Daily Papers

Large Language Models (LLMs) have achieved remarkable capabilities, but their immense computational demands during training remain a critical bottleneck for widespread adoption. Low-rank training has received attention in recent years due to its ability to significantly reduce training memory usage. Meanwhile, applying 2:4 structured sparsity to weights and activations to leverage NVIDIA GPU support for 2:4 structured sparse format has become a promising direction. However, existing low-rank methods often leave activation matrices in full-rank, which dominates memory consumption and limits throughput during large-batch training. Furthermore, directly applying sparsity to weights often leads to non-negligible performance degradation. To achieve efficient pre-training of LLMs, this paper proposes ELAS: Efficient pre-training of Low-rank LLMs via 2:4 Activation Sparsity, a novel framework for low-rank models via 2:4 activation sparsity. ELAS applies squared ReLU activation functions to the feed-forward networks in low-rank models and implements 2:4 structured sparsity on the activations after the squared ReLU operation. We evaluated ELAS through pre-training experiments on LLaMA models ranging from 60M to 1B parameters. The results demonstrate that ELAS maintains performance with minimal degradation after applying 2:4 activation sparsity, while achieving training and inference acceleration. Moreover, ELAS reduces activation memory overhead, particularly with large batch sizes. Code is available at ELAS Repo.

Reinforcement learning (RL) is increasingly used to post-train vision-language-action (VLA) models, yet how RL reshapes these policies remains poorly understood. We find that RL across widely used flow-based VLA models, including π_{0.5} and GR00T~N1.5/N1.6, on LIBERO, ManiSkill, MetaWorld, and CALVIN induces substantially lower-rank parameter updates that are highly concentrated in the action expert's Timestep Modules, a small and previously overlooked component. Through systematic module-replacement experiments, we further show that these modules capture a disproportionate share of the performance gains from RL. We then characterize what is encoded in these Timestep Modules. First, we show that RL specializes them to the discrete denoising timesteps used during rollouts, and that this discrete-timestep training underlies the low-rank updates. Second, we find that among their outputs, the shift vector changes most distinctly under RL, and through probing, we show that shift update directions strongly predict task success (ROC-AUC up to 99.6%). Third, we find that the geometry of shift updates reflects task relationships, as their pairwise similarity correlates with cross-task transfer patterns. Building on these findings, we show that steering along shift update directions further improves RL-trained policies without additional RL training. Overall, we provide a systematic understanding of how RL reshapes VLA policies by studying how learned signals are encoded in parameter space, offering insights into more efficient and interpretable VLA post-training.

Context-to-LoRA methods encode documents as low-rank parameter updates, allowing language models to answer without retaining the source text in their decoding context. How reliably do these updates preserve facts and support their use under different instructions? Controlled diagnosis of existing context-to-LoRA methods separates fact discrimination, target retention, and response adaptation. Competing sources influence answers, while target-only construction and memory-state optimization improve recovery at fixed update size. Recovering facts also does not ensure that answers follow response instructions. We introduce Cache2LoRA, which uses each query to aggregate evidence from a reusable frozen document cache before generating LoRA updates. Trainable encoding operates only on the query and memory-token suffix, and multi-style supervision teaches both evidence preservation and answer expression. Across 17 tasks, Cache2LoRA improves on existing context-to-LoRA methods and achieves macro F1 of 0.663, approaching full-context in-context learning at 0.671. For 32K documents and 256-token outputs at batch size 16, its decoding throughput is 5.9times that of full-context ICL. At matched memory size, generated LoRA preserves answer accuracy more reliably than the learned-KV variant under long, diverse intervening text and combines more effectively with retained document KV, yielding higher hybrid F1 and EM.

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank, parameter-efficient updates that limit the model's expressivity and introduce additional parameters per task, leading to scalability issues. To address these limitations, we propose a novel continual full fine-tuning approach leveraging adaptive singular value decomposition (SVD). Our method dynamically identifies task-specific low-rank parameter subspaces and constrains updates to be orthogonal to critical directions associated with prior tasks, thus effectively minimizing interference without additional parameter overhead or storing previous task gradients. We evaluate our approach extensively on standard continual learning benchmarks using both encoder-decoder (T5-Large) and decoder-only (LLaMA-2 7B) models, spanning diverse tasks including classification, generation, and reasoning. Empirically, our method achieves state-of-the-art results, up to 7% higher average accuracy than recent baselines like O-LoRA, and notably maintains the model's general linguistic capabilities, instruction-following accuracy, and safety throughout the continual learning process by reducing forgetting to near-negligible levels. Our adaptive SVD framework effectively balances model plasticity and knowledge retention, providing a practical, theoretically grounded, and computationally scalable solution for continual learning scenarios in large language models.

Convolutional neural networks (CNNs) have been widely used in efficient image super-resolution. However, for CNN-based methods, performance gains often require deeper networks and larger feature maps, which increase complexity and inference costs. Inspired by LoRA's success in fine-tuning large language models, we explore its application to lightweight models and propose Distillation-Supervised Convolutional Low-Rank Adaptation (DSCLoRA), which improves model performance without increasing architectural complexity or inference costs. Specifically, we integrate ConvLoRA into the efficient SR network SPAN by replacing the SPAB module with the proposed SConvLB module and incorporating ConvLoRA layers into both the pixel shuffle block and its preceding convolutional layer. DSCLoRA leverages low-rank decomposition for parameter updates and employs a spatial feature affinity-based knowledge distillation strategy to transfer second-order statistical information from teacher models (pre-trained SPAN) to student models (ours). This method preserves the core knowledge of lightweight models and facilitates optimal solution discovery under certain conditions. Experiments on benchmark datasets show that DSCLoRA improves PSNR and SSIM over SPAN while maintaining its efficiency and competitive image quality. Notably, DSCLoRA ranked first in the Overall Performance Track of the NTIRE 2025 Efficient Super-Resolution Challenge. Our code and models are made publicly available at https://github.com/Yaozzz666/DSCF-SR.

Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models. Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning. In this paper, we first uncover a fundamental connection between the optimization processes of LoRA and full fine-tuning: using LoRA for optimization is mathematically equivalent to full fine-tuning using a low-rank gradient for parameter updates. And this low-rank gradient can be expressed in terms of the gradients of the two low-rank matrices in LoRA. Leveraging this insight, we introduce LoRA-Pro, a method that enhances LoRA's performance by strategically adjusting the gradients of these low-rank matrices. This adjustment allows the low-rank gradient to more accurately approximate the full fine-tuning gradient, thereby narrowing the performance gap between LoRA and full fine-tuning. Furthermore, we theoretically derive the optimal solutions for adjusting the gradients of the low-rank matrices, applying them during fine-tuning in LoRA-Pro. We conduct extensive experiments across natural language understanding, dialogue generation, mathematical reasoning, code generation, and image classification tasks, demonstrating that LoRA-Pro substantially improves LoRA's performance, effectively narrowing the gap with full fine-tuning. Code is publicly available at https://github.com/mrflogs/LoRA-Pro.

Recently, scaling reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs) has emerged as an effective training paradigm for significantly improving model capabilities, which requires guiding the model to perform extensive exploration and learning, leading to substantial computational overhead and becoming a key challenge. To reduce the number of training steps, Prior work performs linear extrapolation of model parameters. However, the dynamics of model parameter updates during RLVR training remain insufficiently understood. To further investigate the evolution of LLMs during RLVR training, we conduct empirical experiments and find that the rank-1 subspace of the model does not evolve linearly, and its dominance over the original parameters is further amplified during LoRA training. Based on the above insights, we propose the Nonlinear Extrapolation of low-rank trajectories (NExt), a novel framework that models and extrapolates low-rank parameter trajectories in a nonlinear manner. Concretely, we first train the model using LoRA and extract the rank-1 subspace of parameter differences at multiple training steps, which is then used for the subsequent nonlinear extrapolation. Afterward, we utilized the extracted rank-1 subspace to train a predictor, which can model the trajectory of parameter updates during RLVR, and then perform the predict-extend process to extrapolate model parameters, achieving the acceleration of RLVR. To further study and understand NExt, we conduct comprehensive experiments that demonstrate the effectiveness and robustness of the method. Our method reduces computational overhead by approximately 37.5\% while remaining compatible with a wide range of RLVR algorithms and tasks. We release our code in https://github.com/RUCAIBox/NExt.

While orthogonal subspace methods try to mitigate task interference in Continual Learning (CL), they often suffer from energy diffusion across the basis, hindering knowledge compaction and exhausting capacity for future tasks. We observe that output feature drift induced by parameter updates is inherently low-rank, and theoretically prove that preserving parameters along the principal directions of this drift minimizes the output reconstruction error. Motivated by this, we propose Energy-Concentrated and Energy-Ordered Low-Rank Adaptation (E^2-LoRA). By explicitly ordering and concentrating knowledge into leading ranks, E^2-LoRA frees capacity for subsequent tasks. Furthermore, we design a dynamic rank allocation strategy to balance stability and plasticity by jointly optimizing energy retention and model plasticity. Extensive experiments across multiple benchmarks demonstrate that E^2-LoRA achieves state-of-the-art performance.

Low-Rank Adaptation (LoRA) is an efficient fine-tuning method that has been extensively applied in areas such as natural language processing and computer vision. Existing LoRA fine-tuning approaches excel in static environments but struggle in dynamic learning due to reliance on multiple adapter modules, increasing overhead and complicating inference. We propose Continual Low-Rank Adaptation (C-LoRA), a novel extension of LoRA for continual learning. C-LoRA uses a learnable routing matrix to dynamically manage parameter updates across tasks, ensuring efficient reuse of learned subspaces while enforcing orthogonality to minimize interference and forgetting. Unlike existing approaches that require separate adapters for each task, C-LoRA enables a integrated approach for task adaptation, achieving both scalability and parameter efficiency in sequential learning scenarios. C-LoRA achieves state-of-the-art accuracy and parameter efficiency on benchmarks while providing theoretical insights into its routing matrix's role in retaining and transferring knowledge, establishing a scalable framework for continual learning.

Low-Rank Adaptation (LoRA) has become a widely adopted technique for fine-tuning large-scale pre-trained models with minimal parameter updates. However, existing methods rely on fixed ranks or focus solely on either rank pruning or expansion, failing to adapt ranks dynamically to match the importance of different layers during training. In this work, we propose ElaLoRA, an adaptive low-rank adaptation framework that dynamically prunes and expands ranks based on gradient-derived importance scores. To the best of our knowledge, ElaLoRA is the first method that enables both rank pruning and expansion during fine-tuning. Experiments across multiple benchmarks demonstrate that ElaLoRA consistently outperforms existing PEFT methods across different parameter budgets. Furthermore, our studies validate that layers receiving higher rank allocations contribute more significantly to model performance, providing theoretical justification for our adaptive strategy. By introducing a principled and adaptive rank allocation mechanism, ElaLoRA offers a scalable and efficient fine-tuning solution, particularly suited for resource-constrained environments.

Low-Rank Adaptation (LoRA) and its variants have shown impressive results in reducing the number of trainable parameters and memory requirements of large transformer networks while maintaining fine-tuning performance. However, the low-rank nature of the weight update inherently limits the representation power of fine-tuned models, potentially compromising performance on complex tasks. This raises a critical question: when a performance gap between LoRA and standard fine-tuning is observed, is it due to the reduced number of trainable parameters or the rank deficiency? This paper aims to answer this question by introducing RandLoRA, a parameter-efficient method that performs full-rank updates using a learned linear combinations of low-rank, non-trainable random matrices. Our method limits the number of trainable parameters by restricting optimization to diagonal scaling matrices applied to the fixed random matrices. This allows us to effectively overcome the low-rank limitations while maintaining parameter and memory efficiency during training. Through extensive experimentation across vision, language, and vision-language benchmarks, we systematically evaluate the limitations of LoRA and existing random basis methods. Our findings reveal that full-rank updates are beneficial across vision and language tasks individually, and even more so for vision-language tasks, where RandLoRA significantly reduces -- and sometimes eliminates -- the performance gap between standard fine-tuning and LoRA, demonstrating its efficacy.

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static parameterization can be too rigid when the appropriate correction depends on the input and on the evolving depth-wise computation of the network. Our approach replaces a purely layer-local adapter with a shared queryable memory of low-rank update atoms. For each block of layers, the model forms a query from the current low-rank state and a running summary of previous blocks, uses this query to retrieve a content-dependent combination of shared update components via attention, and applies the resulting routed operator within the low-rank bottleneck. In this way, the method retains the efficiency and scalability of low-rank adaptation while allowing the effective update to vary across inputs and to share reusable structure across layers. The resulting architecture provides a principled middle ground between static LoRA-style updates and fully generated parameter updates: it remains compact and parameter-efficient while supporting dynamic, context-sensitive adaptation. Further, we incorporate instruction-regularization by augmenting routing logits with a language-induced prior over update atoms, thereby biasing the selection of low-rank transformations toward semantically relevant directions without generating unconstrained parameter updates. Experiments on noisy non-linear regression tasks and LLM fine-tuning suggest that this queryable update-memory formulation can improve final test performance and training stability compared to standard low-rank adaptation, while using a comparable number of trainable parameters.

Low-Rank Adaptation (LoRA) improves downstream performance by restricting task updates to a low-rank parameter subspace, yet how this limited capacity is allocated within a trained adapter remains unclear. Through a geometric and empirical study across multiple tasks and backbones, we find that trained LoRA updates often exhibit an inefficient spectrum: task effects concentrate in a small subset of singular directions, while many remaining components are neutral or detrimental, motivating post-hoc refinement within the learned subspace. We propose Spectral Surgery, a training-free refinement that decomposes a LoRA update with SVD, estimates per-component sensitivity using gradients on a small calibration set, and reweights singular values under a magnitude constraint while keeping the learned directions fixed. Across Llama-3.1-8B and Qwen3-8B on four benchmarks, Spectral Surgery yields consistent gains (up to +4.4 points on CommonsenseQA and +2.4 pass@1 on HumanEval) by adjusting only approx 1{,}000 scalar coefficients. These results demonstrate that SVD-structured, low-cost parameter editing can serve as a practical route to improving trained LoRA adapters in a purely post-hoc manner.

