One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning

• URL: http://arxiv.org/abs/2609.05885v1
• Date: Sat, 05 Sep 2026 05:14:04 GMT
• Title: One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning
• Abstract summary: Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models.<n>We show that rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra.<n>We propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate.
• Score: 26.741445807383098
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.

Related papers

• Rank-Efficient LoRA via Joint Tangent-Space Optimization under Isotropic Curvature [15.962803593943624]
  Low-Rank Adaptation (LoRA) is an effective approach for adapting large pretrained models by learning low-rank weight updates.<n>We show that while the nominal rank determines the representational capacity, the shape of that capacity is used in the induced weight-space updates.
  arXiv  Detail & Related papers  (2026-09-10T18:50:17Z)
• IFCLoRA: Topology-Aware Rank Allocation for Parameter-Efficient Fine-Tuning [8.041472556779395]
  Low-Rank Adaptation (LoRA) is a widely used parameter-efficient fine-tuning method for large language models.<n>We propose IFCLoRA, a topology-aware rank allocation method applied before fine-tuning.
  arXiv  Detail & Related papers  (2026-07-24T12:34:46Z)
• SMoA: Spectrum Modulation Adapter for Parameter-Efficient Fine-Tuning [57.85676271833619]
  Low-rank Adaptation (LoRA) uses a low-rank update method to simulate full parameter fine-tuning.<n>As the rank increases, more principal singular directions are preserved, which generally improves the model's performance.<n>We propose SMoA, a textbfSpectrum textbfModulation textbfAdapter that enlarges the accessible family of spectrum-aware updates.
  arXiv  Detail & Related papers  (2026-05-20T13:19:28Z)
• Post-Optimization Adaptive Rank Allocation for LoRA [10.796887002907456]
  Post-Optimization Adaptive Rank Allocation (PARA) is a data-free compression method for Low-Rank Adaptation (LoRA)<n>We propose PARA, a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines.<n>We empirically demonstrate that PARA reduces parameter count by 75-90% while preserving the predictive performance of the original, uncompressed LoRA across vision and language benchmarks.
  arXiv  Detail & Related papers  (2026-04-30T12:40:11Z)
• LoRA-Squeeze: Simple and Effective Post-Tuning and In-Tuning Compression of LoRA Modules [10.00294036303927]
  We introduce LoRA-Squeeze, a simple and efficient methodology that aims to improve standard LoRA learning.<n>Our approach posits that it is better to first learn an expressive, higher-rank solution and then compress it, rather than learning a constrained, low-rank solution directly.
  arXiv  Detail & Related papers  (2026-02-11T16:19:58Z)
• Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning [48.66442009036754]
  Low-Rank Adaptation (LoRA) is the prevailing approach for efficient large language model fine-tuning.<n>In this work, we re-evaluate four representative LoRA variants alongside vanilla LoRA.<n>We find that different LoRA methods favor distinct learning rate ranges.
  arXiv  Detail & Related papers  (2026-02-04T19:36:20Z)
• BeamLoRA: Beam-Constraint Low-Rank Adaptation [51.52097743781401]
  Low-Rank Adaptation (LoRA) has been widely adopted as one of the most effective parameter-efficient fine-tuning methods.<n>We propose BeamLoRA, which conceptualizes each LoRA module as a beam where each rank naturally corresponds to a potential sub-solution.
  arXiv  Detail & Related papers  (2025-02-19T10:33:22Z)
• SD-LoRA: Scalable Decoupled Low-Rank Adaptation for Class Incremental Learning [73.93639228235622]
  Continual Learning with foundation models has emerged as a promising paradigm to exploit abundant knowledge acquired during pre-training for tackling sequential tasks.<n>Existing prompt-based and Low-Rank Adaptation-based (LoRA-based) methods often require expanding a prompt/LoRA pool or retaining samples of previous tasks.<n>We propose Scalable Decoupled LoRA (SD-LoRA) for class incremental learning, which continually separates the learning of the magnitude and direction of LoRA components without rehearsal.
  arXiv  Detail & Related papers  (2025-01-22T20:00:41Z)
• PRILoRA: Pruned and Rank-Increasing Low-Rank Adaptation [65.268245109828]
  We introduce PRILoRA, which linearly allocates a different rank for each layer, in an increasing manner, and performs pruning throughout the training process. We validate the effectiveness of PRILoRA through extensive experiments on eight GLUE benchmarks, setting a new state of the art.
  arXiv  Detail & Related papers  (2024-01-20T20:25:17Z)
• Sparse Low-rank Adaptation of Pre-trained Language Models [79.74094517030035]
  We introduce sparse low-rank adaptation (SoRA) that enables dynamic adjustments to the intrinsic rank during the adaptation process. Our approach strengthens the representation power of LoRA by initializing it with a higher rank, while efficiently taming a temporarily increased number of parameters. Our experimental results demonstrate that SoRA can outperform other baselines even with 70% retained parameters and 70% training time.
  arXiv  Detail & Related papers  (2023-11-20T11:56:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.