# MoKA: Mixture of Kronecker Adapters

arXiv: https://arxiv.org/abs/2508.03527 · HTML: https://mlsanity.com/paper/2508.03527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 19 of 19)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [Unnatural Instructions: Tuning Language Models with (Almost) No Human Labor](https://mlsanity.com/paper/2212.09689/) (2022)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [UniPELT: A Unified Framework for Parameter-Efficient Language Model Tuning](https://mlsanity.com/paper/2110.07577/) (2021)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)
- [Parameter-Efficient Fine-Tuning in Large Models: A Survey of Methodologies](https://mlsanity.com/paper/2410.19878/) (2024)
- [SparseBERT: Rethinking the Importance Analysis in Self-attention](https://mlsanity.com/paper/2102.12871/) (2021)
- [QDyLoRA: Quantized Dynamic Low-Rank Adaptation for Efficient Large Language Model Tuning](https://mlsanity.com/paper/2402.10462/) (2024)
- [On the Importance of Local Information in Transformer Based Models](https://mlsanity.com/paper/2008.05828/) (2020)
- [Investigating Public Fine-Tuning Datasets: A Complex Review of Current Practices from a Construction Perspective](https://mlsanity.com/paper/2407.08475/) (2024)

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

- [The Dual-Stream Transformer: Channelized Architecture for Interpretable Language Modeling](https://mlsanity.com/paper/2603.07461/) (2026)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning (PEFT) is essential for reducing the computational overhead of large language models (LLMs). Low-rank family adapters are commonly used to control the parameter size efficiently while maintaining the generative power of LLMs. However, their limited expressiveness due to the rank constraint often restricts their performance on complex tasks. We propose Mixture of Kronecker Adapters (MoKA), a new generation of Kronecker adapters that addresses this limitation by modeling weight updates as a mixture of Kronecker products. Our proposed adapter leverages a gating mechanism that measures the importance of each Kronecker factor, enabling more expressive adaptation. Moreover, MoKA enables a rank flexibility that provides a better trade-off between parameter efficiency and accuracy. To ensure hardware efficiency, we reformulate Kronecker computations using standard matrix operations, allowing seamless deployment on GPU-optimized hardware. We conduct extensive experiments on instruction-tuning and commonsense reasoning tasks using low-bit quantized versions of LLaMA2-7B and LLaMA3-8B models. MoKA not only outperforms PEFT baselines, but also reduces the number of trainable parameters up to 27x, achieving state-of-the-art trade-offs between performance and parameter efficiency.