Geometry-Preserving Orthonormal Initialization for Low-Rank Adaptation in RLVR

• URL: http://arxiv.org/abs/2606.31813v1
• Date: Tue, 30 Jun 2026 15:27:54 GMT
• Title: Geometry-Preserving Orthonormal Initialization for Low-Rank Adaptation in RLVR
• Abstract summary: Low-rank adaptation (LoRA) and its variants enable parameter-efficient fine-tuning of large language models under the supervised fine-tuning paradigm.<n>Two structurally LoRA variants, PiSSA and MiLoRA, can outperform standard LoRA under Reinforcement learning with verifiable rewards (RLVR) and may even exhibit training instability.
• Score: 22.761873383120786
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Low-rank adaptation (LoRA) and its variants enable parameter-efficient fine-tuning of large language models under the supervised fine-tuning (SFT) paradigm. However, their efficacy and behavior under Reinforcement learning with verifiable rewards (RLVR) are less well understood. In particular, two structurally initialized LoRA variants, PiSSA and MiLoRA, which outperform standard LoRA under SFT, can underperform standard LoRA under RLVR and may even exhibit training instability. These observations suggest that how to initialize the low-rank matrices in RLVR remains unclear. In this work, we develop a theoretical analysis of LoRA in RLVR, showing that orthonormal initialization achieves the minimal gap between LoRA outcome and that of full fine-tuning. Guided by this insight, we propose geometry-preserving orthonormal initialization for low-rank adaptation in RLVR, leading to two new variants, RLPO and RLMO. Experiments on mathematical reasoning benchmarks show that the proposed orthonormal initialization stabilizes RLVR training and outperforms standard LoRA, contrasting with PiSSA and MiLoRA. Finally, our unified analysis for LoRA initialization also explains why PiSSA and MiLoRA can underperform in RLVR, which may be of independent interest. Code and checkpoints are publicly available at https://github.com/Richard-ZZZ/geometry-preserving-orthonormal-init-rlvr.

Related papers

• 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)
• 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)
• Evaluating Parameter Efficient Methods for RLVR [38.45552186628944]
  Reinforcement Learning with Verifiable Rewards (RLVR) incentivizes language models to enhance their reasoning capabilities through verifiable feedback.<n>While methods like LoRA are commonly used, the optimal PEFT architecture for RLVR remains unidentified.<n>We conduct the first comprehensive evaluation of over 12 PEFT methodologies across the DeepSeek-R1-Distill families on mathematical reasoning benchmarks.
  arXiv  Detail & Related papers  (2025-12-29T03:13:08Z)
• The Path Not Taken: RLVR Provably Learns Off the Principals [85.41043469428365]
  We show that sparsity is a surface artifact of a model-conditioned optimization bias.<n>We mechanistically explain these dynamics with a Three-Gate Theory.<n>We provide a parameter-level characterization of RLVR's learning dynamics.
  arXiv  Detail & Related papers  (2025-11-11T18:49:45Z)
• Faster Than SVD, Smarter Than SGD: The OPLoRA Alternating Update [50.36542772932594]
  Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights.<n>There is still a gap between full training with low-rank projections (SVDLoRA) and LoRA fine-tuning, indicating that LoRA steps can be further improved.
  arXiv  Detail & Related papers  (2025-09-24T10:32:50Z)
• QR-LoRA: QR-Based Low-Rank Adaptation for Efficient Fine-Tuning of Large Language Models [0.0]
  Low-Rank Adaptation (LoRA) is a technique for reducing the number of trainable parameters by applying low-rank updates to pretrained weights.<n>We show that QR-LoRA matches or exceeds the performance of full fine-tuning, standard LoRA, and SVD-LoRA.
  arXiv  Detail & Related papers  (2025-08-29T17:47:27Z)
• SRLoRA: Subspace Recomposition in Low-Rank Adaptation via Importance-Based Fusion and Reinitialization [2.594346658179846]
  Low-Rank Adaptation (LoRA) constrains updates to a fixed low-rank subspace.<n>We introduce Subspace Recomposition in Low-Rank Adaptation (SRLoRA) via importance-based fusion and reinitialization.<n> SRLoRA consistently achieves faster convergence and improved accuracy over standard LoRA.
  arXiv  Detail & Related papers  (2025-05-18T14:12:40Z)
• Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model? [66.61292196146016]
  Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs)<n>This study critically examines the current state of RLVR.<n>We find that the current training setup does not elicit fundamentally new reasoning patterns.
  arXiv  Detail & Related papers  (2025-04-18T17:59:56Z)
• 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)
• LoRA-Pro: Are Low-Rank Adapters Properly Optimized? [121.0693322732454]
  Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models.<n>Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning.<n>We introduce LoRA-Pro, a method that enhances LoRA's performance by strategically adjusting the gradients of low-rank matrices.
  arXiv  Detail & Related papers  (2024-07-25T17:57:12Z)

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.