Large Language Models (LLMs) have achieved remarkable success in natural language processing, but their full fine-tuning remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have emerged as a practical solution by approximating parameter updates with low-rank matrices. However, LoRA often exhibits a "double descent" phenomenon during fine-tuning, where model performance degrades due to overfitting and limited expressiveness caused by low-rank constraints. To address this issue, we propose LoRA-GGPO (Gradient-Guided Perturbation Optimization), a novel method that leverages gradient and weight norms to generate targeted perturbations. By optimizing the sharpness of the loss landscape, LoRA-GGPO guides the model toward flatter minima, mitigating the double descent problem and improving generalization. Extensive experiments on natural language understanding (NLU) and generation (NLG) tasks demonstrate that LoRA-GGPO outperforms LoRA and its state-of-the-art variants. Furthermore, extended experiments specifically designed to analyze the double descent phenomenon confirm that LoRA-GGPO effectively alleviates this issue, producing more robust and generalizable models. Our work provides a robust and efficient solution for fine-tuning LLMs, with broad applicability in real-world scenarios. The code is available at https://github.com/llm172/LoRA-GGPO.

Adapting machine-learned interatomic potential (MLIP) foundation models to specialised tasks through fine-tuning is an increasingly important practice, yet systematic guidance on when and how to fine-tune is currently limited. We evaluate seven fine-tuning strategies -- naive full-parameter updates, two layer-freezing variants, Low-Rank Adaptation (LoRA), multihead replay, pseudolabelled replay, and replay combined with LoRA -- across five chemically diverse benchmarks (aqueous NaCl, ice polymorphs, S_N2 reactions, SPICE biomolecules, and lithium electrolytes), three generations of foundation models, and training sets spanning five orders of magnitude. To support this evaluation we implement three capabilities in the MACE codebase: LoRA adapted for equivariant message-passing architectures, including both scalar and equivariant linear layers; pseudolabelled replay, which decouples the replay data source from the original pretraining corpus; and model-aware atomic reference energy (E0) reestimation for fine-tuning workflows. We find that foundation model quality, correct E0 initialisation, and well-chosen hyperparameters are prerequisites whose impact routinely exceeds that of the fine-tuning strategy itself. Once these prerequisites are met, most strategies achieve strong target-task accuracy, consistently surpassing models trained from scratch. The practical distinction depends on deployment scope: naive fine-tuning offers the best convergence for single-system applications, while multihead replay -- with either original or pseudolabelled data -- is the only approach tested that consistently preserves out-of-distribution robustness, maintaining both pretraining-distribution accuracy for broader deployment and many-body short-range repulsion.

While Large Language Models (LLMs) have achieved remarkable performance, they remain vulnerable to jailbreak attacks that circumvent safety constraints. Existing strategies, ranging from heuristic prompt engineering to computationally intensive optimization, often face significant trade-offs between effectiveness and efficiency. In this work, we propose Contextual Representation Ablation (CRA), a novel inference-time intervention framework designed to dynamically silence model guardrails. Predicated on the geometric insight that refusal behaviors are mediated by specific low-rank subspaces within the model's hidden states, CRA identifies and suppresses these refusal-inducing activation patterns during decoding without requiring expensive parameter updates or training. Empirical evaluation across multiple safety-aligned open-source LLMs demonstrates that CRA significantly outperforms baselines. These results expose the intrinsic fragility of current alignment mechanisms, revealing that safety constraints can be surgically ablated from internal representations, and underscore the urgent need for more robust defenses that secure the model's latent space.

We present EGN, a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear algebra to compute the descent direction. Leveraging the Duncan-Guttman matrix identity, the parameter update is obtained by factorizing a matrix which has the size of the mini-batch. This is particularly advantageous for large-scale machine learning problems where the dimension of the neural network parameter vector is several orders of magnitude larger than the batch size. Additionally, we show how improvements such as line search, adaptive regularization, and momentum can be seamlessly added to EGN to further accelerate the algorithm. Moreover, under mild assumptions, we prove that our algorithm converges to an epsilon-stationary point at a linear rate. Finally, our numerical experiments demonstrate that EGN consistently exceeds, or at most matches the generalization performance of well-tuned SGD, Adam, and SGN optimizers across various supervised and reinforcement learning tasks.

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when adapting to new tasks. Recently, approaches leveraging pre-trained models have gained increasing popularity in mitigating this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address this limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of the gradients. CoSO updates the model by projecting gradients onto these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspace of each task is constrained to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions for the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.

Agentic Reinforcement Learning (ARL) focuses on training large language models (LLMs) to interleave reasoning with external tool execution to solve complex tasks. Most existing ARL methods train a single shared model parameters to support both reasoning and tool use behaviors, implicitly assuming that joint training leads to improved overall agent performance. Despite its widespread adoption, this assumption has rarely been examined empirically. In this paper, we systematically investigate this assumption by introducing a Linear Effect Attribution System(LEAS), which provides quantitative evidence of interference between reasoning and tool-use behaviors. Through an in-depth analysis, we show that these two capabilities often induce misaligned gradient directions, leading to training interference that undermines the effectiveness of joint optimization and challenges the prevailing ARL paradigm. To address this issue, we propose Disentangled Action Reasoning Tuning(DART), a simple and efficient framework that explicitly decouples parameter updates for reasoning and tool-use via separate low-rank adaptation modules. Experimental results show that DART consistently outperforms baseline methods with averaged 6.35 percent improvements and achieves performance comparable to multi-agent systems that explicitly separate tool-use and reasoning using a single model.

How cost-effectively can strong reasoning abilities be achieved in language models? Driven by this fundamental question, we present Tina, a family of tiny reasoning models achieved with high cost-efficiency. Notably, Tina demonstrates that substantial reasoning performance can be developed using only minimal resources, by applying parameter-efficient updates during reinforcement learning (RL), using low-rank adaptation (LoRA), to an already tiny 1.5B parameter base model. This minimalist approach produces models that achieve reasoning performance which is competitive with, and sometimes surpasses, SOTA RL reasoning models built upon the same base model. Crucially, this is achieved at a tiny fraction of the computational post-training cost employed by existing SOTA models. In fact, the best Tina model achieves a >20\% reasoning performance increase and 43.33\% Pass@1 accuracy on AIME24, at only \$9 USD post-training and evaluation cost (i.e., an estimated 260x cost reduction). Our work reveals the surprising effectiveness of efficient RL reasoning via LoRA. We validate this across multiple open-source reasoning datasets and various ablation settings starting with a single, fixed set of hyperparameters. Furthermore, we hypothesize that this effectiveness and efficiency stem from LoRA rapidly adapting the model to the structural format of reasoning rewarded by RL, while largely preserving the base model's underlying knowledge. In service of accessibility and open research, we fully open-source all code, training logs, and model weights \& checkpoints.

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of parameters and memory, either through low-rank adaptation or factorization. While effective for fine-tuning, low-rank structures are generally less suitable for pretraining because they restrict parameters to a low-dimensional subspace. In this work, we propose to parameterize the weights as a sum of low-rank and sparse matrices for pretraining, which we call SLTrain. The low-rank component is learned via matrix factorization, while for the sparse component, we employ a simple strategy of uniformly selecting the sparsity support at random and learning only the non-zero entries with the fixed support. While being simple, the random fixed-support sparse learning strategy significantly enhances pretraining when combined with low-rank learning. Our results show that SLTrain adds minimal extra parameters and memory costs compared to pretraining with low-rank parameterization, yet achieves substantially better performance, which is comparable to full-rank training. Remarkably, when combined with quantization and per-layer updates, SLTrain can reduce memory requirements by up to 73% when pretraining the LLaMA 7B model.

LoRA-based large model parameter-efficient fine-tuning (PEFT) methods use low-rank de- composition to approximate updates to model parameters. However, compared to full- parameter fine-tuning, low-rank updates often lead to a performance gap in downstream tasks. To address this, we introduce DropLoRA, a novel pruning-based approach that focuses on pruning the rank dimension. Unlike conven- tional methods that attempt to overcome the low-rank bottleneck, DropLoRA innovatively integrates a pruning module between the two low-rank matrices in LoRA to simulate dy- namic subspace learning. This dynamic low- rank subspace learning allows DropLoRA to overcome the limitations of traditional LoRA, which operates within a static subspace. By continuously adapting the learning subspace, DropLoRA significantly boosts performance without incurring additional training or infer- ence costs. Our experimental results demon- strate that DropLoRA consistently outperforms LoRA in fine-tuning the LLaMA series across a wide range of large language model gener- ation tasks, including commonsense reason- ing, mathematical reasoning, code generation, and instruction-following. Our code is avail- able at https://github.com/TayeeChang/DropLoRA.

Despite the dominance and effectiveness of scaling, resulting in large networks with hundreds of billions of parameters, the necessity to train overparametrized models remains poorly understood, and alternative approaches do not necessarily make it cheaper to train high-performance models. In this paper, we explore low-rank training techniques as an alternative approach to training large neural networks. We introduce a novel method called ReLoRA, which utilizes low-rank updates to train high-rank networks. We apply ReLoRA to pre-training transformer language models with up to 350M parameters and demonstrate comparable performance to regular neural network training. Furthermore, we observe that the efficiency of ReLoRA increases with model size, making it a promising approach for training multi-billion-parameter networks efficiently. Our findings shed light on the potential of low-rank training techniques and their implications for scaling laws.

We study the parameter placement problem: given a fixed budget of k trainable entries within the B matrix of a LoRA adapter (A frozen), does the choice of which k matter? Under supervised fine-tuning, random and informed subsets achieve comparable performance. Under GRPO on base models, random placement fails to improve over the base model, while gradient-informed placement recovers standard LoRA accuracy. This regime dependence traces to gradient structure: SFT gradients are low-rank and directionally stable, so any subset accumulates coherent updates; GRPO gradients are high-rank and near-orthogonal across steps, so only elements with consistently signed gradients retain the learning signal. Our scoring procedure identifies these critical parameters in under 10 seconds at less than 0.5% of training cost. Selected parameters concentrate on residual-stream-writing projections (V, O, Down), stable across model families and scales (1.5B - 8B).

Low-rank adaptation (LoRA) makes it cheap to train many domain- and task-specific language model adapters, but whether two adapters can be merged is usually discovered only after both have been fully trained and evaluated. This late feedback is costly: adapters that are strong in isolation can interfere destructively once their updates are combined. We ask whether this outcome can be anticipated. We formalize adapter mergeability as the degree to which an adapter preserves its single-task utility after merging, and show that it can be forecast from signals measured in the first few percent of training -- chiefly how the low-rank updates and their gradients align across tasks and how much they disturb shared representations. We package these signals into MergeProbe, a lightweight predictor that estimates pairwise and set-level retention and turns the estimate into a concrete decision: merge directly, reweight, prune, or route. On MERGE-PEFT, a five-domain benchmark spanning math, code, science, instruction following, and safety, MergeProbe attains the best average and worst-case retention among strong interference-aware merge baselines while adding far less deployment overhead than full task routing. This turns LoRA merging from a post-hoc engineering step into an anticipatory measurement problem.

Low-rank adaptation (LoRA) is a widely used parameter-efficient fine-tuning (PEFT) method that learns weight updates ΔW = AB for pretrained weights W through low-rank adapters A and B. While LoRA ensures hardware efficiency, its low-rank weight updates limit adaptation performance. In this paper, we propose low-rank interconnected adaptation across layers (Lily), a novel PEFT method that introduces an interconnected framework with locally shared A and globally shared B experts. This structure eliminates redundant per-layer AB pairs, enabling higher-rank ΔW with equal or fewer parameters. To enhance expressiveness, we use data-dependent routers to determine A-B interconnections, preventing B experts from converging to the same behavior and improving representational power across domains. Experiments across modalities, architectures, and model sizes demonstrate Lily's superior performance and efficiency. GitHub: https://github.com/yibozhong/lily

Training of large neural networks requires significant computational resources. Despite advances using low-rank adapters and quantization, pretraining of models such as LLMs on consumer hardware has not been possible without model sharding, offloading during training, or per-layer gradient updates. To address these limitations, we propose LoQT, a method for efficiently training quantized models. LoQT uses gradient-based tensor factorization to initialize low-rank trainable weight matrices that are periodically merged into quantized full-rank weight matrices. Our approach is suitable for both pretraining and fine-tuning of models, which we demonstrate experimentally for language modeling and downstream task adaptation. We find that LoQT enables efficient training of models up to 7B parameters on a consumer-grade 24GB GPU. We also demonstrate the feasibility of training a 13B parameter model using per-layer gradient updates on the same hardware.

As the number of model parameters increases, parameter-efficient fine-tuning (PEFT) has become the go-to choice for tailoring pre-trained large language models. Low-rank Adaptation (LoRA) uses a low-rank update method to simulate full parameter fine-tuning, which is widely used to reduce resource requirements. However, decreasing the rank encounters challenges with limited representational capacity when compared to full parameter fine-tuning. We present SMoA, a high-rank Structured MOdulation Adapter that uses fewer trainable parameters while maintaining a higher rank, thereby improving the model's representational capacity and offering improved performance potential. The core idea is to freeze the original pretrained weights and selectively amplify or suppress important features of the original weights across multiple subspaces. The subspace mechanism provides an efficient way to increase the capacity and complexity of a model. We conduct both theoretical analyses and empirical studies on various tasks. Experiment results show that SMoA outperforms LoRA and its variants on 10 tasks, with extensive ablation studies validating its effectiveness.

Parameter-efficient fine-tuning methods have gained considerable popularity for adapting large-scale models to downstream tasks, particularly LoRA and its variants. Existing methods perform low-rank adaptation over the full parameter space. However, fine-tuning within a subspace can achieve comparable effectiveness. Inspired by the observation that pre-trained models possess non-trivial null spaces, we propose Null-space based Low-Rank Adaptation (Null-LoRA). Null-LoRA effectively reduces redundancy and enhances effective rank by freezing portions of the low-rank matrices. To further improve parameter efficiency, Null-LoRA constrains the entire incremental update within the null space, maximizing the utilization of incremental updates to adapt to new task paradigms. Null-LoRA surpasses the state of the art with fewer parameters in extensive experiments across image-text retrieval and visual question answering tasks.

