# Beyond Higher Rank: Token-wise Input-Output Projections for Efficient Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2510.23123 · HTML: https://mlsanity.com/paper/2510.23123/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 49 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [The Expressive Power of Low-Rank Adaptation](https://mlsanity.com/paper/2310.17513/) (2023)
- [LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameters](https://mlsanity.com/paper/2405.17604/) (2024)
- [Residual Prompt Tuning: Improving Prompt Tuning with Residual Reparameterization](https://mlsanity.com/paper/2305.03937/) (2023)
- [MoELoRA: Contrastive Learning Guided Mixture of Experts on Parameter-Efficient Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2402.12851/) (2024)
- [VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Banks](https://mlsanity.com/paper/2405.15179/) (2024)
- [FlowCut: Rethinking Redundancy via Information Flow for Efficient Vision-Language Models](https://mlsanity.com/paper/2505.19536/) (2025)
- [Unleashing the Power of Continual Learning on Non-Centralized Devices: A Survey](https://mlsanity.com/paper/2412.13840/) (2024)
- [Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning](https://mlsanity.com/paper/2411.19557/) (2024)
- [Lightweight Frequency Masker for Cross-Domain Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2410.22135/) (2024)
- [Beyond Zero Initialization: Investigating the Impact of Non-Zero Initialization on LoRA Fine-Tuning Dynamics](https://mlsanity.com/paper/2505.23194/) (2025)
- [Decoupling General and Personalized Knowledge in Federated Learning via Additive and Low-Rank Decomposition](https://mlsanity.com/paper/2406.19931/) (2024)

## Built on by (most cited first, 6 of 6)

- [Nonlinearity as Rank: Generative Low-Rank Adapter with Radial Basis Functions](https://mlsanity.com/paper/2602.05709/) (2026)
- [FourierMoE: Fourier Mixture-of-Experts Adaptation of Large Language Models](https://mlsanity.com/paper/2604.01762/) (2026)
- [ARCA: Adapter-Residual Credit Assignment When Token Signals Degenerate](https://mlsanity.com/paper/2606.00257/) (2026)
- [Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents](https://mlsanity.com/paper/2609.12896/) (2026)
- [Learn Here, Move Less Elsewhere: Input-Conditioned Plasticity from Retained-Domain Activation Atlases](https://mlsanity.com/paper/2609.34478/) (2026)
- [Adaptive Utilization of Low-Rank Adaptation via Conditioned Gating](https://mlsanity.com/paper/2610.05800/) (2026)

## Abstract (arXiv)

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). LoRA essentially describes the projection of an input space into a low-dimensional output space, with the dimensionality determined by the LoRA rank. In standard LoRA, all input tokens share the same weights and undergo an identical input-output projection. This limits LoRA's ability to capture token-specific information due to the inherent semantic differences among tokens. To address this limitation, we propose Token-wise Projected Low-Rank Adaptation (TopLoRA), which dynamically adjusts LoRA weights according to the input token, thereby learning token-wise input-output projections in an end-to-end manner. Formally, the weights of TopLoRA can be expressed as BSigmaX A, where A and B are low-rank matrices (as in standard LoRA), and SigmaX is a diagonal matrix generated from each input token X. Notably, TopLoRA does not increase the rank of LoRA weights but achieves more granular adaptation by learning token-wise LoRA weights (i.e., token-wise input-output projections). Extensive experiments across multiple models and datasets demonstrate that TopLoRA consistently outperforms LoRA and its variants. The code is available at https://github.com/Leopold1423/toplora-neurips25.