Low-Rank Adaptation

We introduce LoRA-CRAFT (Cross-layer Rank Adaptation via Frozen Tucker), abbreviated CRAFT throughout, an extremely parameter-efficient fine-tuning (PEFT) method that applies Tucker tensor decomposition to pre-trained attention weight matrices stacked across transformer layers and trains only small square adaptation matrices on the resulting frozen Tucker factors. Existing tensor-based PEFT methods decompose gradient updates: LoTR applies Tucker decomposition with shared factor matrices, while SuperLoRA groups and reshapes $ΔW$ across layers before applying Tucker decomposition. Separately, methods such as PiSSA apply SVD to pre-trained weights but operate independently per layer. CRAFT bridges these two lines of work: it performs full Tucker decomposition via Higher-Order SVD (HOSVD) directly on pre-trained weights organized as cross-layer 3D tensors, freezes all resulting factors, and adapts the model through lightweight trainable transformations applied to each factor matrix. Experiments on the GLUE benchmark using RoBERTa-base and RoBERTa-large, as well as commonsense reasoning benchmarks using LLaMA2-7B and LLaMA3-8B, demonstrate that CRAFT achieves competitive performance with existing methods while requiring only \rev{extremely low Tucker adaptation parameters}. \fixw{On LLaMA3-8B, CRAFT} \rev{exceeds the average accuracy of LoRA} using hundreds of times fewer parameters\fixw{; on LLaMA2-7B the same holds at a $0.252$M budget}. Our results suggest that CRAFT's efficiency advantage grows with model scale, as the frozen Tucker factors better capture the richer cross-layer structure of larger pre-trained models.

Parameter-efficient fine-tuning techniques such as low-rank adaptation (LoRA) enable large language models (LLMs) to adapt to downstream tasks efficiently. Federated learning (FL) further facilitates this process by enabling collaborative fine-tuning across distributed clients without sharing private data. However, the use of two separate low-rank matrices in LoRA for federated fine-tuning introduces two types of challenges. First, aggregation error can arise from separately aggregating the two low-rank matrices. Second, even if the server aggregates the product of two low-rank matrices, it needs to decompose the aggregated matrix back into low-rank matrices. Since the decomposition is not unique, it can lead to decomposition drift. To tackle the aforementioned challenges, we propose federated low-rank Gram-matrix aggregation (FLoRG), a federated fine-tuning framework which employs a single low-rank matrix for fine-tuning and aggregates its Gram matrix (i.e., the matrix of inner products of its column vectors). FLoRG can eliminate the aggregation error and reduce the communication overhead. It also minimizes the decomposition drift by introducing a Procrustes alignment approach which aligns the decomposed matrix between consecutive fine-tuning rounds for consistent updates. We theoretically analyze the convergence of FLoRG and prove that adopting the Procrustes alignment results in a tighter convergence bound. Experimental results across multiple LLM fine-tuning benchmarks demonstrate that FLoRG outperforms five state-of-the-art baseline schemes by providing higher downstream task accuracy and can reduce the communication overhead by up to 2041$\times$.

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. In this work, we address the gap between training with full steps with low-rank projections (SVDLoRA) and LoRA fine-tuning. We propose LoRSum, a memory-efficient subroutine that closes this gap for gradient descent by casting LoRA optimization as a proximal sub-problem and solving it efficiently with alternating least squares updates, which we prove to be an implicit block power method. We recover several recently proposed preconditioning methods for LoRA as special cases, and show that LoRSum can also be used for updating a low-rank momentum. In order to address full steps with preconditioned gradient descent, we propose a scaled variant of LoRSum that uses structured metrics such as K-FAC and Shampoo, and we show that storing the diagonal of these metrics still allows them to perform well while remaining memory-efficient. Experiments on a synthetic task, CIFAR-100, and language-model fine-tuning on GLUE, SQuAD v2, and WikiText-103, show that our method can match or improve LoRA baselines given modest compute overhead, while avoiding full-matrix SVD projections and retaining LoRA-style parameter efficiency.