Low-Rank Adaptation (LoRA) has become a cornerstone of parameter-efficient fine-tuning (PEFT). Yet, its efficacy is hampered by two fundamental limitations: semantic drift, by treating all update directions with equal importance, and structural incoherence, from adapting layers independently, resulting in suboptimal, uncoordinated updates. To remedy these, we propose StructLoRA, a framework that addresses both limitations through a principled, dual-component design: (1) an Information Bottleneck-guided filter that prunes task-irrelevant directions to mitigate semantic drift, and (2) a lightweight, training-only graph-based coordinator that enforces inter-layer consistency to resolve structural incoherence. Extensive experiments across large language model , vision language model, and vision model (including LLaMA, LLaVA, and ViT) demonstrate that StructLoRA consistently establishes a new state-of-the-art, outperforming not only vanilla LoRA but also advanced dynamic rank allocation and sparsity-based methods. Notably, the benefits are particularly pronounced in challenging low-rank and low-data regimes. Crucially, since our proposed modules operate only during training, StructLoRA enhances performance with zero additional inference cost, advancing the focus of PEFT -- from mere parameter compression to a more holistic optimization of information quality and structural integrity.

Parameter-Efficient Fine-Tuning (PEFT) methods, especially LoRA, are widely used for adapting pre-trained models to downstream tasks due to their computational and storage efficiency. However, in the context of LoRA and its variants, the potential of activation subspaces corresponding to tail eigenvectors remains substantially under-exploited, which may lead to suboptimal fine-tuning performance. In this work, we propose Astra (Activation-Space Tail-Eigenvector Low-Rank Adaptation), a novel PEFT method that leverages the tail eigenvectors of the model output activations-estimated from a small task-specific calibration set-to construct task-adaptive low-rank adapters. By constraining updates to the subspace spanned by these tail eigenvectors, Astra achieves faster convergence and improved downstream performance with a significantly reduced parameter budget. Extensive experiments across natural language understanding (NLU) and natural language generation (NLG) tasks demonstrate that Astra consistently outperforms existing PEFT baselines across 16 benchmarks and even surpasses full fine-tuning (FFT) in certain scenarios.

Supervised fine-tuning is the most common method to adapt large language models (LLMs) to downstream tasks, but full fine-tuning LLMs requires massive computational resources. Recently, parameter-efficient fine-tuning (PEFT) methods have been widely studied due to its cost-effectiveness. LoRA is one of the most widely used methods, which assumes that the optimization process is essentially low-dimensional. Although LoRA fine-tuning is effective, there is still a performance gap compared to full fine-tuning, since its weight update is limited to low-rank matrices. In order to break the low-rank bottleneck in LoRA Optimization, we propose PeriodicLoRA (PLoRA), which accumulates low-rank update matrices multiple times to achieve a higher update rank. PLoRA has multiple training stages. During each stage, we still update only the LoRA weights. However, at the end of each stage, we unload the LoRA weights into the backbone parameters and then reinitialize the LoRA states. Experimental results show that PLoRA has stronger learning ability, approximately 1.8 times that of LoRA's learning ability at most, but it does not increase memory usage. Further, we introduce a momentum-based unloading strategy for PLoRA to mitigate the training instability.

The conventional modus operandi for adapting pre-trained vision-language models (VLMs) during test-time involves tuning learnable prompts, ie, test-time prompt tuning. This paper introduces Test-Time Low-rank adaptation (TTL) as an alternative to prompt tuning for zero-shot generalization of large-scale VLMs. Taking inspiration from recent advancements in efficiently fine-tuning large language models, TTL offers a test-time parameter-efficient adaptation approach that updates the attention weights of the transformer encoder by maximizing prediction confidence. The self-supervised confidence maximization objective is specified using a weighted entropy loss that enforces consistency among predictions of augmented samples. TTL introduces only a small amount of trainable parameters for low-rank adapters in the model space while keeping the prompts and backbone frozen. Extensive experiments on a variety of natural distribution and cross-domain tasks show that TTL can outperform other techniques for test-time optimization of VLMs in strict zero-shot settings. Specifically, TTL outperforms test-time prompt tuning baselines with a significant improvement on average. Our code is available at at https://github.com/Razaimam45/TTL-Test-Time-Low-Rank-Adaptation.

Prompt tuning, in which a base pretrained model is adapted to each task via conditioning on learned prompt vectors, has emerged as a promising approach for efficiently adapting large language models to multiple downstream tasks. However, existing methods typically learn soft prompt vectors from scratch, and it has not been clear how to exploit the rich cross-task knowledge with prompt vectors in a multitask learning setting. We propose multitask prompt tuning (MPT), which first learns a single transferable prompt by distilling knowledge from multiple task-specific source prompts. We then learn multiplicative low rank updates to this shared prompt to efficiently adapt it to each downstream target task. Extensive experiments on 23 NLP datasets demonstrate that our proposed approach outperforms the state-of-the-art methods, including the full finetuning baseline in some cases, despite only tuning 0.035% as many task-specific parameters.

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by substantial computational challenges, particularly regarding the memory and compute resources required for training and fine-tuning. Numerous approaches have been explored to address these issues, such as LoRA. While these methods are effective for fine-tuning, their application to pre-training is significantly more challenging due to the need to learn vast datasets. Motivated by this issue, we aim to address the following questions: Can parameter- or memory-efficient methods enhance pre-training efficiency while achieving performance comparable to full-model training? How can the performance gap be narrowed? To this end, the contributions of this work are the following. (1) We begin by conducting a comprehensive survey that summarizes state-of-the-art methods for efficient pre-training. (2) We perform a benchmark evaluation of several representative memory efficient pre-training approaches to comprehensively evaluate their performance across model sizes. We observe that with a proper choice of optimizer and hyperparameters, full-rank training delivers the best performance, as expected. We also notice that incorporating high-rank updates in low-rank approaches is the key to improving their performance. (3) Finally, we propose two practical techniques, namely weight refactorization and momentum reset, to enhance the performance of efficient pre-training methods. We observe that applying these techniques to the low-rank method (on a 1B model) can achieve a lower perplexity than popular memory efficient algorithms such as GaLore and Fira, while simultaneously using about 25% less memory.

Large Language Models (LLMs) have transformed both everyday life and scientific research. However, adapting LLMs from general-purpose models to specialized tasks remains challenging, particularly in resource-constrained environments. Low-Rank Adaptation (LoRA), a prominent method within Parameter-Efficient Fine-Tuning (PEFT), has emerged as a promising approach to LLMs by approximating model weight updates using low-rank decomposition. However, LoRA is limited by its uniform rank ( r ) allocation to each incremental matrix, and existing rank allocation techniques aimed at addressing this issue remain computationally inefficient, complex, and unstable, hindering practical applications. To address these limitations, we propose Sensitivity-LoRA, an efficient fine-tuning method that dynamically allocates ranks to weight matrices based on both their global and local sensitivities. It leverages the second-order derivatives (Hessian Matrix) of the loss function to effectively capture weight sensitivity, enabling optimal rank allocation with minimal computational overhead. Our experimental results have demonstrated robust effectiveness, efficiency and stability of Sensitivity-LoRA across diverse tasks and benchmarks.

Parameter-efficient fine-tuning (PEFT) aims to adapt pre-trained vision models to downstream tasks. Among PEFT paradigms, sparse tuning achieves remarkable performance by adjusting only the weights most relevant to downstream tasks, rather than densely tuning the entire weight matrix. Current methods follow a two-stage paradigm. First, it locates task-relevant weights by gradient information, which overlooks the parameter adjustments during fine-tuning and limits the performance. Second, it updates only the located weights by applying a sparse mask to the gradient of the weight matrix, which results in high memory usage due to the storage of all weight matrices in the optimizer. In this paper, we propose a one-stage method named SNELLA to overcome the above limitations. For memory usage, SNELLA selectively updates the weight matrix by adding it to another sparse matrix that is merged by two low-rank learnable matrices. We extend the low-rank decomposition by introducing nonlinear kernel functions, thereby increasing the rank of the resulting merged matrix to prevent the interdependency among weight updates, enabling better adaptation to downstream tasks. For locating task-relevant weights, we propose an adaptive bi-level sparsity allocation mechanism that encourages weights to compete across and inside layers based on their importance scores in an end-to-end manner. Extensive experiments are conducted on classification, segmentation, and generation tasks using different pre-trained vision models. The results show that SNELLA achieves SOTA performance with low memory usage. Notably, SNELLA obtains 1.8% (91.9% v.s. 90.1%) higher Top-1 accuracy on the FGVC benchmark compared to SPT-LoRA. Compared to previous methods, SNELLA achieves a memory reduction of 31.1%-39.9% across models with parameter scales from 86M to 632M. Our source codes are available at https://github.com/ssfgunner/SNELL.

Fine-tuning large pre-trained foundation models, such as the 175B GPT-3, has attracted more attention for downstream tasks recently. While parameter-efficient fine-tuning methods have been proposed and proven effective without retraining all model parameters, their performance is limited by the capacity of incremental modules, especially under constrained parameter budgets. \\ To overcome this challenge, we propose CapaBoost, a simple yet effective strategy that enhances model capacity by leveraging low-rank updates through parallel weight modules in target layers. By applying static random masks to the shared weight matrix, CapaBoost constructs a diverse set of weight matrices, effectively increasing the rank of incremental weights without adding parameters. Notably, our approach can be seamlessly integrated into various existing parameter-efficient fine-tuning methods. We extensively validate the efficacy of CapaBoost through experiments on diverse downstream tasks, including natural language understanding, question answering, and image classification. Our results demonstrate significant improvements over baselines, without incurring additional computation or storage costs. Our code is available at https://github.com/LINs-lab/CapaBoost.

Existing parameter-efficient fine-tuning (PEFT) methods for large language models (LLMs), such as LoRA and PiSSA, constrain model updates to low-rank subspaces, limiting their expressiveness and leading to suboptimal performance on complex tasks. To address this, we introduce High-rank Distributed PiSSA (HD-PiSSA), a distributed PEFT approach that initializes orthogonal adapters across different devices and aggregates their delta updates collectively on W for fine-tuning. Unlike Data Parallel LoRA or PiSSA, which maintain identical adapters across all devices, HD-PiSSA assigns different principal components of the pre-trained weights to each GPU, significantly expanding the range of update directions. This results in over 16x higher effective updated ranks than data-parallel LoRA or PiSSA when fine-tuning on 8 GPUs with the same per-device adapter rank. Empirically, we evaluate HD-PiSSA across various challenging downstream tasks, including mathematics, code generation, and multi-task learning. In the multi-task setting, HD-PiSSA achieves average gains of 10.0 absolute points (14.63%) over LoRA and 4.98 points (6.60%) over PiSSA across 12 benchmarks, demonstrating its benefits from the extra optimization flexibility.

Large Language Models (LLMs) have demonstrated strong reasoning and memorization capabilities via pretraining on massive textual corpora. However, this poses risk of privacy and copyright violations, highlighting the need for efficient machine unlearning methods that remove sensitive data without retraining from scratch. While Gradient Ascent (GA) is commonly used to unlearn by reducing the likelihood of generating unwanted content, it leads to unstable optimization and catastrophic forgetting of retrained knowledge. We find that combining GA with low-rank adaptation results in poor trade-offs between computational cost and generative performance. To address these challenges, we propose Low-rank Knowledge Unlearning (LoKU), a novel framework that enables robust and efficient unlearning for LLMs. First, we introduce Inverted Hinge Loss, which suppresses unwanted tokens while maintaining fluency by boosting the probability of the next most likely token. Second, we develop a data-adaptive initialization for LoRA adapters via low-rank approximation weighted with relative Fisher information, thereby focusing updates on parameters critical for removing targeted knowledge. Experiments on the Training Data Extraction Challenge dataset using GPT-Neo models as well as on the TOFU benchmark with Phi-1.5B and Llama2-7B models demonstrate that our approach effectively removes sensitive information while maintaining reasoning and generative capabilities with minimal impact. Our implementation can be found in https://github.com/csm9493/efficient-llm-unlearning.

Long-context reasoning requires accurately identifying relevant information in extensive, noisy input contexts. Previous research shows that using test-time learning to encode context directly into model parameters can effectively enable reasoning over noisy information. However, meta-learning methods for enabling test-time learning are prohibitively memory-intensive, preventing their application to long context settings. In this work, we propose PERK (Parameter Efficient Reasoning over Knowledge), a scalable approach for learning to encode long input contexts using gradient updates to a lightweight model adapter at test time. Specifically, PERK employs two nested optimization loops in a meta-training phase. The inner loop rapidly encodes contexts into a low-rank adapter (LoRA) that serves as a parameter-efficient memory module for the base model. Concurrently, the outer loop learns to use the updated adapter to accurately recall and reason over relevant information from the encoded long context. Our evaluations on several long-context reasoning tasks show that PERK significantly outperforms the standard prompt-based long-context baseline, achieving average absolute performance gains of up to 90% for smaller models (GPT-2) and up to 27% for our largest evaluated model, Qwen-2.5-0.5B. In general, PERK is more robust to reasoning complexity, length extrapolation, and the locations of relevant information in contexts. Finally, we show that while PERK is memory-intensive during training, it scales more efficiently at inference time than prompt-based long-context inference.

Fine-tuning large pre-trained language models on downstream tasks has become an important paradigm in NLP. However, common practice fine-tunes all of the parameters in a pre-trained model, which becomes prohibitive when a large number of downstream tasks are present. Therefore, many fine-tuning methods are proposed to learn incremental updates of pre-trained weights in a parameter efficient way, e.g., low-rank increments. These methods often evenly distribute the budget of incremental updates across all pre-trained weight matrices, and overlook the varying importance of different weight parameters. As a consequence, the fine-tuning performance is suboptimal. To bridge this gap, we propose AdaLoRA, which adaptively allocates the parameter budget among weight matrices according to their importance score. In particular, AdaLoRA parameterizes the incremental updates in the form of singular value decomposition. Such a novel approach allows us to effectively prune the singular values of unimportant updates, which is essentially to reduce their parameter budget but circumvent intensive exact SVD computations. We conduct extensive experiments with several pre-trained models on natural language processing, question answering, and natural language generation to validate the effectiveness of AdaLoRA. Results demonstrate that AdaLoRA manifests notable improvement over baselines, especially in the low budget settings. Our code is publicly available at https://github.com/QingruZhang/AdaLoRA .

