# Towards Higher Effective Rank in Parameter-efficient Fine-tuning using Khatri--Rao Product

arXiv: https://arxiv.org/abs/2508.00230 · HTML: https://mlsanity.com/paper/2508.00230/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 62 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Builds on (most cited first, 30 of 45)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Flower: A Friendly Federated Learning Research Framework](https://mlsanity.com/paper/2007.14390/) (2020)
- [A Large-scale Study of Representation Learning with the Visual Task Adaptation Benchmark](https://mlsanity.com/paper/1910.04867/) (2019)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (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)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)

## Built on by (most cited first, 10 of 10)

- [Cutting the Skip: Training Residual-Free Transformers](https://mlsanity.com/paper/2510.00345/) (2025)
- [SineProject: Machine Unlearning for Stable Vision Language Alignment](https://mlsanity.com/paper/2511.18444/) (2025)
- [Spectral Conditioning of Attention Improves Transformer Performance](https://mlsanity.com/paper/2603.07162/) (2026)
- [Timber: Training-free Instruct Model Refining with Base via Effective Rank](https://mlsanity.com/paper/2509.23595/) (2025)
- [STCDiT: Spatio-Temporally Consistent Diffusion Transformer for High-Quality Video Super-Resolution](https://mlsanity.com/paper/2511.18786/) (2025)
- [Mask the Target: A Plug-and-Play Regularizer Against LoRA Forgetting](https://mlsanity.com/paper/2605.29498/) (2026)
- [Finer Parameter Steps for Low-Rank PEFT: A Controlled Study with CP Tensor Adapters](https://mlsanity.com/paper/2606.00428/) (2026)
- [Parameter-Efficient Fine-Tuning with Learnable Rank](https://mlsanity.com/paper/2606.04325/) (2026)
- [Structured Hyperedge Adaptation for Parameter-Efficient Fine-Tuning of Vision Transformers](https://mlsanity.com/paper/2606.22383/) (2026)
- [Conditioned Initialization for Attention](https://mlsanity.com/paper/2609.07086/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning (PEFT) has become a standard approach for adapting large pre-trained models. Amongst PEFT methods, low-rank adaptation (LoRA) has achieved notable success. However, recent studies have highlighted its limitations compared against full-rank alternatives, particularly when applied to multimodal and large language models. In this work, we present a quantitative comparison amongst full-rank and low-rank PEFT methods using a synthetic matrix approximation benchmark with controlled spectral properties. Our results confirm that LoRA struggles to approximate matrices with relatively flat spectrums or high frequency components -- signs of high effective ranks. To this end, we introduce KRAdapter, a novel PEFT algorithm that leverages the Khatri-Rao product to produce weight updates, which, by construction, tends to produce matrix product with a high effective rank. We demonstrate performance gains with KRAdapter on vision-language models up to 1B parameters and on large language models up to 8B parameters, particularly on unseen common-sense reasoning tasks. In addition, KRAdapter maintains the memory and compute efficiency of LoRA, making it a practical and robust alternative to fine-tune billion-scale parameter models.