Low-Rank Adaptation

Face presentation attack detection (PAD) aims to reliably detect a wide range of presentation attacks. While PAD methods achieve strong performance within individual datasets, their performance degrades under cross-dataset evaluation. Variations in sensors or lighting conditions can reduce the effectiveness of detectors from near-perfect to nearly random. Foundation models (FMs) have emerged as a promising alternative because typical PAD datasets, such as the MCIO benchmarks (MSU-MFSD, CASIA-FASD, Replay-Attack, and OULU-NPU), are small relative to the scale used for web-based pretraining. However, existing PAD systems primarily focus on CLIP-based foundation models, while overlooking other FMs with different architectures and training procedures. This study addresses this question by systematically evaluating 32 FMs. Zero-shot prompting achieves performance near chance across model families and scales. The vision encoders, when low-rankadapted (LoRA) with fewer than 1% trainable weights, achieve below 2% intra-dataset ACER in most cases, while cross-dataset ACER is substantially higher. LoRA primarily refines the decision boundary within a dataset, suggesting that pretrained representations and the adaptation dataset play a larger role in cross-dataset generalization than the evaluated lightweight adaptation strategy.

Omnimodal language models (OLMs) enable unified audio-visual understanding, but processing long joint token sequences makes inference computationally prohibitive. While recent token compression methods attempt to alleviate this burden, compressing modalities in isolation often destroys the temporal cross-modal anchors necessary for coherent reasoning. We introduce Omni2LoRA, a two-stage framework for efficient parametric memory compression via coherence-preserving context distillation that bypasses the token bottleneck entirely. First, a Perceiver hypernetwork processes intermediate representations from a frozen OLM to encode the multimodal context into a full-rank Low-Rank Adaptation (LoRA) adapter in a single forward pass. To prevent the resulting parameter footprint from scaling linearly with recording length, we optimize a discrete rank allocation policy via Group Relative Policy Optimization (GRPO) that uses a modality-ablated counterfactual reward to explicitly penalize the loss of audio-visual coherence, forcing the model to allocate its fixed sub-linear rank budget to synergistic cross-modal anchors rather than isolated visual features. Across three omnimodal backbones, Omni2LoRA operating at a 30% rank budget outperforms direct full-context inference and strong token-compression baselines (OmniZip, OMAC, O-MARC) on four audio-visual question answering benchmarks, improving average accuracy by 8-12% over the strongest baseline and remaining stable under compression ratios as tight as 75%, where token-pruning methods degrade sharply. By converting multimodal memory into a fixed-budget, reusable parameter state, our method drives answer-time multimodal-token load to zero, cutting per-query Time to First Token (TTFT) by up to 12x relative to full-context inference and amortizing to under 0.5s after a handful of queries.

Retinal vessel segmentation in multi-domain deployment requires a source model to adapt to domains that differ in imaging conditions and annotation conventions. Conventional parameter-efficient fine-tuning reduces target-specific storage, but its highly restricted adaptation subspace can be insufficient for reconstructing thin, connected vascular structures. We therefore ask how target-specific capacity should be allocated so that topology-aware supervision remains effective under a strict per-domain parameter budget. Based on this principle, we propose TAPDecoderFT, a topology-responsive, role-structured adaptation framework. Specifically, TAPDecoderFT shares a fixed source parameter state across deployment domains, uses low-rank residuals for target-specific private/fusion feature mixing, and retains a trainable dense-reconstruction path comprising the decoder, output head, and refinement module. To promote structurally faithful predictions, the compact target state is jointly optimized with a region-overlap and topology-aware objective that encourages centerline continuity and thin-branch recovery. It improves both DSC and clDice over GenericLoRA-r4 and narrow TAP-r4 in all six directions and is comparable to full fine-tuning.