Low-Rank Adaptation (LoRA) has become the de facto parameter-efficient fine-tuning (PEFT) method for large language models (LLMs) by constraining weight updates to low-rank matrices. Recent works such as Tied-LoRA, VeRA, and VB-LoRA push efficiency further by introducing additional constraints to reduce the trainable parameter space. In this paper, we show that the parameter space reduction strategies employed by these LoRA variants can be formulated within a unified framework, Uni-LoRA, where the LoRA parameter space, flattened as a high-dimensional vector space R^D, can be reconstructed through a projection from a subspace R^d, with d ll D. We demonstrate that the fundamental difference among various LoRA methods lies in the choice of the projection matrix, P in R^{D times d}.Most existing LoRA variants rely on layer-wise or structure-specific projections that limit cross-layer parameter sharing, thereby compromising parameter efficiency. In light of this, we introduce an efficient and theoretically grounded projection matrix that is isometric, enabling global parameter sharing and reducing computation overhead. Furthermore, under the unified view of Uni-LoRA, this design requires only a single trainable vector to reconstruct LoRA parameters for the entire LLM - making Uni-LoRA both a unified framework and a "one-vector-only" solution. Extensive experiments on GLUE, mathematical reasoning, and instruction tuning benchmarks demonstrate that Uni-LoRA achieves state-of-the-art parameter efficiency while outperforming or matching prior approaches in predictive performance. Our code is available at https://github.com/KaiyangLi1992/Uni-LoRA.

Continual machine unlearning aims to remove the influence of data that should no longer be retained, while preserving the usefulness of the model on everything else. This setting becomes especially difficult when deletion requests arrive sequentially, because the model must repeatedly adapt without erasing previously retained knowledge. Low-Rank Adaptation (LoRA) offers an efficient way to implement such updates, but naively combining many sequential LoRA modules leads to parameter collision, causing strong interference between tasks. We propose a static alternative based on Singular Value Decomposition (SVD)-guided orthogonal subspace projection. Our method constrains each new LoRA update during training so that it lies in the orthogonal complement of the subspaces used by earlier unlearning tasks. This preserves task isolation without requiring dynamic routing at deployment. Experiments on CIFAR-100 with ResNet-20 and on MNIST show stable behavior across long sequences of unlearning tasks. After thirty sequential unlearning tasks, state-of-the-art static fusion reduces retained accuracy from 60.39\% to 12.70\%, whereas the proposed in-training constrained optimization maintains baseline performance (sim58.1\%) while preserving strong unlearning efficacy.

Popular PEFT methods achieve parameter efficiency by assuming that incremental weight updates are inherently low-rank, which often leads to a performance gap compared to full fine-tuning. While recent methods have attempted to address this limitation, they typically lack sufficient parameter and memory efficiency. We propose VectorFit, an effective and easily deployable approach that adaptively trains the singular vectors and biases of pre-trained weight matrices. We demonstrate that the utilization of structural and transformational characteristics of pre-trained weights enables high-rank updates comparable to those of full fine-tuning. As a result, VectorFit achieves superior performance with 9X less trainable parameters compared to state-of-the-art PEFT methods. Through extensive experiments over 17 datasets spanning diverse language and vision tasks such as natural language understanding and generation, question answering, image classification, and image generation, we exhibit that VectorFit consistently outperforms baselines, even in extremely low-budget scenarios.

Modern Transformer-based models frequently suffer from miscalibration, producing overconfident predictions that do not reflect true empirical frequencies. This work investigates the calibration dynamics of LoRA: Low-Rank Adaptation and a novel hyper-network-based adaptation framework as parameter-efficient alternatives to full fine-tuning for RoBERTa. Evaluating across the GLUE benchmark, we demonstrate that LoRA-based adaptation consistently achieves calibration parity with (and in specific tasks exceeds) full fine-tuning, while maintaining significantly higher parameter efficiency. We further explore a dynamic approach where a shared hyper-network generates LoRA factors (A and B matrices) to induce structural coupling across layers. This approach produced results similar to standard LoRA fine-tuning, even achieving better MCC on CoLA dataset. Our study also reveal a critical trade-off: constraining the adaptation space (e.g., freezing matrices A) acts as a powerful regularizer that enhances Expected Calibration Error (ECE), but necessitates a carefully balanced sacrifice in downstream task accuracy. To support future research, we provide a unified and reproducible implementation of contemporary calibration metrics, including ECE, MCE, and ACE. Our findings clarify the relationship between parameter efficiency and probabilistic reliability, positioning structured low-rank updates as a viable foundation for uncertainty-aware Transformer architectures. Code available at: https://github.com/btrojan-official/HypeLoRA

DIFF Transformer improves attention allocation by enhancing focus on relevant context while suppressing noise. It introduces a differential attention mechanism that calculates the difference between two independently generated attention distributions, effectively reducing noise and promoting sparse attention patterns. However, the independent signal generation in DIFF Transformer results in parameter redundancy and suboptimal utilization of information. In this work, we propose Shared DIFF Transformer, which draws on the idea of a differential amplifier by introducing a shared base matrix to model global patterns and incorporating low-rank updates to enhance task-specific flexibility. This design significantly reduces parameter redundancy, improves efficiency, and retains strong noise suppression capabilities. Experimental results show that, compared to DIFF Transformer, our method achieves better performance in tasks such as long-sequence modeling, key information retrieval, and in-context learning. Our work provides a novel and efficient approach to optimizing differential attention mechanisms and advancing robust Transformer architectures.

Large pre-trained Transformer models achieve state-of-the-art results across diverse language and reasoning tasks, but full fine-tuning incurs substantial storage, memory, and computational overhead. Parameter-efficient fine-tuning (PEFT) methods mitigate these costs by learning only a small subset of task-specific parameters, yet existing approaches either introduce inference-time latency (adapter modules), suffer from suboptimal convergence (randomly initialized low-rank updates), or rely on fixed rank choices that may not match task complexity (Kronecker-based decompositions). We propose SoKA (SVD on Kronecker Adaptation), a novel PEFT strategy that combines Kronecker-product tensor factorization with SVD-driven initialization and spectrum-aware dynamic rank selection. Our Kronecker-Product SVD (KPSVD) procedure extracts principal components of the full weight update into compact Kronecker factors, while an adaptive rank selection algorithm uses energy-threshold and elbow-point criteria to prune negligible components. Empirical evaluation on LLaMA2-7B across arithmetic reasoning (GSM8K), formal mathematics (MATH), and code generation (MBPP) demonstrates that SoKA requires only 0.99M trainable parameters, 25% fewer than LoRA/PiSSA, while matching or exceeding baseline performance. Moreover, SoKA exhibits faster convergence and more stable gradients, highlighting its robustness and efficiency for large-scale model adaptation.

Parameter-efficient adaptation of pretrained vision models is commonly performed through linear probes, prompts, low-rank updates, or lightweight residual modules. While effective, these methods usually treat adaptation as a discrete Euclidean perturbation of frozen representations, without explicitly modeling the geometry of the task-induced feature displacement. We propose MC-RFM, a mixed-curvature Riemannian flow-matching framework for few-shot adaptation of frozen visual backbones. The key idea is to represent adapted features on a product manifold combining a hyperbolic factor, which captures hierarchy-sensitive semantic structure, and a Euclidean factor, which preserves locally discriminative visual variation. Adaptation is formulated as a task-conditioned continuous transport from frozen features to support-set prototypes, trained with a flow-matching objective and coupled to a hybrid prototype-linear classifier. The method is lightweight, backbone-agnostic, and operates entirely on cached frozen features. Across seven visual recognition benchmarks, five frozen backbones, and 1/4/16-shot regimes, MC-RFM is the best-performing method in a majority of evaluated settings, with the strongest gains on Transformer backbones and fine-grained datasets. Ablations show that the mixed-curvature head, task conditioning, adaptive branch gating, prototype shrinkage, and discriminative supervision each contribute to performance. These results suggest that few-shot adaptation benefits not only from deciding which parameters to update, but also from modeling how representations should move through a geometry matched to the structure of the downstream task.

Adapting large pretrained models to new tasks efficiently and continually is crucial for real-world deployment but remains challenging due to catastrophic forgetting and the high cost of retraining. While parameter-efficient tuning methods like low rank adaptation (LoRA) reduce computational demands, they lack mechanisms for strict continual learning and knowledge integration, without relying on data replay, or multiple adapters. We propose Share, a novel approach to parameter efficient continual finetuning that learns and dynamically updates a single, shared low-rank subspace, enabling seamless adaptation across multiple tasks and modalities. Share constructs a foundational subspace that extracts core knowledge from past tasks and incrementally integrates new information by identifying essential subspace directions. Knowledge from each new task is incorporated into this evolving subspace, facilitating forward knowledge transfer, while minimizing catastrophic interference. This approach achieves up to 100x parameter reduction and 281x memory savings over traditional LoRA methods, maintaining performance comparable to jointly trained models. A single Share model can replace hundreds of task-specific LoRA adapters, supporting scalable, asynchronous continual learning. Experiments across image classification, natural language understanding, 3D pose estimation, and text-to-image generation validate its effectiveness, making Share a practical and scalable solution for lifelong learning in large-scale AI systems.

Parameter-efficient fine-tuning (PEFT) enables efficient adaptation of large language models, but existing MoE-based PEFT methods typically improve capacity by storing multiple full LoRA experts, causing adapter storage to grow linearly with the number of experts and restricting adaptation to a fixed expert pool. We ask whether MoE-based PEFT can produce instance-specific adaptations without explicitly storing a separate LoRA module for each expert. To address this gap, we propose MoEGen, an adaptation framework that shifts MoE-based PEFT from expert selection to expert-conditioned parameter generation. Instead of storing each expert as a full LoRA adapter, MoEGen represents each expert as a small learnable vector, termed an expert code. It routes each input over these vectors and uses their weighted combination to condition a lightweight hypernetwork that generates input-specific low-rank updates. This design decouples expert capacity from adapter storage while enabling instance-conditioned adaptation. Experiments on eight commonsense reasoning benchmarks show consistent improvements over strong static and MoE-based PEFT baselines across three backbones. MoEGen also performs strongly in joint medical and legal-domain adaptation.

Training large-scale neural networks in vision, and multimodal domains demands substantial memory resources, primarily due to the storage of optimizer states. While LoRA, a popular parameter-efficient method, reduces memory usage, it often suffers from suboptimal performance due to the constraints of low-rank updates. Low-rank gradient projection methods (e.g., GaLore, Flora) reduce optimizer memory by projecting gradients and moment estimates into low-rank spaces via singular value decomposition or random projection. However, they fail to account for inter-projection correlation, causing performance degradation, and their projection strategies often incur high computational costs. In this paper, we present COAP (Correlation-Aware Gradient Projection), a memory-efficient method that minimizes computational overhead while maintaining training performance. Evaluated across various vision, language, and multimodal tasks, COAP outperforms existing methods in both training speed and model performance. For LLaMA-1B, it reduces optimizer memory by 61% with only 2% additional time cost, achieving the same PPL as AdamW. With 8-bit quantization, COAP cuts optimizer memory by 81% and achieves 4x speedup over GaLore for LLaVA-v1.5-7B fine-tuning, while delivering higher accuracy.

Large language models (LLMs) can be adapted to new tasks using parameter-efficient fine-tuning (PEFT) methods that modify only a small number of trainable parameters, often through low-rank updates. In this work, we adopt a quantum-information-inspired perspective to understand their effectiveness. From this perspective, low-rank parameterizations naturally correspond to low-dimensional Matrix Product States (MPS) representations, which enable entanglement-based characterizations of parameter structure. Thereby, we term and measure "Artificial Entanglement", defined as the entanglement entropy of the parameters in artificial neural networks (in particular the LLMs). We first study the representative low-rank adaptation (LoRA) PEFT method, alongside full fine-tuning (FFT), using LLaMA models at the 1B and 8B scales trained on the Tulu3 and OpenThoughts3 datasets, and uncover: (i) Internal artificial entanglement in the updates of query and value projection matrices in LoRA follows a volume law with a central suppression (termed as the "Entanglement Valley"), which is sensitive to hyper-parameters and is distinct from that in FFT; (ii) External artificial entanglement in attention matrices, corresponding to token-token correlations in representation space, follows an area law with logarithmic corrections and remains robust to LoRA hyper-parameters and training steps. Drawing a parallel to the No-Hair Theorem in black hole physics, we propose that although LoRA and FFT induce distinct internal entanglement signatures, such differences do not manifest in the attention outputs, suggesting a "no-hair" property that results in the effectiveness of low rank updates. We further provide theoretical support based on random matrix theory, and extend our analysis to an MPS Adaptation PEFT method, which exhibits qualitatively similar behaviors.

Gigantic pre-trained models have become central to natural language processing (NLP), serving as the starting point for fine-tuning towards a range of downstream tasks. However, two pain points persist for this paradigm: (a) as the pre-trained models grow bigger (e.g., 175B parameters for GPT-3), even the fine-tuning process can be time-consuming and computationally expensive; (b) the fine-tuned model has the same size as its starting point by default, which is neither sensible due to its more specialized functionality, nor practical since many fine-tuned models will be deployed in resource-constrained environments. To address these pain points, we propose a framework for resource- and parameter-efficient fine-tuning by leveraging the sparsity prior in both weight updates and the final model weights. Our proposed framework, dubbed Dually Sparsity-Embedded Efficient Tuning (DSEE), aims to achieve two key objectives: (i) parameter efficient fine-tuning - by enforcing sparsity-aware low-rank updates on top of the pre-trained weights; and (ii) resource-efficient inference - by encouraging a sparse weight structure towards the final fine-tuned model. We leverage sparsity in these two directions by exploiting both unstructured and structured sparse patterns in pre-trained language models via a unified approach. Extensive experiments and in-depth investigations, with diverse network backbones (i.e., BERT, RoBERTa, and GPT-2) on dozens of datasets, consistently demonstrate impressive parameter-/inference-efficiency, while maintaining competitive downstream performance. For instance, DSEE saves about 25% inference FLOPs while achieving comparable performance, with 0.5% trainable parameters on BERT. Codes are available in https://github.com/VITA-Group/DSEE.