Visual analogy learning enables image editing via demonstration rather than textual description, allowing users to specify complex transformations difficult to articulate in words. Given a triplet $\{\mathbf{a}$, $\mathbf{a}'$, $\mathbf{b}\}$, the goal is to generate $\mathbf{b}'$ such that $\mathbf{a} : \mathbf{a}' :: \mathbf{b} : \mathbf{b}'$. Recent methods adapt text-to-image models with a single Low-Rank Adaptation (LoRA) module, but they face a fundamental limitation: attempting to capture the diverse space of visual transformations within a fixed module constrains generalization. Inspired by recent work showing that LoRAs in constrained domains span meaningful, interpolatable semantic spaces, we propose LoRWeB, which specializes the model for each analogy task in a single inference pass. LoRWeB dynamically composes learned transformation primitives, informally, choosing a point in a "space of LoRAs". We introduce two key components: (1) a learnable basis of LoRAs to span the space of different visual transformations, and (2) a lightweight encoder that dynamically weighs these basis LoRAs given the input analogy pair. Comprehensive evaluations demonstrate state-of-the-art performance and significantly improved generalization to unseen transformations. Our findings suggest LoRA basis decompositions are a promising direction for flexible visual manipulation tasks. See https://research.nvidia.com/labs/par/lorweb for code.

LoRA adapters let users fine-tune large language models (LLMs) efficiently. However, LoRA adapters are shared through open repositories like Hugging Face Hub \citep{huggingface_hub_docs}, making them vulnerable to backdoor attacks. Current detection methods require running the model with test input data -- making them impractical for screening thousands of adapters where the trigger for backdoor behavior is unknown. We detect poisoned adapters by analyzing their weight matrices directly, without running the model -- making our method trigger-agnostic. For each attention projection (Q, K, V, O), our method extracts five spectral statistics from the low-rank update $ΔW$, yielding a 20-dimensional signature for each adapter. A logistic regression detector trained on this representation separates benign and poisoned adapters across three model families -- Llama-3.2-3B~\citep{llama3}, Qwen2.5-3B~\citep{qwen25}, and Gemma-2-2B~\citep{gemma2} -- on unseen test adapters drawn from instruction-following, reasoning, question-answering, code, and classification tasks. Across all three architectures, the detector achieves 100% accuracy.

We systematically investigate the parameter-efficient fine-tuning design space under practical data and compute constraints, and propose D2-LoRA. D2-LoRA achieves 76.4 percent average accuracy across eight question answering and reading comprehension benchmarks using only 5k training samples per task and two epochs, while preserving algebraic mergeability at inference with near-exact numerical equivalence. The method combines signed low-rank residual updates with additive and subtractive components, together with a train-time column-wise projection that keeps each column close to its original norm. After training, the adapter is merged into a single weight matrix, adding zero inference latency. Compared with LoRA, D2-LoRA improves average accuracy by 2.2 percentage points; at matched parameter counts (LoRA rank 2r versus D2-LoRA rank r), the improvement is 1.6 points, indicating gains from architectural design rather than increased parameterization. Compared with DoRA, it matches or exceeds performance on most tasks. Beyond QA and reading comprehension, D2-LoRA improves generative tasks (plus 1.2 ROUGE-L and plus 1.1 percent win rate) and shows 36 percent lower training volatility. The merge preserves numerical fidelity (mean gap about 0.03 percentage points) and recovers about 1.91x evaluation throughput. Training overhead is 19 percent, comparable to DoRA, and decreases with longer input sequences. We provide a geometric analysis explaining how the projection stabilizes training, together with ablation studies isolating the contribution of each design component.

Large Language Models (LLMs) have achieved remarkable progress, with Parameter-Efficient Fine-Tuning (PEFT) emerging as a key technique for downstream task adaptation. However, existing PEFT methods mainly operate in Euclidean space, fundamentally limiting their capacity to capture complex geometric structures inherent in language data. While alternative geometric spaces, like hyperbolic geometries for hierarchical data and spherical manifolds for circular patterns, offer theoretical advantages, forcing representations into a single manifold type ultimately limits expressiveness, even when curvature parameters are learnable. To address this, we propose Mixture of Space (MoS), a unified framework that leverages multiple geometric spaces simultaneously to learn richer, curvature-aware representations. Building on this scheme, we develop MoSLoRA, which extends Low-Rank Adaptation (LoRA) with heterogeneous geometric experts, enabling models to dynamically select or combine appropriate geometric spaces based on input context. Furthermore, to address the computational overhead of frequent manifold switching, we develop a lightweight routing mechanism. Moreover, we provide empirical insights into how curvature optimization impacts training stability and model performance. Our experiments across diverse benchmarks demonstrate that MoSLoRA consistently outperforms strong baselines, achieving up to 5.6% improvement on MATH500 and 15.9% on MAWPS.