Parameter-efficient fine-tuning enables the adaptation of vision foundation models to biomedical tasks under limited computational resources, but a single low-rank update can constrain all task-specific changes to one narrow parameter subspace. This restriction may prevent the model from simultaneously representing globally shared task structure and localized residual directions required for generalization to unseen imaging domains. We introduce LoRSA, a global--residual adaptation framework that jointly learns a dense low-rank component and a dynamically structured-sparse low-rank component. The dense component captures globally coordinated task adaptation, while the structured component provides complementary residual corrections whose support evolves during training. We characterize the representational capacity, approximation properties, rank structure, and singular-subspace complementarity of this decomposition. We evaluate LoRSA for four-class breast-density classification using DINOv3-Base, with VinDr-Mammo as the source domain and MammosighTR and RSNA as unseen external domains. LoRSA remains competitive on the internal validation set and achieves the best external macro-F1 on both target datasets, improving upon the strongest competing method by 2.15 percentage points on MammosighTR and 3.09 percentage points on RSNA. Weight-matrix analysis further shows that approximately $92\%$ of the energy of each adaptation component lies outside the bilateral singular subspace of the other, indicating that the two components learn largely complementary update directions. These results suggest that organizing adaptation capacity into distinct global and residual paths can improve the external-domain generalization of parameter-efficiently adapted biomedical vision models.

Pretrained partial differential equation (PDE) foundation models can generalize across different equations, but adapting them to unseen PDE systems typically requires dense solution data, which is often expensive or unavailable. To address this limitation, we propose an unsupervised PDE-based finetuning framework that eliminates the need for ground-truth solutions. We first pretrain a neighborhood attention Transformer on diverse time-dependent PDEs spanning varying spatial scales, yielding transferable representations across heterogeneous equations. In the adaptation stage, we construct a physics-based objective using the PDE residual and boundary conditions, and finetune the model on unseen equations via low-rank adaptation (LoRA). To address the uneven learning across physical quantities in standard LoRA, we introduce NSLoRA, a Newton-Schulz orthogonalized variant that rebalances adaptation. Our method achieves performance comparable to supervised LoRA finetuning without requiring any ground-truth solutions, while consistently outperforming competitive neural operator baselines and recent PDE foundation models across heterogeneous PDE benchmarks spanning multiple spatial dimensions.

Low-rank adaptation (LoRA) enables efficient specialization and distribution of large language models through compact adapters. However, untrusted adapters introduce a supply-chain threat: a backdoored adapter can cause a model to generate harmful content, malicious code, political propaganda, or covert advertisements when an input contains a hidden trigger. Adapter-agnostic defenses merge the adapter with the base model, which dilutes backdoor signals and reduces detection performance. Existing adapter-aware methods do not address how to safely use a potentially backdoored adapter. Instead, they either train a defensive adapter to repair a backdoored base model, addressing the inverse problem rather than securing the adapter itself, or rely on a classifier that flags the entire adapter as suspicious and requires separate mitigation. These methods overlook the distinct latent-space signatures produced by trigger-bearing inputs in backdoored adapters. We introduce LoRAScan, the first adapter-aware defense that detects and rejects trigger-bearing inputs at inference time without modifying adapter parameters. Our key observation is that a small subset of LoRA insertion sites, approximately 5%, remains stable across clean inputs but exhibits highly concentrated spikes in LoRA down-projection activations when a trigger is present. LoRAScan identifies these low-variance insertion sites before model deployment and monitors them during inference. Across standard LLM backdoor benchmarks, LoRAScan rejects 98.49% of malicious inputs with a small error rate on clean inputs, outperforming existing defenses across diverse evaluation settings.

Machine learning and optimization have advanced together, with practical demands motivating new theory and theoretical breakthroughs enabling new applications. Modern large-scale training relies on classical optimization principles, but the constraints of distributed systems require these foundations to be reconsidered. This thesis addresses seven challenges at the intersection of theory and practice, focusing on key bottlenecks in federated learning and distributed optimization. First, we introduce ProxSkip and prove that local gradient steps can accelerate communication, providing a theoretical foundation for this widely used heuristic. Second, we develop Variance Reduced ProxSkip, which eliminates the neighborhood error of stochastic local updates while balancing communication and local computation. Third, we show that local steps retain their communication acceleration under partial client participation. Fourth, we prove that server-side stepsizes and sampling without replacement improve convergence in heterogeneous settings. Fifth, for Random Reshuffling, we demonstrate that compressing gradient differences rather than gradients yields better theoretical and practical performance. Sixth, we establish that Byzantine robustness and partial participation can be achieved simultaneously using gradient-difference clipping. Finally, we develop the first theoretical framework for low-rank adaptation based on randomized asymmetric chains, providing new insights into fine-tuning large models. Across these contributions, we introduce novel algorithmic frameworks, establish sharp guarantees under realistic assumptions, and support the theory with numerical experiments.