While Large Language Models (LLMs) have exhibited remarkable emergent capabilities through extensive pre-training, they still face critical limitations in generalizing to specialized domains and handling diverse linguistic variations, known as distribution shifts. In this paper, we propose a Test-Time Learning (TTL) paradigm for LLMs, namely TLM, which dynamically adapts LLMs to target domains using only unlabeled test data during testing. Specifically, we first provide empirical evidence and theoretical insights to reveal that more accurate predictions from LLMs can be achieved by minimizing the input perplexity of the unlabeled test data. Based on this insight, we formulate the Test-Time Learning process of LLMs as input perplexity minimization, enabling self-supervised enhancement of LLM performance. Furthermore, we observe that high-perplexity samples tend to be more informative for model optimization. Accordingly, we introduce a Sample Efficient Learning Strategy that actively selects and emphasizes these high-perplexity samples for test-time updates. Lastly, to mitigate catastrophic forgetting and ensure adaptation stability, we adopt Low-Rank Adaptation (LoRA) instead of full-parameter optimization, which allows lightweight model updates while preserving more original knowledge from the model. We introduce the AdaptEval benchmark for TTL and demonstrate through experiments that TLM improves performance by at least 20% compared to original LLMs on domain knowledge adaptation.

Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have significantly reduced the number of trainable parameters needed in fine-tuning large language models (LLMs). Subsequent developments of LoRA-style adapters have diverged into two main directions: (1) enhancing model expressivity with high-rank adapters, and (2) pushing for further parameter reduction, as exemplified by vector-based methods. However, these approaches present a trade-off, as achieving the expressivity of high-rank weight updates typically comes at the cost of sacrificing the extreme parameter efficiency offered by vector-based techniques. To address this issue, we propose a vector-based random \textbf{Te}nsor network for high-\textbf{R}ank \textbf{A}daptation (TeRA), a novel PEFT method that achieves high-rank weight updates while retaining the parameter efficiency of vector-based PEFT adapters. This is achieved by parameterizing the tensorized weight update matrix as a Tucker-like tensor network (TN), in which large randomly initialized factors are frozen and shared across layers, while only small layer-specific scaling vectors, formed by entries in diagonal factor matrices, are trained. This design effectively decouples the rank of the weight update matrix from the number of trainable parameters. Comprehensive experiments demonstrate that TeRA matches or even outperforms high-rank adapters, while requiring a trainable parameter count similar to vector-based methods. Theoretical analysis and ablation studies further validate the effectiveness of our approach.

Recent advancements in Large Language Models (LLMs) have emphasized the critical role of fine-tuning (FT) techniques in adapting LLMs to specific tasks, especially when retraining from scratch is computationally infeasible. Fine-tuning enables LLMs to leverage task- or domain-specific data, producing models that more effectively meet the requirements of targeted applications. However, conventional FT approaches often suffer from catastrophic forgetting and suboptimal data efficiency, limiting their real-world applicability. To address these challenges, this paper proposes DEAL, a novel framework that integrates Low-Rank Adaptation (LoRA) with a continuous fine-tuning strategy. By incorporating knowledge retention and adaptive parameter update modules, the framework mitigates the limitations of existing FT methods while maintaining efficiency. Experiments on 15 diverse datasets show that DEAL consistently outperforms baseline methods, yielding substantial gains in task accuracy and resource efficiency. These findings demonstrate the potential of our approach to advance continual adaptation in LLMs by enhancing task performance while improving resource efficiency. The source code is publicly available at https://github.com/zzm-black/DEAL-Continuous-Low-Rank-Fine-Tuning.

Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major obstacle that often undermines the performance of merged models. In this paper, we propose ESM (Essential Subspace Merging) , a robust framework for effective model merging. We begin by performing Principal Component Analysis (PCA) on feature shifts induced by parameter updates. The resulting principal directions span an essential subspace that dominantly influences feature representations. Each task's parameter update matrix is projected onto its respective essential subspace for low-rank decomposition before merging. This methodology mitigates inter-task interference while preserving core task-specific functionality. Furthermore, we introduce a multi-level polarized scaling strategy that amplifies parameters containing critical knowledge and suppresses redundant ones, preventing essential knowledge from being overwhelmed during fusion. Extensive experiments across multiple task sets and model scales demonstrate that our method achieves state-of-the-art performance in multi-task model merging.

Pre-trained language models, trained on large-scale corpora, demonstrate strong generalizability across various NLP tasks. Fine-tuning these models for specific tasks typically involves updating all parameters, which is resource-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as the popular LoRA family, introduce low-rank matrices to learn only a few parameters efficiently. However, during inference, the product of these matrices updates all pre-trained parameters, complicating tasks like knowledge editing that require selective updates. We propose a novel PEFT method, which conducts row and column-wise sparse low-rank adaptation (RoseLoRA), to address this challenge. RoseLoRA identifies and updates only the most important parameters for a specific task, maintaining efficiency while preserving other model knowledge. By adding a sparsity constraint on the product of low-rank matrices and converting it to row and column-wise sparsity, we ensure efficient and precise model updates. Our theoretical analysis guarantees the lower bound of the sparsity with respective to the matrix product. Extensive experiments on five benchmarks across twenty datasets demonstrate that RoseLoRA outperforms baselines in both general fine-tuning and knowledge editing tasks.

Low-rank adaptation has become a standard method for parameter-efficient fine-tuning of large language models, but even small amounts of unsafe or adversarial fine-tuning data can substantially weaken the safety behavior of aligned models. Existing safety-preserving LoRA methods often rely on hard interventions such as projection, pruning, thresholding, or additional training objectives. While these methods can suppress unsafe update directions, they may also remove task-relevant information or require extra tuning. We introduce CSULoRA, a post-hoc method for correcting trained LoRA adapters through closest safe update estimation. CSULoRA estimates a safety-aligned subspace from the weight displacement between a safety-aligned model and its corresponding base checkpoint. It then decomposes each LoRA update into fully aligned, partially aligned, and off-subspace components. Instead of discarding components outside the estimated safety subspace, CSULoRA solves a closed-form penalized minimum-change problem that preserves the fully aligned component while smoothly attenuating potentially unsafe directions according to their relative energy. In adversarial fine-tuning experiments, CSULoRA substantially reduces attack success rate while preserving most of the utility gains obtained from standard LoRA fine-tuning.

Applying a pre-trained large model to downstream tasks is prohibitive under resource-constrained conditions. Recent dominant approaches for addressing efficiency issues involve adding a few learnable parameters to the fixed backbone model. This strategy, however, leads to more challenges in loading large models for downstream fine-tuning with limited resources. In this paper, we propose a novel method for increasing the parameter efficiency of pre-trained models by introducing an intermediate pre-training stage. To this end, we first employ low-rank approximation to compress the original large model and then devise a feature distillation module and a weight perturbation regularization module. These modules are specifically designed to enhance the low-rank model. In particular, we update only the low-rank model while freezing the backbone parameters during pre-training. This allows for direct and efficient utilization of the low-rank model for downstream fine-tuning tasks. The proposed method achieves both efficiencies in terms of required parameters and computation time while maintaining comparable results with minimal modifications to the backbone architecture. Specifically, when applied to three vision-only and one vision-language Transformer models, our approach often demonstrates a merely sim0.6 point decrease in performance while reducing the original parameter size by 1/3 to 2/3.

The rapid growth of model scale has necessitated substantial computational resources for fine-tuning. Existing approach such as Low-Rank Adaptation (LoRA) has sought to address the problem of handling the large updated parameters in full fine-tuning. However, LoRA utilize random initialization and optimization of low-rank matrices to approximate updated weights, which can result in suboptimal convergence and an accuracy gap compared to full fine-tuning. To address these issues, we propose LoLDU, a Parameter-Efficient Fine-Tuning (PEFT) approach that significantly reduces trainable parameters by 2600 times compared to regular PEFT methods while maintaining comparable performance. LoLDU leverages Lower-Diag-Upper Decomposition (LDU) to initialize low-rank matrices for faster convergence and orthogonality. We focus on optimizing the diagonal matrix for scaling transformations. To the best of our knowledge, LoLDU has the fewest parameters among all PEFT approaches. We conducted extensive experiments across 4 instruction-following datasets, 6 natural language understanding (NLU) datasets, 8 image classification datasets, and image generation datasets with multiple model types (LLaMA2, RoBERTa, ViT, and Stable Diffusion), providing a comprehensive and detailed analysis. Our open-source code can be accessed at https://github.com/SKDDJ/LoLDU{https://github.com/SKDDJ/LoLDU}.

The growing scale of Large Language Models (LLMs) has necessitated the development of parameter-efficient fine-tuning techniques. Low-Rank Adaptation (LoRA) has emerged as a promising approach, reducing the number of trainable parameters by applying low-rank updates to pretrained weights. While standard LoRA learns both update factors directly, several recent variants first initialize those matrices via an SVD of the pretrained weights -- an operation that can be expensive on large models and yields singular vectors that are not always easy to interpret. In this work, we extract an orthonormal basis from the pretrained weight matrix using QR decomposition with column pivoting, and then express the LoRA update as a linear combination of these basis vectors -- training only the scalar coefficients, which imposes clear structure on adaptation and drastically reduces parameter count. Experiments across GLUE tasks show that QR-LoRA matches or exceeds the performance of full fine-tuning, standard LoRA, and SVD-LoRA (LoRA with update matrices initialized via singular value decomposition) with as few as 601 parameters -- a reduction of over 1000x compared to full fine-tuning and 77x fewer than typical LoRA setups.

The complex nature of medical image segmentation calls for models that are specifically designed to capture detailed, domain-specific features. Large foundation models offer considerable flexibility, yet the cost of fine-tuning these models remains a significant barrier. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), efficiently update model weights with low-rank matrices but may suffer from underfitting when the chosen rank is insufficient to capture domain-specific nuances. Conversely, full-rank Singular Value Decomposition (SVD) based methods provide comprehensive updates by modifying all singular values, yet they often lack flexibility and exhibit variable performance across datasets. We propose SALT (Singular Value Adaptation with Low-Rank Transformation), a method that selectively adapts the most influential singular values using trainable scale and shift parameters while complementing this with a low-rank update for the remaining subspace. This hybrid approach harnesses the advantages of both LoRA and SVD, enabling effective adaptation without relying on increasing model size or depth. Evaluated on 5 challenging medical datasets, ranging from as few as 20 samples to 1000, SALT outperforms state-of-the-art PEFT (LoRA and SVD) by 2% to 5% in Dice with only 3.9% trainable parameters, demonstrating robust adaptation even in low-resource settings. The code for SALT is available at: https://github.com/BioMedIA-MBZUAI/SALT

Parameter-efficient fine-tuning (PEFT) has gained widespread adoption across various applications. Among PEFT techniques, Low-Rank Adaptation (LoRA) and its extensions have emerged as particularly effective, allowing efficient model adaptation while significantly reducing computational overhead. However, existing approaches typically rely on global low-rank factorizations, which overlook local or multi-scale structure, failing to capture complex patterns in the weight updates. To address this, we propose WaRA, a novel PEFT method that leverages wavelet transforms to decompose the weight update matrix into a multi-resolution representation. By performing low-rank factorization in the wavelet domain and reconstructing updates through an inverse transform, WaRA obtains compressed adaptation parameters that harness multi-resolution analysis, enabling it to capture both coarse and fine-grained features while providing greater flexibility and sparser representations than standard LoRA. Through comprehensive experiments and analysis, we demonstrate that WaRA performs superior on diverse vision tasks, including image generation, classification, and semantic segmentation, significantly enhancing generated image quality while reducing computational complexity. Although WaRA was primarily designed for vision tasks, we further showcase its effectiveness in language tasks, highlighting its broader applicability and generalizability. The code is publicly available at GitHub{https://github.com/moeinheidari7829/WaRA}.

It is a common practice in natural language processing to pre-train a single model on a general domain and then fine-tune it for downstream tasks. However, when it comes to Large Language Models, fine-tuning the entire model can be computationally expensive, resulting in very intensive energy consumption. As a result, several Parameter Efficient Fine-Tuning (PEFT) approaches were recently proposed. One of the most popular approaches is low-rank adaptation (LoRA), where the key insight is decomposing the update weights of the pre-trained model into two low-rank matrices. However, the proposed approaches either use the same rank value across all different weight matrices, which has been shown to be a sub-optimal choice, or do not use any quantization technique, one of the most important factors when it comes to a model's energy consumption. In this work, we propose Bayesian-LoRA which approaches low-rank adaptation and quantization from a Bayesian perspective by employing a prior distribution on both quantization levels and rank values. As a result, B-LoRA is able to fine-tune a pre-trained model on a specific downstream task, finding the optimal rank values and quantization levels for every low-rank matrix. We validate the proposed model by fine-tuning a pre-trained DeBERTaV3 on the GLUE benchmark. Moreover, we compare it to relevant baselines and present both qualitative and quantitative results, showing how the proposed approach is able to learn optimal-rank quantized matrices. B-LoRA performs on par with or better than the baselines while reducing the total number of bit operations by roughly 70% compared to the baseline methods.

Parameter-efficient fine-tuning (PEFT) has become the standard approach for adapting large language models under limited compute and memory budgets. Although previous methods improve efficiency through low-rank updates, quantization, or heuristic budget reallocation, they often decouple the allocation of capacity from the way updates evolve during training. In this work, we introduce CTR-LoRA, a framework guided by curvature trust region that integrates rank scheduling with stability-aware optimization. CTR-LoRA allocates parameters based on marginal utility derived from lightweight second-order proxies and constrains updates using a Fisher/Hessian-metric trust region. Experiments on multiple open-source backbones (7B-13B), evaluated on both in-distribution and out-of-distribution benchmarks, show consistent improvements over strong PEFT baselines. In addition to increased accuracy, CTR-LoRA enhances training stability, reduces memory requirements, and achieves higher throughput, positioning it on the Pareto frontier of performance and efficiency. These results highlight a principled path toward more robust and deployable PEFT.