Temporal domain generalization (TDG) learns from a sequence of observed domains to predict models for unseen future domains. Existing parameter-dynamics methods become prohibitively expensive at modern backbone scales because their temporal encoders and generators operate on the entire adapted parameter state. Replacing full-model updates with LoRA does not remove this failure mode: the dynamics model must still encode and reconstruct every adapter parameter, making the auxiliary model itself prohibitively large for modern backbones. We propose Low-rank Time-varying Core (LoTiC), a parameter-efficient TDG method that decomposes temporal updates into shared low-rank bases and a compact core. The bases define a stable update subspace, while only the core evolves. LoTiC therefore learns temporal dynamics in an r*r space instead of tracking the full adapter. We justify this factorization through the geometry of parameter increments and support continuous, recurrent, and time-conditioned core models. Experiments span six controlled and real-world benchmarks, three data modalities, classification and generation, and backbones from 66M to 8B parameters. LoTiC ranks first in 14 of 15 settings, including near-perfect future-domain accuracy with an 8B backbone on Rotating 2-Moons. It adds only 0.13--0.51% trainable parameters beyond LoRA and trains 1.8--7.1$\times$ faster than parameter-dynamics baselines. These results establish that temporal parameter dynamics can remain both learnable and efficient as pretrained backbones scale.

Deep learning models trained to optimize average accuracy often exhibit systematic failures on particular subpopulations. In real-world settings like healthcare, the subpopulations most affected by such disparities are frequently unlabeled, partially observed, or not known in advance. Existing group-robust methods typically assume prior knowledge of the relevant subgroups, using group annotations for training, validation, or model selection. We propose Misclassification Aware Rank-Limited Adaptation (MARLA), a parameter-efficient method for improving worst group performance without explicit subgroup annotations. MARLA leverages an ERM-trained model by calculating the model's misclassification probability scores on a held-out adaptation set to identify a low-dimensional subspace where errors concentrate. We then learn a rank-restricted additive correction to the classifier logits within that subspace. Across seven real-world datasets, we evaluate group robustness under three settings: no knowledge of subgroup relevance, partial knowledge of subgroup relevance, and full knowledge of subgroup relevance. MARLA improves worst-group performance while remaining fast and parameter-efficient, with data-guided hyperparameter selection.

We propose SHINE (Scalable Hyper In-context NEtwork), a scalable hypernetwork that can map diverse meaningful contexts into high-quality LoRA adapters for large language models (LLMs). By reusing the frozen LLM's own parameters in an in-context hypernetwork design and introducing architectural innovations, SHINE overcomes key limitations of prior hypernetworks and achieves strong expressive power with a relatively small number of parameters. We introduce a pretraining and instruction fine-tuning pipeline, and train our hypernetwork to generate high quality LoRA adapters from diverse meaningful contexts in a single forward pass. It updates LLM parameters without any fine-tuning, and immediately enables complex question answering tasks related to the context without directly accessing the context, effectively transforming in-context knowledge to in-parameter knowledge in one pass. Our work achieves outstanding results on various tasks, greatly saves time, computation and memory costs compared to SFT-based LLM adaptation, and shows great potential for scaling. Our code is available at https://github.com/MuLabPKU/SHINE

Low-rank adaptation (LoRA) approximates the update of a pretrained weight matrix using the product of two low-rank matrices. However, standard LoRA follows an explicit-rank paradigm, where increasing model capacity requires adding more rows or columns (i.e., basis vectors) to the low-rank matrices, leading to substantial parameter growth. In this paper, we find that these basis vectors exhibit significant parameter redundancy and can be compactly represented by lightweight nonlinear functions. Therefore, we propose Generative Low-Rank Adapter (GenLoRA), which replaces explicit basis vector storage with nonlinear basis vector generation. Specifically, GenLoRA maintains a latent vector for each low-rank matrix and employs a set of lightweight radial basis functions (RBFs) to synthesize the basis vectors. Each RBF requires far fewer parameters than an explicit basis vector, enabling higher parameter efficiency in GenLoRA. Extensive experiments across multiple datasets and architectures show that GenLoRA attains higher effective LoRA ranks under smaller parameter budgets, resulting in superior fine-tuning performance. The code is available at https://anonymous.4open.science/r/GenLoRA.