Multi-task supervised fine-tuning (SFT) often casts a heterogeneous data mixture as a single optimization problem, even though different tasks may reach their best generalization at different times. msft exposes this mismatch through task-wise roll-out, exclusion, and rollback, but its original formulation materializes the scheduler state as full-model checkpoints, making stage transitions costly to store, restore, and deploy. This paper introduces AuroSFT, a parameter-efficient framework that recasts the carried state of overfitting-aware multi-task SFT as a compact, mergeable adapter state. AuroSFT freezes the pretrained backbone, trains only injected adapters, rolls back adapter checkpoints at task-wise peaks, and continues on the remaining active mixture. At the layer level, each adapter applies an AuroRA-inspired adaptive nonlinear layer to a low-rank weight factor rather than to the sample representation. The resulting update remains linear in the input, rank-bounded, and exactly mergeable into the frozen projection. Under the retained-backbone comparison protocol, AuroSFT achieves 61.36% average accuracy, compared with 59.85% for the corresponding msft reference row, and obtains higher accuracy on all five backbones. Our code is available at the anonymous repository: https://anonymous.4open.science/r/AuroSFT-80D1.

Federated learning (FL) enables collaborative training of deep learning models across decentralized image archives without requiring data centralization. This paradigm is particularly relevant in remote sensing (RS), where legal regulations, privacy concerns, and bandwidth constraints restrict data sharing. However, the presence of training data heterogeneity across clients (known as non-IID data) can impede convergence and limit the generalization capability of the aggregated global model. To mitigate the adverse effects of training data heterogeneity, vision-language models (VLMs) can be leveraged in FL due to their transferable representations, which have demonstrated robustness under distribution shifts. However, their large parameter size may substantially increase communication overhead and local computational complexity in federated settings. Therefore, it is crucial to select an appropriate VLM adaptation strategy that balances the generalization ability with the communication and computational constraints. To address this issue, in this paper, we present the first comparative study of VLM adaptation strategies for FL in the context of RS image classification. We investigate full fine-tuning, encoder-specific fine-tuning, prompt learning, and low-rank adaptation (LoRA) tuning, and analyze them with respect to three criteria: 1) generalization capability under non-IID data, 2) communication overhead, and 3) local computational complexity. Experiments on BigEarthNet-S2, EuroSAT, RESISC45, and ImageNet reveal distinct trade-offs between task specialization, cross-domain generalization, and efficiency. Based on our findings, we derive a guideline for the selection of an appropriate VLM adaptation strategy in FL for RS image classification under different operational constraints. The code of this work is publicly available at https://git.tu-berlin.de/rsim/FL-RS-VLM.

Financial sentiment classifiers are commonly evaluated against human labels, but strong linguistic performance does not necessarily imply economically useful return predictability. This study separates these questions through two experiments. First, we construct a unified three-class benchmark from five financial text datasets and compare TF--IDF Naive Bayes, off-the-shelf FinBERT and Financial-RoBERTa encoders, zero-shot Qwen2.5-7B, and QLoRA-adapted Qwen2.5-7B, LLaMA3-8B, and Mistral-7B models. Mistral-7B achieves the best test accuracy (0.8840) and macro-F1 (0.8771), while QLoRA raises Qwen2.5's macro-F1 from 0.7274 to 0.8615. An inverse-frequency class-weighted loss does not improve Qwen2.5. Second, we evaluate economic validity on a temporally separate 2019 Benzinga sample containing 10,637 unique headlines and 13,115 headline--stock observations for a fixed S&P~100 universe. Model probabilities are converted into continuous sentiment scores, aggregated by stock and signal date, and aligned with next-session returns over one-, two-, three-, and five-day horizons. All seven downstream models produce positive but small mean rank information coefficients at the one-day horizon; the largest is 0.0143 for FinBERT. None of the 28 model--horizon tests remains significant after Newey--West inference and false-discovery-rate correction. Portfolio results likewise fail to establish a robust advantage for the best-performing classifiers. The findings show that QLoRA is effective for financial sentiment adaptation, while also documenting a clear gap between classification accuracy and tradable cross-sectional signals.