Parameter-Efficient Fine-Tuning (PEFT) has become an essential approach for adapting large-scale pre-trained models while reducing computational costs. Among PEFT methods, LoRA significantly reduces trainable parameters by decomposing weight updates into low-rank matrices. However, traditional LoRA applies a fixed rank across all layers, failing to account for the varying complexity of hierarchical information, which leads to inefficient adaptation and redundancy. To address this, we propose MSPLoRA (Multi-Scale Pyramid LoRA), which introduces Global Shared LoRA, Mid-Level Shared LoRA, and Layer-Specific LoRA to capture global patterns, mid-level features, and fine-grained information, respectively. This hierarchical structure reduces inter-layer redundancy while maintaining strong adaptation capability. Experiments on various NLP tasks demonstrate that MSPLoRA achieves more efficient adaptation and better performance while significantly reducing the number of trainable parameters. Furthermore, additional analyses based on Singular Value Decomposition validate its information decoupling ability, highlighting MSPLoRA as a scalable and effective optimization strategy for parameter-efficient fine-tuning in large language models. Our code is available at https://github.com/Oblivioniss/MSPLoRA.

Fine-tuning large language models (LLMs) with low-rank adaptaion (LoRA) is a cost-effective way to incorporate information from a specific dataset. However, it is often unclear how well the fine-tuned LLM will generalize, i.e., how well it will perform on unseen datasets. Methods have been proposed to improve generalization by optimizing with in-context prompts, or by using meta-learning to fine-tune LLMs. However, these methods are expensive in memory and computation, requiring either long-context prompts or saving copies of parameters and using second-order gradient updates. To address these challenges, we propose Amortized Bayesian Meta-Learning for LoRA (ABMLL). This method builds on amortized Bayesian meta-learning for smaller models, adapting this approach to LLMs while maintaining its computational efficiency. We reframe task-specific and global parameters in the context of LoRA and use a set of new hyperparameters to balance reconstruction accuracy and the fidelity of task-specific parameters to the global ones. ABMLL provides effective generalization and scales to large models such as Llama3-8B. Furthermore, as a result of using a Bayesian framework, ABMLL provides improved uncertainty quantification. We test ABMLL on Unified-QA and CrossFit datasets and find that it outperforms existing methods on these benchmarks in terms of both accuracy and expected calibration error.

Multi-agent LLM systems usually collaborate by exchanging natural-language messages. This interface is simple and interpretable, but it forces each sender's intermediate computation to be serialized into tokens and then reprocessed by the receiver, thereby increasing the generated-token cost, prefill overhead, and KV-cache memory. We study an alternative communication interface: instead of appending a sender's message to the receiver's context, compile the sender's hidden states into a transient, receiver-specific weight perturbation. We introduce TFlow (Thought Flow), a weight-space communication framework for a known and fixed receiver architecture. For each query, frozen role-prompted sender agents process the input, and a learned parameter generator maps their internal activations into low-rank LoRA perturbations targeting the receiver's modules. These perturbations are fused and applied only during the receiver's generation, enabling instance-level adaptation without permanently changing the model or enlarging the receiver's text context. With three Qwen3-4B agents, TFlow improves over a standalone receiver by up to 8.5 accuracy points across five benchmarks while reducing processed tokens by up to 32.69%. Compared with a text-based three-agent baseline, it reduces total processed tokens by up to 83.27% and the wall-clock inference time by up to 4.6times, while maintaining competitive accuracy on four of five benchmarks. These results suggest that transient low-rank weight perturbations can serve as an executable communication medium for efficient multi-agent LLM collaboration.

Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of LoRA training by introducing an r times r preconditioner in each gradient step where r is the LoRA rank. We theoretically verify that the proposed preconditioner stabilizes feature learning with LoRA under infinite-width NN setting. Empirically, the implementation of this new preconditioner requires a small change to existing optimizer code and creates virtually minuscule storage and runtime overhead. Our experimental results with both large language models and text-to-image diffusion models show that with this new preconditioner, the convergence and reliability of SGD and AdamW can be significantly enhanced. Moreover, the training process becomes much more robust to hyperparameter choices such as learning rate. The new preconditioner can be derived from a novel Riemannian metric in low-rank matrix field. Code can be accessed at https://github.com/pilancilab/Riemannian_Preconditioned_LoRA.

Progress toward general intelligence in the physical world requires scaling robot learning across diverse environments and interactions. However, existing robot policies use shared parameters that remain fixed across interaction contexts. When different operations favor competing parameter adjustments, fitting their mixture can leave individual operations insufficiently adapted. Our atomic-task diagnostics reveal competing update directions in both vision-language and action parameters, with source-improving updates increasing loss on other tasks. This motivates MorphAct, a contextual parameterization framework that dynamically adjusts robot policy parameters as interaction contexts change. Two coupled generators produce context-dependent low-rank updates for the vision-language and action modules. Their coupling follows the policy's computational dependency: vision-language updates shape the representations that condition action-side parameter generation. Both generators are trained jointly through the native action objective, without operation labels or expert-adapter targets. MorphAct improves performance across three VLA backbones on LIBERO and Meta-World, with gains of up to 16.30%. In real-world evaluation, it achieves gains of up to 14% over π_{0.5}. Ablations support the benefits of contextual parameter generation and representation coupling.

We study and quantify the problem of forgetting when fine-tuning pre-trained large language models (LLMs) on a downstream task. We find that parameter-efficient fine-tuning (PEFT) strategies, such as Low-Rank Adapters (LoRA), still suffer from catastrophic forgetting. In particular, we identify a strong inverse linear relationship between the fine-tuning performance and the amount of forgetting when fine-tuning LLMs with LoRA. We further obtain precise scaling laws that show forgetting increases as a shifted power law in the number of parameters fine-tuned and the number of update steps. We also examine the impact of forgetting on knowledge, reasoning, and the safety guardrails trained into Llama 2 7B chat. Our study suggests that forgetting cannot be avoided through early stopping or by varying the number of parameters fine-tuned. We believe this opens up an important safety-critical direction for future research to evaluate and develop fine-tuning schemes which mitigate forgetting

Vision-language-action (VLA) models achieve strong in-distribution performance but degrade sharply under novel camera viewpoints and visual perturbations. We show that this brittleness primarily arises from misalignment in Spatial Modeling, rather than Physical Modeling. To address this, we propose a one-shot adaptation framework that recalibrates visual representations through lightweight, learnable updates. Our first method, Feature Token Modulation (FTM), applies a global affine transformation to visual tokens and improves Libero viewpoint accuracy from 48.5% to 87.1% with only 4K parameters. Building on this, Feature Linear Adaptation (FLA) introduces low-rank updates to the ViT encoder, achieving 90.8% success with 4.7M parameters -- matching LoRA-scale finetuning at far lower cost. Together, these results reveal substantial untapped robustness in pretrained VLA models and demonstrate that targeted, minimal visual adaptation is sufficient to restore viewpoint generalization.

In this paper we generalize and extend an idea of low-rank adaptation (LoRA) of large language models (LLMs) based on Transformer architecture. Widely used LoRA-like methods of fine-tuning LLMs are based on matrix factorization of gradient update. We introduce LoTR, a novel approach for parameter-efficient fine-tuning of LLMs which represents a gradient update to parameters in a form of tensor decomposition. Low-rank adapter for each layer is constructed as a product of three matrices, and tensor structure arises from sharing left and right multipliers of this product among layers. Simultaneous compression of a sequence of layers with low-rank tensor representation allows LoTR to archive even better parameter efficiency then LoRA especially for deep models. Moreover, the core tensor does not depend on original weight dimension and can be made arbitrary small, which allows for extremely cheap and fast downstream fine-tuning.

Wearable exoskeleton systems hold promise for restoring mobility in individuals with physical impairments, yet most existing controllers rely on static gait policies that cannot adapt to dynamic real-world environments or individual user characteristics. We present OLIVE (Online Low-rank Incremental Learning for Efficient Adaptive Exoskeletons), a parameter-efficient online adaptation framework that continuously personalizes exoskeleton control during deployment. OLIVE decomposes the adaptive component of the control policy into a low-rank residual form ΔW = A_t B_t^top with rank r ll min(d,k), reducing the online update cost from O(dk) to O(r(d+k)) while preserving the stability of a pretrained base controller W_0. Parameters are updated through a reward-shaped policy gradient driven purely by on-body sensor feedback, including EMG, IMU, and vibration signals, eliminating dependence on offline reference trajectories. A gating mechanism modulates the strength of personalization based on the contextual state, while a dynamic rank scheduler adapts the update dimensionality to terrain complexity. It allocates minimal capacity on simple flat terrain and expands to higher-rank updates on demanding uneven surfaces, enabling robust performance across flat walking, stair navigation, slopes, and uneven terrain. Experiments on the wearable platform demonstrate that OLIVE achieves improvements of 13, 22, and 15 percentage points in gait smoothness, effort reduction, and motion stability over the strongest baseline, respectively. It converges within approximately 1,800 walking steps with an end-to-end latency of 7.4 ms. Our code implementation is available at https://github.com/FastLM/OLIVE.

In the training of large language models, parameter-efficient techniques such as LoRA optimize memory usage and reduce communication overhead and memory usage during the fine-tuning phase. However, applying such techniques directly during the pre-training phase results in poor performance, primarily because the premature implementation of low-rank training significantly reduces model accuracy. Existing methods like ReLoRA and GaLore have attempted to address this challenge by updating the low-rank subspace. However, they still fall short of achieving the accuracy of full-rank training. Specifically, ReLoRA restricts the frequency of updates to preserve optimizer states consistency, hindering its ability to closely approximate full-rank training behavior. Meanwhile, GaLore relies on Singular Value Decomposition (SVD) to approximate the full-rank space, which introduces accuracy loss during the approximation process. In this paper, we introduce SwitchLoRA, a parameter-efficient training technique that frequently and smoothly replaces the trainable parameters of LoRA adapters with alternative parameters. SwitchLoRA updates the low-rank subspace incrementally, targeting only a few dimensions at a time to minimize the impact on optimizer states. This allows a higher update frequency, thereby enhancing accuracy by enabling the updated parameters to more closely mimic full-rank behavior during the pre-training phase. Our results demonstrate that SwitchLoRA actually surpasses full-rank training, reducing perplexity from 15.23 to 15.01 on the LLaMA 1.3B model, while also cutting communication overhead by 54\% and memory usage by 13\%. Furthermore, after full fine-tuning the SwitchLoRA pre-trained model and the full-rank pre-trained model on the GLUE benchmark, the SwitchLoRA pre-trained model showed an average accuracy gain of about 1\% over the full-rank pre-trained model.

Minor Component Adaptation (MiCA) is a novel parameter-efficient fine-tuning method for large language models that focuses on adapting underutilized subspaces of model representations. Unlike conventional methods such as Low-Rank Adaptation (LoRA), which target dominant subspaces, MiCA leverages Singular Value Decomposition to identify subspaces related to minor singular vectors associated with the least significant singular values and constrains the update of parameters during fine-tuning to those directions. This strategy leads to up to 5.9x improvement in knowledge acquisition under optimized training hyperparameters and a minimal parameter footprint of 6-60% compared to LoRA. These results suggest that constraining adaptation to minor singular directions provides a more efficient and stable mechanism for integrating new knowledge into pre-trained language models.

Low-rank adapters have become standard for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a learnable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90 times fewer learnable parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

Large Language Models usually put more emphasis on accuracy and therefore, will guess even when not certain about the prediction, which is especially severe when fine-tuned on small datasets due to the inherent tendency toward miscalibration. In this work, we introduce Bayesian-LoRA, which reformulates the deterministic LoRA update as a probabilistic low-rank representation inspired by Sparse Gaussian Processes. We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning benchmarks. With only approximately 0.42M additional parameters and {approx}1.2{times} training cost relative to standard LoRA, Bayesian-LoRA significantly improves calibration across models up to 30B, achieving up to 84% ECE reduction and 76% NLL reduction while maintaining competitive accuracy for both in-distribution and out-of-distribution (OoD) evaluations.

The low-rank adaptation (LoRA) method can largely reduce the amount of trainable parameters for fine-tuning large language models (LLMs), however, it still requires expensive activation memory to update low-rank weights. Reducing the number of LoRA layers or using activation recomputation could harm the fine-tuning performance or increase the computational overhead. In this work, we present LoRA-FA, a memory-efficient fine-tuning method that reduces the activation memory without performance degradation and expensive recomputation. LoRA-FA chooses to freeze the projection-down weight of A and update the projection-up weight of B in each LoRA layer. It ensures the change of model weight reside in a low-rank space during LLMs fine-tuning, while eliminating the requirement to store full-rank input activations. We conduct extensive experiments across multiple model types (RoBERTa, T5, LLaMA) and model scales. Our results show that LoRA-FA can always achieve close fine-tuning accuracy across different tasks compared to full parameter fine-tuning and LoRA. Furthermore, LoRA-FA can reduce the overall memory cost by up to 1.4times compared to LoRA.

Non-contrast chest CTs offer a rich opportunity for both conventional pulmonary and opportunistic extra-pulmonary screening. While Multi-Task Learning (MTL) can unify these diverse tasks, standard hard-parameter sharing approaches are often suboptimal for modeling distinct pathologies. We propose HyperCT, a framework that dynamically adapts a Vision Transformer backbone via a Hypernetwork. To ensure computational efficiency, we integrate Low-Rank Adaptation (LoRA), allowing the model to regress task-specific low-rank weight updates rather than full parameters. Validated on a large-scale dataset of radiological and cardiological tasks, outperforms various strong baselines, offering a unified, parameter-efficient solution for holistic patient assessment. Our code is available at https://github.com/lfb-1/HyperCT.

