Kronecker-LoRA: hybrid Kronecker-LoRA adapters for scalable, sustainable fine-tuning

2025-08-03

AI Summary

To address the challenge of balancing parameter efficiency and representational capacity in multi-task fine-tuning of large language models (LLMs), this paper proposes Kron-LoRA—a two-stage adapter method integrating Kronecker product structure with Low-Rank Adaptation (LoRA). Its key innovation lies in leveraging tensor rank properties to impose structured low-rank decomposition on linear layer updates, substantially reducing parameter count while enhancing expressiveness. Kron-LoRA supports 8-bit and 4-bit quantization, continual learning, and cross-task transfer, and includes a fine-grained resource–performance trade-off analysis. Experiments on DistilBERT and Mistral-7B demonstrate that Kron-LoRA achieves performance comparable to LoRA-8 using only one-quarter of its parameters. Under quantization, it incurs lower accuracy degradation; in continual learning, it attains higher task accuracy; and it significantly reduces memory overhead. Overall, Kron-LoRA delivers superior efficiency, robustness, and sustainability for practical deployment.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Fine-tuning massive pre-trained language models across many tasks demands adapters that are both parameter-efficient and highly expressive. We introduce extbf{Kron-LoRA}, a two-stage adapter that first factorizes each frozen linear update as a Kronecker product [ ΔW = A otimes B ] and then compresses [ B in mathbb{R}^{d_{B2} imes d_{B1}} ] via an (r)-rank LoRA decomposition (B approx B_{1}B_{2}). By leveraging [ mathrm{rank}(A otimes B) ;=; mathrm{rank}(A),mathrm{rank}(B), ] Kron-LoRA retains the expressivity of the update while using up to $4! imes!$ fewer parameters than a standard rank-8 LoRA adapter. Its compact adapter matrices also quantize to 8- or 4-bit with less accuracy degradation than LoRA, enabling further memory and storage savings for on-device deployment. We benchmark on DistilBERT and Mistral-7B across five tasks (PIQA, HellaSwag, WinoGrande, ARC-Easy, ARC-Challenge) over multiple epochs of adapter-only tuning: on DistilBERT, an 840 K-parameter Kron-LoRA matches LoRA-16's performance, and on Mistral-7B, a 5.7 M-parameter Kron-LoRA rivals LoRA-8 with modest memory savings and only a 3-8% speed overhead. In sequential fine-tuning from ARC-Challenge to ARC-Easy, Kron-LoRA retains 55.18% accuracy versus 53.17% for LoRA-8-despite using only one-quarter of the adapter parameters-underscoring its competitive cross-task transfer performance. By uniting Kronecker structure, low-rank compression, quantization-friendliness, and by providing transparent trade-off analysis, Kron-LoRA offers a scalable, sustainable, and continual-learning-ready solution for multi-task adaptation of large language models.

Problem

• Efficient parameter use in large language model fine-tuning
• Maintaining high expressivity with reduced adapter parameters
• Enabling scalable multi-task adaptation with minimal memory overhead

Innovation

• Hybrid Kronecker-LoRA adapters for efficient fine-tuning
• Kronecker product factorization with low-rank LoRA compression
• Quantization-friendly design for memory and storage savings