on by (most cited first, 7 of 7)

- [MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2506.09105/) (2025)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [Beyond LoRA: Is Sparsity-Induced Adaptation Better?](https://mlsanity.com/paper/2606.13767/) (2026)
- [Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability](https://mlsanity.com/paper/2608.30505/) (2026)
- [TensLoRA: Tensor Alternatives for Low-Rank Adaptation](https://mlsanity.com/paper/2509.19391/) (2025)
- [FuRA: Full-Rank Parameter-Efficient Fine-Tuning with Spectral Preconditioning](https://mlsanity.com/paper/2605.22869/) (2026)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer, significantly reducing the number of trainable parameters and, consequently, resource requirements during fine-tuning. However, the lower bound on the number of trainable parameters remains high due to the use of the low-rank matrix model. Recent works have addressed this limitation by proposing low rank tensor parameterizations for model updates. However, they only exploit redundancy across layers, or tensorize individual matrices using ad-hoc schemes that introduce additional hyperparameters. In this work, we propose a higher-order Candecomp/Parafac (CP) decomposition, enabling a more compact and flexible representation compared to existing matrix and tensor based PEFT methods. Our experiments on Natural Language Understanding, Instruction Tuning, Preference Optimization and Protein Folding benchmarks demonstrate that our method can achieve a reduction in the number of parameters while maintaining comparable performance.