# MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning

arXiv: https://arxiv.org/abs/2506.09105 · HTML: https://mlsanity.com/paper/2506.09105/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 68 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 30 of 55)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Conditional Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2203.05557/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Parameter-efficient Multi-task Fine-tuning for Transformers via Shared Hypernetworks](https://mlsanity.com/paper/2106.04489/) (2021)
- [Self-regulating Prompts: Foundational Model Adaptation without Forgetting](https://mlsanity.com/paper/2307.06948/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [FacT: Factor-Tuning for Lightweight Adaptation on Vision Transformer](https://mlsanity.com/paper/2212.03145/) (2022)
- [When MOE Meets LLMs: Parameter Efficient Fine-tuning for Multi-task Medical Applications](https://mlsanity.com/paper/2310.18339/) (2023)
- [Low-Rank Few-Shot Adaptation of Vision-Language Models](https://mlsanity.com/paper/2405.18541/) (2024)
- [Delta-LoRA: Fine-Tuning High-Rank Parameters with the Delta of Low-Rank Matrices](https://mlsanity.com/paper/2309.02411/) (2023)

## Built on by (most cited first, 4 of 4)

- [A Practical Tensor-Network Compression Pipeline for Production-Scale Large Language Models](https://mlsanity.com/paper/2602.01613/) (2026)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [All-day Multi-scenes Lifelong Vision-and-Language Navigation with Tucker Adaptation](https://mlsanity.com/paper/2603.14276/) (2026)
- [GLT-PEFT: Gated Lie-Tucker Parameter-Efficient Fine-Tuning for Alzheimer's Disease Diagnosis with Hippocampal Segmentation Pretraining](https://mlsanity.com/paper/2605.16769/) (2026)

## Abstract (arXiv)

We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This factorization indexes key structural dimensions, including layer and matrix type, and can optionally incorporate heads and tasks. This design allows MetaTT's parameter count to scale with the sum, rather than the product, of the modes, resulting in a substantially more compact adapter. Our benchmarks compare MetaTT with LoRA along with recent state-of-the-art matrix and tensor decomposition based fine-tuning methods. We observe that when tested on single-task standard language modeling benchmarks, MetaTT achieves competitive parameter efficiency to accuracy tradeoff. We further demonstrate that MetaTT performs competitively when compared to state-of-the-art methods on multi-task learning. Finally, we leverage the TT decomposition to design a rank adaptive optimizer inspired by the DMRG method from many-body physics. Our results demonstrate that integrating this approach with AdamW enhances optimization performance for a specified target rank.