# Tensor Train Low-rank Approximation (TT-LoRA): Democratizing AI with Accelerated LLMs

arXiv: https://arxiv.org/abs/2408.01008 · HTML: https://mlsanity.com/paper/2408.01008/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [A Tensorized Transformer for Language Modeling](https://mlsanity.com/paper/1906.09777/) (2019)
- [LLMCarbon: Modeling the end-to-end Carbon Footprint of Large Language Models](https://mlsanity.com/paper/2309.14393/) (2023)
- [A Comparative Study of Open-Source Large Language Models, GPT-4 and Claude 2: Multiple-Choice Test Taking in Nephrology](https://mlsanity.com/paper/2308.04709/) (2023)
- [LoRETTA: Low-Rank Economic Tensor-Train Adaptation for Ultra-Low-Parameter Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2402.11417/) (2024)
- [Distributed Non-Negative Tensor Train Decomposition](https://mlsanity.com/paper/2008.01340/) (2020)

## Built on by (most cited first, 14 of 14)

- [Low-Rank Adaptation for Foundation Models: A Comprehensive Review](https://mlsanity.com/paper/2501.00365/) (2024)
- [TT-LoRA MoE: Unifying Parameter-Efficient Fine-Tuning and Sparse Mixture-of-Experts](https://mlsanity.com/paper/2504.21190/) (2025)
- [MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2506.09105/) (2025)
- [Rethinking the Role of Tensor Decompositions in Post-Training LLM Compression](https://mlsanity.com/paper/2606.03465/) (2026)
- [Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models](https://mlsanity.com/paper/2501.08727/) (2025)
- [FedVLM: Scalable Personalized Vision-Language Models through Federated Learning](https://mlsanity.com/paper/2507.17088/) (2025)
- [Artificial Entanglement in the Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2601.06788/) (2026)
- [The Structure of Relation Decoding Linear Operators in Large Language Models](https://mlsanity.com/paper/2510.26543/) (2025)
- [LoRA-Edge: Tensor-Train-Assisted LoRA for Practical CNN Fine-Tuning on Edge Devices](https://mlsanity.com/paper/2511.03765/) (2025)
- [Decomposed Trust: Privacy, Adversarial Robustness, Ethics, and Fairness in Low-Rank LLMs](https://mlsanity.com/paper/2511.22099/) (2025)
- [Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications](https://mlsanity.com/paper/2512.23917/) (2025)
- [Privacy Enhanced PEFT: Tensor Train Decomposition Improves Privacy Utility Tradeoffs under DP-SGD](https://mlsanity.com/paper/2601.10045/) (2026)
- [Strategic Over-Parameterization for Generalizable Low-Rank Adaptation](https://mlsanity.com/paper/2605.16470/) (2026)
- [ChainDoRA: Tensor-Train Factorized Weight-Decomposed Low-Rank Adaptation for Parameter-Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2609.25058/) (2026)

## Abstract (arXiv)

In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing (NLP) tasks, such as question-answering, sentiment analysis, text summarization, and machine translation. However, the ever-growing complexity of LLMs demands immense computational resources, hindering the broader research and application of these models. To address this, various parameter-efficient fine-tuning strategies, such as Low-Rank Approximation (LoRA) and Adapters, have been developed. Despite their potential, these methods often face limitations in compressibility. Specifically, LoRA struggles to scale effectively with the increasing number of trainable parameters in modern large scale LLMs. Additionally, Low-Rank Economic Tensor-Train Adaptation (LoRETTA), which utilizes tensor train decomposition, has not yet achieved the level of compression necessary for fine-tuning very large scale models with limited resources. This paper introduces Tensor Train Low-Rank Approximation (TT-LoRA), a novel parameter-efficient fine-tuning (PEFT) approach that extends LoRETTA with optimized tensor train (TT) decomposition integration. By eliminating Adapters and traditional LoRA-based structures, TT-LoRA achieves greater model compression without compromising downstream task performance, along with reduced inference latency and computational overhead. We conduct an exhaustive parameter search to establish benchmarks that highlight the trade-off between model compression and performance. Our results demonstrate significant compression of LLMs while maintaining comparable performance to larger models, facilitating their deployment on resource-constraint platforms.