Low-Rank Adaptation (LoRA) methods have emerged as crucial techniques for adapting large pre-trained models to downstream tasks under computational and memory constraints. However, they face a fundamental challenge in balancing task-specific performance gains against catastrophic forgetting of pre-trained knowledge, where existing methods provide inconsistent recommendations. This paper presents a comprehensive analysis of the performance-forgetting trade-offs inherent in low-rank adaptation using principal components of weight matrices as initialization. Our investigation reveals that fine-tuning intermediate components leads to better balance and robustness to high learning rates than first (PiSSA) and last (MiLoRA) components in existing work. Building on these findings, we provide practical guidelines for initialization of LoRA methods to balance the performance-forgetting trade-off. In a thorough empirical study on a variety of computer vision and NLP tasks we confirm that these guidelines achieve high accuracy and reduced forgetting.

Parameter-efficient continual learning aims to adapt pre-trained models to sequential tasks without forgetting previously acquired knowledge. Most existing approaches treat continual learning as avoiding interference with past updates, rather than considering what properties make the current task-specific update naturally preserve previously acquired knowledge. From a knowledge-decomposition perspective, we observe that low-rank adaptations exhibit highly imbalanced singular value spectra: a few dominant components absorb most of the adaptation energy, thereby (i) more likely to disrupt previously acquired knowledge and (ii) making the update more vulnerable to interference from subsequent tasks. To enable explicit balance among components, we decouple the magnitude of the task update from its directional structure and formulate it as a constrained optimization problem on a restricted Stiefel manifold. We address this problem using a projected first-order method compatible with standard deep-learning optimizers used in vision-language models. Our method mitigates both backward and forward forgetting, consistently outperforming continual learning baselines. The implementation code is available at https://github.com/haodotgu/EBLoRA.

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.

Mixture-of-Experts (MoE) has become a prominent paradigm for scaling Large Language Models (LLMs). Parameter-efficient fine-tuning methods, such as LoRA, are widely adopted to adapt pretrained MoE LLMs to downstream tasks. However, existing approaches typically assign identical LoRA ranks to all expert modules, ignoring the heterogeneous specialization of pretrained experts. This uniform allocation leads to a resource mismatch: task-relevant experts are under-provisioned, while less relevant ones receive redundant parameters. To address this, we propose DR-LoRA, a Dynamic Rank LoRA framework for fine-tuning pretrained MoE models. Specifically, DR-LoRA initializes all expert LoRA modules with a small active rank and uses an expert saliency score, which combines routing frequency and gradient-based rank importance, to identify which experts would benefit most from additional capacity. It then periodically expands the active ranks of the task-critical expert LoRA, progressively constructing a heterogeneous rank distribution tailored to the target task. Experiments on three MoE models across six tasks show that DR-LoRA consistently outperforms LoRA and other strong baselines, demonstrating that task-adaptive heterogeneous rank allocation is an effective strategy to improve active capacity utilization in MoE fine-tuning.

We investigate the potential of weights to serve as effective representations, focusing on neural fields. Our key insight is that constraining the optimization space through a pre-trained base model and low-rank adaptation (LoRA) can induce structure in weight space. Across reconstruction, generation, and analysis tasks on 2D and 3D data, we find that multiplicative LoRA weights achieve high representation quality while exhibiting distinctiveness and semantic structure. When used with latent diffusion models, multiplicative LoRA weights enable higher-quality generation than existing weight-space methods.