Vision-language models exhibit remarkable zero-shot capabilities but suffer significant performance degradation under distribution shifts. While test-time adaptation (TTA) via Low-Rank Adaptation offers a parameter-efficient solution, we identify a fundamental bottleneck in current methods: the reliance on static rank configurations. Because visual inputs inherently possess varying information densities, a fixed rank forces an inevitable optimization compromise, leading to underfitting on complex scenes and overfitting on simple ones. To bridge this gap, we propose Multi-Rank Adaptation (MuRA), a novel framework that dynamically selects and fuses adaptation modules of varying capacities based on token-level visual complexity. MuRA synergizes Multi-Rank Orthogonal Decomposition to provide a superior, knowledge-preserving initialization, and Unified Component Fusion with Continuous Router Updating to sustainably learn semantic-to-rank mappings. Furthermore, we provide rigorous theoretical justifications mathematically proving the necessity and gradient stability of this adaptive mechanism. Crucially, MuRA's dynamic design uniquely thrives at the deepest visual layer, capitalizing on the shortest gradient backpropagation path. Extensive experiments demonstrate that MuRA achieves state-of-the-art accuracy across extensive domain generalization and cross-dataset benchmarks while significantly reducing both computational and memory overhead.

Federated fine-tuning with Low-Rank Adaptation (LoRA) enables efficient collaborative adaptation of Large Language Models (LLMs) without centralizing private data. However, LoRA's two-factor parameterization creates an aggregation mismatch across clients: naively averaging the factors does not recover the average of their induced updates. This mismatch can be avoided by forming the exact aggregate in the full weight space and then recompressing it, but decomposing the resulting dense matrix is computationally expensive and memory-intensive. We propose FraQ, an efficient coordinate-space recompression method for federated LoRA. Starting from stacked factors that exactly represent the aggregate, FraQ factorizes it into an orthonormal basis and a compact coordinate matrix. It then recovers the singular spectrum from a small Gram matrix, selects the smallest rank satisfying a prescribed energy threshold, and maps the selected coordinate subspace back through the basis to construct the global adapter. Experiments on text classification and commonsense reasoning benchmarks show that FraQ achieves accuracy close to uncompressed baselines while substantially reducing downlink communication with low server-side recompression overhead.

Modern multi-tenant Low-Rank Adapters (LoRAs) serving systems concurrently host tens to hundreds of LoRA adapters. Though powerful, this introduces a critical system dilemma between serving efficiency and task performance: higher-rank adapters generally achieve better downstream task performance, but their GPU VRAM footprint and Host-to-Device PCIe swapping overhead severely constrain scalability. Conversely, ultra-low-rank adapters ($r \le 2$) minimize both VRAM footprint and PCIe transfer overhead, but suffer from downstream task performance degradation. To solve this problem, we propose Subspace-Aligned LoRA Training (SALT), a serving efficiency-aware hierarchical fine-tuning framework. Our solution operates in three phases. First, a provider jointly trains high-capacity domain centroids on public data within the domain using a novel alignment regularizer that coheres in-domain task subspaces into a unified basis. Next, users fine-tune ultra-low-rank task residual adapters on private data atop those frozen centroids. Finally, during inference, the provider pins the centroid in GPU VRAM and dynamically swaps in each user's task residual on demand. Across LLMs of varying scales, SALT recovers high-rank accuracy using $r \le 2$ residuals, achieving up to 18.5% absolute accuracy gains over state-of-the-art compression baselines and reducing per-adapter memory by up to 16x. When integrated into vLLM, SALT improves serving throughput by up to 51% under PCIe bandwidth pressure and 28% under GPU VRAM constraints for Llama-3.2-3B.

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.

Parameter-efficient post-training reduces the number of trainable parameters, but still requires repeated end-to-end backpropagation through the frozen backbone. Every adaptation step therefore needs backward-capable hardware and must store or recompute activations. We ask whether this repeated backward chain can be replaced by a one-time calibration. We introduce Local Credit Assignment (LoCA), a two-stage method for small-shift adaptation. One probe backward pass fits a low-rank map at each transformer block from the final prediction error to a local hidden-state correction. LoCA then reuses these maps to form blockwise regression targets from forward activations and fits low-rank adapters with closed-form ridge solves. No further backbone backward pass is required. We evaluate LoCA on five discriminative benchmarks with Qwen2.5 models from 0.5B to 14B. In 16 of 25 reported task--scale comparisons, LoCA yields lower evaluation cross-entropy than the corresponding LoRA run. Its measured full-run GPU peak, including calibration, is 26--29% lower than LoRA's. After calibration, its CPU steady-state memory is 36--52% lower and its per-pass time is 43--48% lower. A shared scale-normalized candidate set is reused across all tested Qwen2.5 sizes and on SmolLM2-1.7B. LoCA thus amortizes global credit assignment into one calibration and enables later forward-only tuning when repeated backpropagation is impractical. The code associated with this paper is available here.