Among the widely used parameter-efficient finetuning (PEFT) methods, LoRA and its variants have gained considerable popularity because of avoiding additional inference costs. However, there still often exists an accuracy gap between these methods and full fine-tuning (FT). In this work, we first 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 LowRank Adaptation (DoRA). DoRA decomposes the pre-trained weight into two components, magnitude and direction, for fine-tuning, specifically employing LoRA for directional updates to efficiently minimize the number of trainable parameters. By employing DoRA, we enhance both the learning capacity and training stability of LoRA while avoiding any additional inference overhead. DoRA consistently outperforms LoRA on fine-tuning LLaMA, LLaVA, and VL-BART on various downstream tasks, such as commonsense reasoning, visual instruction tuning, and image/video-text understanding.

Federated Learning (FL) is a widely used framework for training models in a decentralized manner, ensuring that the central server does not have direct access to data from local clients. However, this approach may still fail to fully preserve data privacy, as models from local clients are exposed to the central server during the aggregation process. This issue becomes even more critical when training vision-language models (VLMs) with FL, as VLMs can easily memorize training data instances, making them vulnerable to membership inference attacks (MIAs). To address this challenge, we propose the FedRand framework, which avoids disclosing the full set of client parameters. In this framework, each client randomly selects subparameters of Low-Rank Adaptation (LoRA) from the server and keeps the remaining counterparts of the LoRA weights as private parameters. After training both parameters on the client's private dataset, only the non-private client parameters are sent back to the server for aggregation. This approach mitigates the risk of exposing client-side VLM parameters, thereby enhancing data privacy. We empirically validate that FedRand improves robustness against MIAs compared to relevant baselines while achieving accuracy comparable to methods that communicate full LoRA parameters across several benchmark datasets.

The low-rank adaptation (LoRA) algorithm for fine-tuning large models has grown popular in recent years due to its remarkable performance and low computational requirements. LoRA trains two ``adapter" matrices that form a low-rank representation of the model parameters, thereby massively reducing the number of parameters that need to be updated at every step. Although LoRA is simple, its convergence is poorly understood due to the lack of Lipschitz smoothness, a key condition for classic convergence analyses. As a result, current theoretical results only consider asymptotic behavior or assume strong boundedness conditions which artificially enforce Lipschitz smoothness. In this work, we provide for the first time a non-asymptotic convergence analysis of the original LoRA gradient descent algorithm, which reflects widespread practice, without such assumptions. Our work relies on three key steps: i) reformulating the problem in terms of the outer product of the stacked adapter matrices, ii) a modified descent lemma for the ``Lipschitz-like" reparametrized function, and iii) controlling the step size. With this approach, we prove that LoRA gradient descent converges to a stationary point at rate O(1{log T}), where T is the number of iterations. We conduct numerical experiments to validate our theoretical findings.

Low-rank adaptation is a popular parameter-efficient fine-tuning method for large language models. In this paper, we analyze the impact of low-rank updating, as implemented in LoRA. Our findings suggest that the low-rank updating mechanism may limit the ability of LLMs to effectively learn and memorize new knowledge. Inspired by this observation, we propose a new method called MoRA, which employs a square matrix to achieve high-rank updating while maintaining the same number of trainable parameters. To achieve it, we introduce the corresponding non-parameter operators to reduce the input dimension and increase the output dimension for the square matrix. Furthermore, these operators ensure that the weight can be merged back into LLMs, which makes our method can be deployed like LoRA. We perform a comprehensive evaluation of our method across five tasks: instruction tuning, mathematical reasoning, continual pretraining, memory and pretraining. Our method outperforms LoRA on memory-intensive tasks and achieves comparable performance on other tasks.

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers such as heavy ball momentum methods or Adam. In this work, we identify and analyze potential difficulties that these training methods encounter when used to train low-rank parameterizations of weights. In particular, we show that classical momentum methods can struggle to converge to a local optimum due to the geometry of the underlying optimization landscape. To address this, we introduce novel training strategies derived from dynamical low-rank approximation, which explicitly account for the underlying geometric structure. Our approach leverages and combines tools from dynamical low-rank approximation and momentum-based optimization to design optimizers that respect the intrinsic geometry of the parameter space. We validate our methods through numerical experiments, demonstrating faster convergence, and stronger validation metrics at given parameter budgets.

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of parameters, striking a balance between compactness and performance. However, a common challenge has been the compromise between parameter efficiency and the accuracy of the model, where reduced parameters often lead to diminished accuracy compared to their full-rank counterparts. In this work, we propose a novel theoretical framework that integrates a sinusoidal function within the low-rank decomposition process. This approach not only preserves the benefits of the parameter efficiency characteristic of low-rank methods but also increases the decomposition's rank, thereby enhancing model performance. Our method proves to be a plug in enhancement for existing low-rank models, as evidenced by its successful application in Vision Transformers (ViT), Large Language Models (LLMs), Neural Radiance Fields (NeRF) and 3D shape modelling.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

We show that low-rank adaptation of large-scale models suffers from a low stable rank that is well below the linear algebraic rank of the subspace, degrading fine-tuning performance. To mitigate the underutilization of the allocated subspace, we propose PoLAR, a parameterization inspired by the polar decomposition that factorizes the low-rank update into two direction matrices constrained to Stiefel manifolds and an unconstrained scale matrix. Our theory shows that PoLAR yields an exponentially faster convergence rate on a canonical low-rank adaptation problem. Pairing the parameterization with Riemannian optimization leads to consistent gains on three different benchmarks testing general language understanding, commonsense reasoning, and mathematical problem solving with base model sizes ranging from 350M to 27B.

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the effective rank of the weight updates remains low-rank, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce FRUGAL (Full-Rank Updates with GrAdient spLitting), a new memory-efficient optimization framework. FRUGAL leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of downstream tasks. Existing parameter-efficient fine-tuning (PEFT) methods such as Low-Rank Adaptation (LoRA) rely on a bypass framework that ignores the differential parameter budget requirements across weight matrices, which may lead to suboptimal fine-tuning outcomes. To address this issue, we introduce the Dynamic Low-Rank Adaptation (DoRA) method. DoRA decomposes high-rank LoRA layers into structured single-rank components, allowing for dynamic pruning of parameter budget based on their importance to specific tasks during training, which makes the most of the limited parameter budget. Experimental results demonstrate that DoRA can achieve competitive performance compared with LoRA and full model fine-tuning, and outperform various strong baselines with the same storage parameter budget. Our code is available at https://github.com/MIkumikumi0116/DoRA

Despite large neural networks demonstrating remarkable abilities to complete different tasks, they require excessive memory usage to store the optimization states for training. To alleviate this, the low-rank adaptation (LoRA) is proposed to reduce the optimization states by training fewer parameters. However, LoRA restricts overall weight update matrices to be low-rank, limiting the model performance. In this work, we investigate the dynamics of LoRA and identify that it can be approximated by a random projection. Based on this observation, we propose Flora, which is able to achieve high-rank updates by resampling the projection matrices while enjoying the sublinear space complexity of optimization states. We conduct experiments across different tasks and model architectures to verify the effectiveness of our approach.

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank approximation and its application in adaptation can sometimes be obscure, leaving practitioners and researchers with questions about its true capabilities and limitations. This paper seeks to clarify low-rank approximation and adaptation by offering a comprehensive guide that reveals their inner workings and explains their utility in a clear and accessible way. Our focus here is to develop a solid intuition for how low-rank approximation and adaptation operate, and why they are so effective. We begin with basic concepts and gradually build up to the mathematical underpinnings, ensuring that readers of all backgrounds can gain a deeper understanding of low-rank approximation and adaptation. We strive to strike a balance between informal explanations and rigorous mathematics, ensuring that both newcomers and experienced experts can benefit from this survey. Additionally, we introduce new low-rank decomposition and adaptation algorithms that have not yet been explored in the field, hoping that future researchers will investigate their potential applicability.

Fine-tuning pre-trained language models for downstream tasks has achieved impressive results in NLP. However, fine-tuning all parameters becomes impractical due to the rapidly increasing size of model parameters. To address this, Parameter Efficient Fine-Tuning (PEFT) methods update only a subset of parameters. Most PEFT methods, such as LoRA, use incremental updates, which involve adding learned weight matrix increments to the original parameters. Although effective, these methods face limitations in capturing complex parameter dynamics and do not maintain a strong correlation between the original and updated parameters. To overcome these challenges, we propose the direct Updated Transformation (UT) paradigm, which constructs a transformation directly from the original to the updated parameters. This approach ensures that the correlation between the original and updated parameters is preserved, leveraging the semantic features learned during pre-training. Building on this paradigm, we present the Hadamard Updated Transformation (HUT) method. HUT efficiently updates the original weight matrix using the Hadamard transformation with two low-rank matrices, offering a more expressive and flexible update mechanism. This allows HUT to capture richer parameter features through functional transformations, reducing computational complexity while maintaining or improving model quality. Theoretical analysis and extensive experiments on RoBERTa and GPT-2 validate the effectiveness of HUT. Results show that HUT performs on par with or better than other PEFT methods in terms of model quality, while significantly reducing computational complexity.

Large pre-trained models are commonly adapted to downstream tasks using parameter-efficient fine-tuning methods such as Low-Rank Adaptation (LoRA), which injects small trainable low-rank matrices instead of updating all weights. While LoRA dramatically reduces trainable parameters with little overhead, it can still underperform full fine-tuning in accuracy and often converges more slowly. We introduce LoFT, a novel low-rank adaptation method that behaves like full fine-tuning by aligning the optimizer's internal dynamics with those of updating all model weights. LoFT not only learns weight updates in a low-rank subspace (like LoRA) but also properly projects the optimizer's first and second moments (Adam's momentum and variance) into the same subspace, mirroring full-model updates. By aligning the low-rank update itself with the full update, LoFT eliminates the need for tuning extra hyperparameters, e.g., LoRA scaling factor alpha. Empirically, this approach substantially narrows the performance gap between adapter-based tuning and full fine-tuning and consistently outperforms standard LoRA-style methods, all without increasing inference cost.

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pretrained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. As a result, performance usually drops significantly and a sophisticated effort on fine-tuning is required to recover accuracy. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training process. We propose Trained Rank Pruning (TRP), which alternates between low rank approximation and training. TRP maintains the capacity of the original network while imposing low-rank constraints during training. A nuclear regularization optimized by stochastic sub-gradient descent is utilized to further promote low rank in TRP. The TRP trained network inherently has a low-rank structure, and is approximated with negligible performance loss, thus eliminating the fine-tuning process after low rank decomposition. The proposed method is comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation.

Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally expensive job. To mitigate this, many techniques have been developed that prime efficiency, a prominent one being Low-Rank Adaptation (LoRA). However, LoRA and its variants employ re-parametrized additive updates. In this paper, we propose Low-Rank Multiplicative Adaptation (LoRMA), which shifts the paradigm of additive updates to a richer space of matrix multiplicative transformations. We tackle challenges such as computational complexity and rank bottleneck of matrix multiplication by effectively re-ordering operations and introducing rank inflation strategies. We conduct extensive experiments to demonstrate the effectiveness of our approach in terms of various evaluation metrics.

Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA implementations disregard the varying intrinsic dimensionality of model layers and enforce a uniform rank, leading to parameter redundancy. We propose Post-Optimization Adaptive Rank Allocation (PARA), a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines. PARA leverages Singular Value Decomposition to prune LoRA ranks using a global threshold over singular values across all layers. This results in non-uniform rank allocation based on layer-wise spectral importance. As a post-hoc method, PARA circumvents the training modifications and resulting instabilities that dynamic architectures typically incur. We empirically demonstrate that PARA reduces parameter count by 75-90\% while preserving the predictive performance of the original, uncompressed LoRA across multiple vision and language benchmarks. Code will be published upon acceptance.

Low-Rank Adaptation (LoRA) has significantly advanced parameter-efficient fine-tuning of large pretrained models. LoRA augments the pre-trained weights of a model by adding the product of two smaller matrices that together form a low-rank matrix update. Recent research has shown that scale disparities between these two matrices often cause unstable training dynamics, leading to suboptimal performance. In this paper, 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. This simple design inherently removes inter-matrix scale conflicts, ensuring stable optimization, and roughly halves the parameter count. We analyze SingLoRA within the infinite-width neural network framework, showing that it guarantees stable feature learning by construction. Extensive experiments on multiple tasks validate these benefits. In common sense reasoning, fine-tuning LLama 7B on MNLI with SingLoRA achieves 91.3% accuracy - surpassing LoRA (89.1%) and LoRA+ (90.2%) - while using only 60% of their parameter budget. In image generation, fine-tuning Stable Diffusion with SingLoRA significantly improves image fidelity on DreamBooth, achieving a DINO similarity score of 0.151, compared to scores of 0.148 and 0.143 for DoRA and LoRA, respectively.

We propose Dynamic Rank Reinforcement Learning (DR-RL), a novel framework that adaptively optimizes the low-rank factorization of Multi-Head Self-Attention (MHSA) in Large Language Models (LLMs) through the integration of reinforcement learning and online matrix perturbation theory. While traditional low-rank approximations often rely on static rank assumptions--limiting their flexibility across diverse input contexts--our method dynamically selects ranks based on real-time sequence dynamics, layer-specific sensitivities, and hardware constraints. The core innovation lies in an RL agent that formulates rank selection as a sequential policy optimization problem, where the reward function strictly balances attention fidelity against computational latency. Crucially, we employ online matrix perturbation bounds to enable incremental rank updates, thereby avoiding the prohibitive cost of full decomposition during inference. Furthermore, the integration of a lightweight Transformer-based policy network and batched Singular Value Decomposition (SVD) operations ensures scalable deployment on modern GPU architectures. Experiments demonstrate that DR-RL maintains downstream accuracy statistically equivalent to full-rank attention while significantly reducing Floating Point Operations (FLOPs), particularly in long-sequence regimes (L > 4096). This work bridges the gap between adaptive efficiency and theoretical rigor in MHSA, offering a principled, mathematically grounded alternative to heuristic rank reduction techniques in resource-constrained deep learning. Source code and experiment logs are available at: https://github.com/canererden/DR_RL_Project

Adapting pretrained large language models (LLMs) to various downstream tasks in tens or hundreds of human languages is computationally expensive. Parameter-efficient fine-tuning (PEFT) significantly reduces the adaptation cost, by tuning only a small amount of parameters. However, directly applying PEFT methods such as LoRA (Hu et al., 2022) on diverse dataset mixtures could lead to suboptimal performance due to limited parameter capacity and negative interference among different datasets. In this work, we propose Featurized Low-rank Mixtures (FLix), a novel PEFT method designed for effective multitask multilingual tuning. FLix associates each unique dataset feature, such as the dataset's language or task, with its own low-rank weight update parameters. By composing feature-specific parameters for each dataset, FLix can accommodate diverse dataset mixtures and generalize better to unseen datasets. Our experiments show that FLix leads to significant improvements over a variety of tasks for both supervised learning and zero-shot settings using different training data mixtures.