On-device deployment of Large Language Models (LLMs) frequently leverages Low-Rank Adapters (LoRAs) to support diverse downstream tasks under tight resource constraints. To address the limited storage capacity of mobile devices, recent works have explored model merging techniques to fuse multiple LoRAs into a single one. In practice, however, LoRAs are often delivered incrementally, as users request support for new tasks (e.g., novel problem types or languages). This scenario introduces a new challenge: on-device online continual merging, where the objective is to incorporate new LoRAs while preserving the performance on previously supported tasks. In this paper, we propose a data-free and computationally efficient strategy for selecting and merging LoRAs when a new one becomes available, assuming the device can store only a limited number of adapters. Extensive experiments across real-world tasks demonstrate the superiority of our approach compared to alternative strategies while adhering to the storage budget and compute limitations of on-device settings. The project page is available at: https://donaldssh.github.io/K-Merge.

Preference tuning typically distributes adapter updates across every Transformer layer. We study how the placement of a fixed LoRA budget affects Direct Preference Optimization (DPO). Hierarchical Alignment partitions decoder depth into Local, Intermediate, and Global regions and restricts LoRA updates to a chosen contiguous block. Across Qwen and Llama models, three-seed sliding-window sweeps reveal broad low-loss basins around intermediate depth. Under exact trainableparameter matching, Middle achieves lower held-out DPO loss than an all-depth allocation on Qwen2.5-7B and Llama-3.1-8B. Generationlevel evidence is more variable. LLM judges and a blinded human study leave Selected versus All unresolved on Qwen; on Llama, two pairwise judges favor All while the human interval includes zero. Trained-adapter interventions show that learned depth components affect the optimization objective; removing the Llama Selected window also lowers generation quality. Across Qwen2.5 at 3B, 7B, and 14B, Middle versus All remains unresolved under Qwen3-Max; at 3B and 14B, both improve over Base. In our implementation, Middle also uses less peak memory and takes shorter steps than a parameter-matched all-depth allocation. Together, the results support intermediate depth as a practical starting point for fixed-budget preference tuning, though the best window and its behavioral value still need per-setting validation.

As increasingly large pre-trained models are released, deploying them on edge devices for privacy-preserving applications requires effective compression. Recent works combine quantization with the fine-tuning of high-precision LoRA adapters, which can substantially reduce model size while mitigating the accuracy loss from quantization. However, edge devices have inherently heterogeneous capabilities, while performing configuration-wise fine-tuning for every quantization setting is computationally prohibitive. In this paper, we propose CoA-LoRA, a method that dynamically adjusts the LoRA adapter to arbitrary quantization configurations (i.e., the per-layer bit-width choices of a pre-trained model) without requiring repeated fine-tuning. This is accomplished via a configuration-aware model that maps each configuration to its low-rank adjustments. The effectiveness of this model critically depends on the training configuration set, a collection of configurations chosen to cover different total bit-width budgets. However, constructing a high-quality configuration set is non-trivial. We therefore design a Pareto-based configuration search that iteratively optimizes the training configuration set, yielding more precise low-rank adjustments. Our experiments demonstrate that, unlike the state-of-the-art methods that require fine-tuning a separate LoRA adapter for each configuration, CoA-LoRA incurs no additional time cost while achieving comparable or even superior performance to those methods.

Low-Rank Adaptation (LoRA) has become a widely adopted technique in text-to-image diffusion models, enabling the personalisation of visual concepts such as characters, styles, and objects. However, existing approaches struggle to effectively compose multiple LoRA adapters, particularly in open-ended settings where the number and nature of required skills are not known in advance. In this work, we present LoRAtorio, a novel train-free framework for multi-LoRA composition that leverages intrinsic model behaviour. Our method is motivated by two key observations: (1) LoRA adapters trained on narrow domains produce denoised outputs that diverge from the base model, and (2) when operating out-of-distribution, LoRA outputs show behaviour closer to the base model than when conditioned in distribution. The balance between these two observations allows for exceptional performance in the single LoRA scenario, which nevertheless deteriorates when multiple LoRAs are loaded. Our method operates in the latent space by dividing it into spatial patches and computing cosine similarity between each patch's predicted noise and that of the base model. These similarities are used to construct a spatially-aware weight matrix, which guides a weighted aggregation of LoRA outputs. To address domain drift, we further propose a modification to classifier-free guidance that incorporates the base model's unconditional score into the composition. We extend this formulation to a dynamic module selection setting, enabling inference-time selection of relevant LoRA adapters from a large pool. LoRAtorio achieves state-of-the-art performance, showing up to a 1.3% improvement in ClipScore and a 72.43% win rate in GPT-4V pairwise evaluations, and generalises effectively to multiple latent diffusion models. Project page: https://nickyfot.github.io/loratorio-skill-composer/

