D2-LoRA: A Synergistic Approach to Differential and Directional Low-Rank Adaptation

• URL: http://arxiv.org/abs/2602.14728v1
• Date: Mon, 16 Feb 2026 13:19:42 GMT
• Title: D2-LoRA: A Synergistic Approach to Differential and Directional Low-Rank Adaptation
• Authors: Nozomu Fujisawa, Masaaki Kondo,
• Abstract summary: D2-LoRA achieves 76.4 percent average accuracy across eight question answering and reading comprehension benchmarks.<n>The method combines signed low-rank residual updates with additive and subtractive components, together with a train-time column-wise projection.
• Score: 0.24636535146231608
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We systematically investigate the parameter-efficient fine-tuning design space under practical data and compute constraints, and propose D2-LoRA. D2-LoRA achieves 76.4 percent average accuracy across eight question answering and reading comprehension benchmarks using only 5k training samples per task and two epochs, while preserving algebraic mergeability at inference with near-exact numerical equivalence. The method combines signed low-rank residual updates with additive and subtractive components, together with a train-time column-wise projection that keeps each column close to its original norm. After training, the adapter is merged into a single weight matrix, adding zero inference latency. Compared with LoRA, D2-LoRA improves average accuracy by 2.2 percentage points; at matched parameter counts (LoRA rank 2r versus D2-LoRA rank r), the improvement is 1.6 points, indicating gains from architectural design rather than increased parameterization. Compared with DoRA, it matches or exceeds performance on most tasks. Beyond QA and reading comprehension, D2-LoRA improves generative tasks (plus 1.2 ROUGE-L and plus 1.1 percent win rate) and shows 36 percent lower training volatility. The merge preserves numerical fidelity (mean gap about 0.03 percentage points) and recovers about 1.91x evaluation throughput. Training overhead is 19 percent, comparable to DoRA, and decreases with longer input sequences. We provide a geometric analysis explaining how the projection stabilizes training, together with ablation studies isolating the contribution of each design component.

Related papers

• Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation [85.89510825889168]
  We introduce LoRA-Pre, a novel low-rank system for efficient pre-training.<n>LoRA-Pre decomposing the momentum matrix into a compact low-rank subspace within the online linear learner.<n>We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family.
  arXiv  Detail & Related papers  (2026-02-27T18:57:06Z)
• Beyond SGD, Without SVD: Proximal Subspace Iteration LoRA with Diagonal Fractional K-FAC [50.36542772932594]
  Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights.<n>In this work, we address the gap between training with full steps with low-rank projections (SVDLoRA) and LoRA fine-tuning.<n>We propose LoRSum, a memory-efficient subroutine that closes this gap for gradient descent.
  arXiv  Detail & Related papers  (2026-02-18T13:41:41Z)
• 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)
• Efficient Modular Learning through Naive LoRA Summation: Leveraging Orthogonality in High-Dimensional Models [1.0923877073891446]
  Low-Rank Adaptation (LoRA) stores parameter deltas as the product of two small matrices.<n>Naive summation requires no additional training, can be applied in seconds, and achieves performance comparable to models trained on merged data.
  arXiv  Detail & Related papers  (2025-08-16T08:49:02Z)
• SingLoRA: Low Rank Adaptation Using a Single Matrix [7.828928639229988]
  Low-Rank Adaptation (LoRA) has significantly advanced parameter-efficient fine-tuning of large pretrained models.<n>We propose SingLoRA, which reformulates low-rank adaptation by learning the weights update as a decomposition of a single low-rank matrix multiplied by its transpose.
  arXiv  Detail & Related papers  (2025-07-08T01:11:30Z)
• Automatic Rank Determination for Low-Rank Adaptation via Submodular Function Maximization [56.78271181959529]
  SubLoRA is a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function.<n>Our method combines solid theoretical foundations, second-order accuracy, and practical computational efficiency.
  arXiv  Detail & Related papers  (2025-07-02T15:56:40Z)
• LoRA Done RITE: Robust Invariant Transformation Equilibration for LoRA Optimization [78.93425154518705]
  Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements.<n>This paper introduces LoRA-RITE, a novel adaptive matrix preconditioning method for LoRA optimization.
  arXiv  Detail & Related papers  (2024-10-27T22:57:12Z)
• LoRA$^2$ : Multi-Scale Low-Rank Approximations for Fine-Tuning Large Language Models [3.7049613588433497]
  Low-Rank Adaptation (LoRA) significantly reduces the number of trainable parameters for fine-tuning. We extend the LoRA to multiple scales, dubbed as LoRA$2$.
  arXiv  Detail & Related papers  (2024-08-13T12:31:30Z)
• DoRA: Weight-Decomposed Low-Rank Adaptation [57.68678247436207]
  We introduce a novel weight decomposition analysis to investigate the inherent differences between FT and LoRA. Aiming to resemble the learning capacity of FT from the findings, we propose Weight-Decomposed Low-Rank Adaptation (DoRA) DoRA decomposes the pre-trained weight into two components, magnitude and direction, for fine-tuning.
  arXiv  Detail & Related papers  (2024-02-14T17:59:34Z)

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.