# Kron-LoRA: Hybrid Kronecker-LoRA Adapters for Scalable, Sustainable Fine-tuning

arXiv: https://arxiv.org/abs/2508.01961 · HTML: https://mlsanity.com/paper/2508.01961/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 18 of 18)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (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)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [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)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Recall and Learn: Fine-tuning Deep Pretrained Language Models with Less Forgetting](https://mlsanity.com/paper/2004.12651/) (2020)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)

## Built on by (most cited first, 2 of 2)

- [On the Convergence Rate of LoRA Gradient Descent](https://mlsanity.com/paper/2512.18248/) (2025)
- [ADPTNet: Adaptive with Prescriptive Timescales Non-Linear SSM for Sequence Modelling](https://mlsanity.com/paper/2609.34034/) (2026)

## Abstract (arXiv)

Fine-tuning massive pre-trained language models across many tasks demands adapters that are both parameter-efficient and expressive. We introduce Kron-LoRA, a hybrid adapter that combines Kronecker-structured factorization with low-rank LoRA compression-an integration that, to our knowledge, has not been explored in parameter-efficient fine-tuning or in matrix approximation literature. Kron-LoRA achieves up to 4× fewer parameters than standard LoRA while retaining similar expressivity. Experiments on DistilBERT, Mistral-7B, LLaMA-2-7B, and LLaMA-3-8B across eight benchmarks show that Kron-LoRA matches or exceeds LoRA baselines with modest memory savings and only a 5-8% speed overhead. In sequential fine-tuning, it also delivers competitive cross-task transfer despite using only one-quarter of the adapter parameters. Kron-LoRA thus offers a scalable, sustainable solution for multi-task adaptation of large language models.