Parameter-Efficient Fine-Tuning (PEFT) is essential for adapting Large Language Models (LLMs) to multi-task scenarios. A prevailing trend in this field involves complex LoRA variants with multiple adapters or heads, which rely on the premise that architectural isolation of task-specific knowledge is necessary. However, this design often introduces dynamic routing, preventing weight merging and causing significant inference latency. In this work, we present a direct challenge to this paradigm. We first reveal a paradox where a simplified, router-free multi-head model with high inter-head redundancy outperforms complex, diversity-driven baselines. Furthermore, we demonstrate that a unified, single-adapter LoRA with increased rank achieves highly competitive performance, questioning the necessity of multi-component structures. Based on these findings, we propose Align-LoRA, a unified and efficient framework that shifts the focus from architectural isolation to representation alignment. Align-LoRA incorporates an explicit alignment loss to encourage the learning of task-shared representations within a shared latent space. Crucially, our method maintains the standard LoRA architecture, ensuring zero inference latency via weight merging. Theoretical analysis and extensive experiments confirm that Align-LoRA significantly surpasses prevailing approaches, establishing a simpler, more effective, and production-friendly paradigm for multi-task PEFT. The code is available at https://github.com/jinda-liu/Align-LoRA.

Low-Rank Adaptation (LoRA) has gained popularity as a fine-tuning approach for Large Language Models (LLMs) due to its low resource requirements and good performance. While numerous studies have investigated ways to improve LoRA serving efficiency by serving multiple LoRAs concurrently, existing methods assume that a wide range of LoRA adapters are available for serving. In our work, we conduct extensive empirical studies to show that current LoRA training paradigms do not efficiently utilize hardware resources and incur high overhead to obtain a performant LoRA adapter. Leveraging these insights, we propose PLoRA, which automatically orchestrates concurrent LoRA fine-tuning jobs under given hardware and model constraints and develops performant kernels to improve training efficiency. Across a range of LLMs and LoRA configurations, PLoRA improves training throughput by up to 12.8x and reduces the overall fine-tuning makespan by up to 7.52x compared to existing approaches.

Adapting large pretrained vision models to medical image classification is often limited by memory, computation, and task-specific specializations. Parameter-efficient fine-tuning (PEFT) methods like LoRA reduce this cost by learning low-rank updates, but operating directly in feature space can struggle to capture the localized, multi-scale features common in medical imaging. We propose WaRA, a wavelet-structured adaptation module that performs low-rank adaptation in a wavelet domain. WaRA reshapes patch tokens into a spatial grid, applies a fixed discrete wavelet transform, updates subband coefficients using a shared low-rank adapter, and reconstructs the additive update through an inverse wavelet transform. This design provides a compact trainable interface while biasing the update toward both coarse structure and fine detail. For extremely low-resource settings, we introduce Tiny-WaRA, which further reduces trainable parameters by learning only a small set of coefficients in a fixed basis derived from the pretrained weights through a truncated SVD. Experiments on medical image classification across four modalities and datasets demonstrate that WaRA consistently improves performance over strong PEFT baselines, while retaining a favorable efficiency profile. Our code is publicly available at https://github.com/moeinheidari7829/WaRA.

Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates continual learning (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of large pre-trained models (LPMs), efficiency has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs layer-wise adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ bandit techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both vision transformers (ViTs) and large language models (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.