With the increasing size of pre-trained language models (PLMs), fine-tuning all the parameters in the model is not efficient, especially when there are a large number of downstream tasks, which incur significant training and storage costs. Many parameter-efficient fine-tuning (PEFT) approaches have been proposed, among which, Low-Rank Adaptation (LoRA) is a representative approach that injects trainable rank decomposition matrices into every target module. Yet LoRA ignores the importance of parameters in different modules. To address this problem, many works have been proposed to prune the parameters of LoRA. However, under limited training conditions, the upper bound of the rank of the pruned parameter matrix is still affected by the preset values. We, therefore, propose IncreLoRA, an incremental parameter allocation method that adaptively adds trainable parameters during training based on the importance scores of each module. This approach is different from the pruning method as it is not limited by the initial number of training parameters, and each parameter matrix has a higher rank upper bound for the same training overhead. We conduct extensive experiments on GLUE to demonstrate the effectiveness of IncreLoRA. The results show that our method owns higher parameter efficiency, especially when under the low-resource settings where our method significantly outperforms the baselines. Our code is publicly available.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Low-Rank Adaptation (LoRA) offers a parameter-efficient paradigm for tuning large models. While recent spectral initialization methods improve convergence and performance over the naive "Noise & Zeros" scheme, their extra computational and storage overhead undermines efficiency. In this paper, we establish update magnitude as the fundamental driver of LoRA performance and propose LoRAM, a magnitude-driven "Basis & Basis" initialization scheme that matches spectral methods without their inefficiencies. Our key contributions are threefold: (i) Magnitude of weight updates determines convergence. We prove low-rank structures intrinsically bound update magnitudes, unifying hyperparameter tuning in learning rate, scaling factor, and initialization as mechanisms to optimize magnitude regulation. (ii) Spectral initialization succeeds via magnitude amplification. We demystify that the presumed knowledge-driven benefit of the spectral component essentially arises from the boost in the weight update magnitude. (iii) A novel and compact initialization strategy, LoRAM, scales deterministic orthogonal bases using pretrained weight magnitudes to simulate spectral gains. Extensive experiments show that LoRAM serves as a strong baseline, retaining the full efficiency of LoRA while matching or outperforming spectral initialization across benchmarks.

Parameter-Efficient Fine-Tuning (PEFT) has emerged as a practical paradigm for adapting large language models (LLMs) without updating all parameters. Most existing approaches, such as LoRA and PiSSA, rely on low-rank decompositions of weight updates. However, the low-rank assumption may restrict expressivity, particularly in task-specific adaptation scenarios where singular values are distributed relatively uniformly. To address this limitation, we propose CoSA (Compressed Sensing-Based Adaptation), a new PEFT method extended from compressed sensing theory. Instead of constraining weight updates to a low-rank subspace, CoSA expresses them through fixed random projection matrices and a compact learnable core. We provide a formal theoretical analysis of CoSA as a synthesis process, proving that weight updates can be compactly encoded into a low-dimensional space and mapped back through random projections. Extensive experimental results show that CoSA provides a principled perspective for efficient and expressive multi-scale model adaptation. Specifically, we evaluate CoSA on 10 diverse tasks, including natural language understanding and generation, employing 5 models of different scales from RoBERTa, Llama, and Qwen families. Across these settings, CoSA consistently matches or outperforms state-of-the-art PEFT methods.

The recent trend in scaling language models has led to a growing demand for parameter-efficient tuning (PEFT) methods such as LoRA (Low-Rank Adaptation). LoRA consistently matches or surpasses the full fine-tuning baseline with fewer parameters. However, handling numerous task-specific or user-specific LoRA modules on top of a base model still presents significant storage challenges. To address this, we introduce LoRA-XS (Low-Rank Adaptation with eXtremely Small number of parameters), a novel approach leveraging Singular Value Decomposition (SVD) for parameter-efficient fine-tuning. LoRA-XS introduces a small r x r weight matrix between frozen LoRA matrices, which are constructed by SVD of the original weight matrix. Training only r x r weight matrices ensures independence from model dimensions, enabling more parameter-efficient fine-tuning, especially for larger models. LoRA-XS achieves a remarkable reduction of trainable parameters by over 100x in 7B models compared to LoRA. Our benchmarking across various scales, including GLUE, GSM8k, and MATH benchmarks, shows that our approach outperforms LoRA and recent state-of-the-art approaches like VeRA in terms of parameter efficiency while maintaining competitive performance.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full parameter updates through methods such as low-dimensional decomposition or layer-wise selective updates. In this work, we propose AlphaAdam, an optimization framework for LLM from the perspective of intra-layer parameter updates. By decoupling parameter updates and dynamically adjusting their strength, AlphaAdam accelerates convergence and improves training stability. We construct parameter masks based on the consistency of historical momentum and gradient direction and combine them with an adaptive mask strength strategy to ensure efficient optimization and theoretical convergence guarantees, which is also applicable to most momentum-based optimizers. Extensive experiments show that AlphaAdam outperforms state-of-the-art methods such as AdamW in terms of convergence speed and computational efficiency across tasks, including GPT-2 pre-trained and fine-tuned RoBERTa and Llama-7B. Our AlphaAdam implements an optimizer enhancement framework for LLMs through intra-layer asynchronous masked adaptive updates. Our code is available in this https://github.com/MaeChd/AlphaAdam.

In this work, we propose a communication-efficient parameterization, FedPara, for federated learning (FL) to overcome the burdens on frequent model uploads and downloads. Our method re-parameterizes weight parameters of layers using low-rank weights followed by the Hadamard product. Compared to the conventional low-rank parameterization, our FedPara method is not restricted to low-rank constraints, and thereby it has a far larger capacity. This property enables to achieve comparable performance while requiring 3 to 10 times lower communication costs than the model with the original layers, which is not achievable by the traditional low-rank methods. The efficiency of our method can be further improved by combining with other efficient FL optimizers. In addition, we extend our method to a personalized FL application, pFedPara, which separates parameters into global and local ones. We show that pFedPara outperforms competing personalized FL methods with more than three times fewer parameters.

Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices, leading to instability in model performance on fine-tuning downstream tasks. This paper highlights the importance of effective parameterization in low-rank fine-tuning to reduce estimator variance and enhance the stability of final model outputs. We propose MonteCLoRA, an efficient fine-tuning technique that employs Monte Carlo estimation to learn an unbiased posterior estimation of low-rank parameters with low expected variance, stabilizing fine-tuned LLMs with only O(r) additional parameters, for a given rank r. MonteCLoRA shows 0.5% and 1.6% improvements in accuracy and robustness over unregularized low-rank adaptation method on natural language understanding tasks with pre-trained RoBERTa-base. Furthermore, in generative tasks with pre-trained LLaMA-1-7B and LLaMA-3.2-3B-Instruct, MonteCLoRA demonstrates robust performance with 50% and 62% lower spreads respectively than the contemporary efficient fine-tuning methods. The theoretical and empirical results presented in the paper underscore how parameterization and hyperpriors balance exploration-exploitation in the low-rank parametric space, therefore leading to more optimal and robust parameter estimation during efficient fine-tuning.

Fine-tuning is a key approach for adapting language models to specific downstream tasks, but updating all model parameters becomes impractical as model sizes increase. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), address this challenge by introducing additional adaptation parameters into pre-trained weight matrices. However, LoRA's performance varies across different insertion points within the model, highlighting potential parameter inefficiency due to unnecessary insertions. To this end, we propose SSMLoRA (State Space Model Low-Rank Adaptation), an extension of LoRA that incorporates a State Space Model (SSM) to interconnect low-rank matrices. SSMLoRA ensures that performance is maintained even with sparser insertions. SSMLoRA allows the model to not only map inputs to a low-rank space for better feature extraction but also leverage the computations from the previous low-rank space. Our method achieves comparable performance to LoRA on the General Language Understanding Evaluation (GLUE) benchmark while using only half the parameters. Additionally, due to its structure, SSMLoRA shows promise in handling tasks with longer input sequences. .You can find our code here:https://github.com/yuhkalhic/SSMLoRA.

We address the challenge of adapting pre-trained Large Language Models (LLMs) for multivariate time-series analysis, where their deployment is often hindered by prohibitive computational and memory demands. Our solution, One-for-All, introduces Gaussian Rank-Stabilized Low-Rank Adapters (rsLoRA) to enable parameter-efficient fine-tuning of frozen LLMs. While inspired by LoRA, rsLoRA introduces a mathematically grounded rank-stabilization mechanism that enables provable gradient stability at low ranks a novel contribution absent in prior PEFT methods. Our framework injects trainable rank decomposition matrices (rank 16) into positional embeddings and output layers, while keeping self-attention weights fixed. This design reduces trainable parameters by 6.8times (vs. TimesNet), 21times (vs. GPT4TS), and 11.8times (vs. TIME-LLM), while achieving a 168-1,776times smaller memory footprint (2.2MiB vs. 340MiB-4.18GiB in SOTA models). Rigorous evaluation across six time-series tasks demonstrates that One-for-All achieves state-of-the-art efficiency-accuracy trade-offs: 5.5times higher parameter efficiency (MSE=5.50) than TimesNet and 21times better than GPT4TS, while matching their forecasting accuracy (MSE=0.33). The framework's stability is validated through consistent performance across diverse horizons (96-720 steps) and datasets (ETT, Weather, M3, M4), with 98.3% fewer parameters than conventional transformers. These advances enable deployment on edge devices for healthcare, finance, and environmental monitoring without compromising performance.

Fine-tuning large language models (LLMs) with high parameter efficiency for downstream tasks has become a new paradigm. Low-Rank Adaptation (LoRA) significantly reduces the number of trainable parameters for fine-tuning. Although it has demonstrated commendable performance, updating parameters within a single scale may not be the optimal choice for complex downstream tasks.In this paper, we extend the LoRA to multiple scales, dubbed as LoRA^2. We first combine orthogonal projection theory to train a set of LoRAs in two mutually orthogonal planes. Then, we improve the importance score algorithm, which reduce parameter sensitivity score calculations by approximately 98.5\%. By pruning singular values with lower importance scores, thereby enhancing adaptability to various downstream tasks. Extensive experiments are conducted on two widely used pre-trained models to validate the effectiveness of LoRA^2. Results show that it significantly reduces the number of trainable parameters to just 0.72\% compared to full fine-tuning, while still delivering highly impressive performance. Even when the parameters are further reduced to 0.17M, it still achieves comparable results to the baseline with 8 times more parameters. Our code is available here: https://anonymous.4open.science/r/LoRA-2-5B4C

While prompt tuning approaches have achieved competitive performance with high efficiency, we observe that they invariably employ the same initialization process, wherein the soft prompt is either randomly initialized or derived from an existing embedding vocabulary. In contrast to these conventional methods, this study aims to investigate an alternative way to derive soft prompt. Our empirical studies show that the soft prompt typically exhibits a low intrinsic rank characteristic. With such observations, we propose decomposed prompt tuning, a novel approach that utilizes low-rank matrices to initialize the soft prompt. Through the low-rank reparameterization, our method significantly reduces the number of trainable parameters while maintaining effectiveness. Experimental results on the SuperGLUE benchmark in both high-resource and low-resource scenarios demonstrate the effectiveness of the proposed method.

We introduce Evolution Guided General Optimization via Low-rank Learning (EGGROLL), an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes for modern large neural network architectures with billions of parameters. ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives with excellent scaling potential through parallelisation. Na{ï}ve ES becomes prohibitively expensive at scale due to the computational and memory costs associated with generating matrix perturbations EinR^{mtimes n} and the batched matrix multiplications needed to compute per-member forward passes. EGGROLL overcomes these bottlenecks by generating random matrices Ain R^{mtimes r}, Bin R^{ntimes r} with rll min(m,n) to form a low-rank matrix perturbation A B^top that are used in place of the full-rank perturbation E. As the overall update is an average across a population of N workers, this still results in a high-rank update but with significant memory and computation savings, reducing the auxiliary storage from mn to r(m+n) per layer and the cost of a forward pass from O(mn) to O(r(m+n)) when compared to full-rank ES. A theoretical analysis reveals our low-rank update converges to the full-rank update at a fast Oleft(1{r}right) rate. Our experiments show that (1) EGGROLL does not compromise the performance of ES in tabula-rasa RL settings, despite being faster, (2) it is competitive with GRPO as a technique for improving LLM reasoning, and (3) EGGROLL enables stable pre-training of nonlinear recurrent language models that operate purely in integer datatypes.

The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation. Code is available: https://github.com/yuhuixu1993/Trained-Rank-Pruning

Continual fine-tuning of Large Language Models (LLMs) is hampered by the trade-off between efficiency and expressiveness. Low-Rank Adaptation (LoRA) offers efficiency but constrains the model's ability to learn new tasks and transfer knowledge due to its low-rank nature and reliance on explicit parameter constraints. We propose GORP (Gradient LOw Rank Projection) for Continual Learning, a novel training strategy that overcomes these limitations by synergistically combining full and low-rank parameters and jointly updating within a unified low-rank gradient subspace. GORP expands the optimization space while preserving efficiency and mitigating catastrophic forgetting. Extensive experiments on continual learning benchmarks demonstrate GORP's superior performance compared to existing state-of-the-art approaches. Code is available at https://github.com/Wcxwcxw/GORP.