We introduce CoLoRA (Convolutional Low-Rank Adaptation), a parameter-efficient fine-tuning method for convolutional neural networks (CNNs). CoLoRA extends LoRA to convolutional layers by decomposing kernel updates into lightweight depthwise and pointwise components. This design reduces the number of trainable convolutional-update parameters by over 80% compared with full convolutional fine-tuning, while allowing the learned updates to be merged into the pretrained convolutional kernels, thereby preserving the original model size and inference complexity. Experiments on MedMNIST datasets, particularly OCTMNISTv2, demonstrate that CoLoRA applied to VGG16 and ResNet50 achieves competitive classification performance while substantially reducing the number of trainable parameters. Comparisons with transfer learning, adapters, BitFit, and convolutional LoRA variants further characterize the trade-offs among predictive performance, trainable parameters, and training cost. Additional experiments on CIFAR-100 and Cats vs. Dogs provide preliminary evidence that the proposed adaptation strategy also transfers to non-medical image-classification tasks. Peak GPU-memory measurements further show that parameter efficiency does not translate directly into proportional training-memory savings, with memory consumption depending strongly on the placement of the adapted convolutional layers. Overall, CoLoRA provides a parameter-efficient and deployment-efficient alternative to full fine-tuning for convolutional models.

Pre-trained visual models have become fundamental in computer vision, but they face challenges in continual learning scenarios where data and tasks evolve over time. Low-Rank Adaptation (LoRA) offers efficient fine-tuning capabilities but remains limited for such dynamic environments. Standard LoRA cannot distinguish important subspaces, causing critical knowledge to be overwritten in sequential training. Existing approaches address this by dynamically expanding the set of LoRA adapters, either maintaining a growing pool of task-specific modules or merging new adapters into prior ones, at the cost of unbounded parameter growth or increasing inference complexity. We propose Continual Low-Rank Adaptation (C-LoRA), a method that enables a single, shared LoRA adapter to handle sequential tasks without catastrophic forgetting, without requiring any module selection or fusion at inference. The core of C-LoRA is a learnable routing matrix R that explicitly controls how each rank-one subspace contributes to the weight update. This matrix is decomposed into a stability component (R_base), which preserves knowledge from prior tasks, and a plasticity component (R_delta), which drives adaptation to the current task, providing direct control over the stability-plasticity trade-off. We analyze how R governs gradient flow during sequential training, and demonstrate competitive performance across multiple benchmarks.

Low-Rank Adaptation (LoRA) has become a standard approach for parameter-efficient fine-tuning of image diffusion models, with over 200K models trained to replicate artistic styles and shared in online communities. One way to analyze styles of LoRA models is to generate image samples and apply image-based features like CLIP. However, this generation requires additional computation and prompt selection. In this work, we propose analyzing styles directly in the LoRA weight space, bypassing these limitations while achieving better performance even on unseen LoRAs. Since in-the-wild LoRAs lack ground truth model details, we design an experimental setup and show that LoRA weights alone serve as effective feature representations of adapted styles, robust to variations in fine-tuning seeds and image selection. We extensively evaluate using SD1.5 (the most popular base model within online communities) across data domains (fine-art paintings, architectural photos) and diverse prompt settings, with a small-scale SDXL experiment further verifying generalization. These evaluations confirm that our approach, under the selected aspects of variability, preserves fine-grained styles and outperforms image-based methods in clustering and retrieval of unseen LoRAs.

Parameter-efficient fine-tuning (PEFT) has become a de facto standard for adapting large language models (LLMs). However, we identify a critical vulnerability within popular low-rank adaptation methods such as LoRA: they can exacerbate "Catastrophic Inheritance" - the unchecked propagation of biases, noise, and data imbalances from pre-training. This phenomenon can degrade model robustness and fairness, undermining the benefits of efficient adaptation. To address this, we introduce Bias-Alleviating Low-Rank Adaptation (BA-LoRA). Our approach is founded on a principled decomposition of Catastrophic Inheritance into three core challenges: Knowledge Drift, Representation Collapse, and Overfitting to Noise. BA-LoRA systematically mitigates these issues by incorporating a trio of targeted regularizers: consistency, diversity, and an SVD-based term, designed to preserve core knowledge, promote representational richness, and encourage robust, low-rank output representations, respectively. We conduct comprehensive evaluations on a suite of Natural Language Generation (NLG) and Natural Language Understanding (NLU) tasks using diverse, prominent open-source language models (e.g., LLaMA-2-7B and DeBERTa-v3-base). Our results show that BA-LoRA not only outperforms state-of-the-art LoRA variants in terms of performance and stability, but also demonstrates superior robustness and bias mitigation on targeted evaluations. These results provide evidence that BA-LoRA can counteract the adverse effects of Catastrophic Inheritance.