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

Geospatial foundation models (GeoFMs), pretrained on large-scale geospatial data such as Earth observation (EO), climate, and weather data, have shown promising performance when fine-tuned on diverse downstream tasks. However, there are two challenges of adapting EO-pretrained GeoFMs to practical downstream datasets. The first challenge is how to handle spectral mismatch: pretrained patch embeddings expect a fixed set of input bands, whereas downstream sensors may provide different channels. The second challenge is how to reduce fine-tuning cost and make it efficient. While existing work has made efforts on these challenges individually, jointly improving fine-tuning performance under spectral mismatch while reducing adaptation cost remains underexplored. We propose SPECTRA, a parameter-efficient fine-tuning framework that addresses both spectral mismatch and adaptation cost. To handle spectral mismatch, SPECTRA introduces Band-Routed Embedding (BRE), which maps all available downstream bands into the band space expected by the pretrained GeoFM. By using BRE, all available bands in the downstream dataset are utilized to improve the selected-band input without changing the pretrained patch embedding interface. To reduce adaptation cost, SPECTRA further introduces a Stage-wise Transferability-aware LoRA (ST-LoRA) fine-tuning. ST-LoRA estimates stage-wise transferability before fine-tuning and assigns stage-specific LoRA ranks, concentrating trainable parameters on the stages with high transferability for the target task. Across three EO-pretrained GeoFMs and four downstream segmentation datasets, experiments show that BRE improves performance by utilizing all spectral bands, while ST-LoRA reduces trainable parameters compared with full fine-tuning and standard LoRA. Code is available at https://github.com/big-data-lab-umbc/SPECTRA.

Reliable decision support in digital agriculture requires not only accurate predictions but also well-calibrated uncertainty estimates, particularly for dense prediction tasks such as semantic segmentation. Ensembles provide strong uncertainty quantification but are computationally and memory demanding, while single-model approximations often sacrifice uncertainty quality. We propose ST-LoRA, a parameter-efficient ensemble that builds diverse members from a single training trajectory by combining Low-Rank Adaptation (LoRA) with snapshot ensembling. All members share a frozen pretrained backbone and differ only in lightweight low-rank adapters, which sharply reduces trainable parameters, checkpoint storage, and I/O overhead. We evaluate SegFormer, Mask2Former, and EoMT on GrowliFlower-L (cauliflower, open field) and BUP20 (sweet pepper, glasshouse), covering in-distribution performance, calibration under covariate shift, and near- and far-out-of-distribution (OoD) detection, with BUTom21 (tomato) as near-OoD data. Extensive ablations show that feed-forward layers, not attention projections, are the critical LoRA target for dense prediction, and that the scaling ratio $α/r$ governs an accuracy--calibration trade-off. Against full-rank snapshot ensembles, ST-LoRA is competitive in segmentation quality, with architecture-dependent training time and energy savings. Against MC Dropout, DDU, and six post-hoc calibrators, it achieves the strongest far-OoD image-level detection and near-OoD pixel-level localization with low cross-seed variance, although full-rank ensembles remain better calibrated. These results show that LoRA-based ensembling offers a compelling efficiency--performance trade-off for agricultural vision systems.

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning, but standard LoRA produces a single deterministic model and does not directly support predictive uncertainty estimation. We introduce EulerLoRA, a stochastic extension of LoRA that generates multiple predictive trajectories by sampling structured variations along the rank-one components of shared low-rank adapters, while preserving the deterministic LoRA transformation in expectation. We evaluate EulerLoRA with vision transformers on CIFAR-10, CIFAR-100, and HAM10000, together with out-of-distribution detection on SVHN. Across these benchmarks, EulerLoRA achieves comparable or improved performance relative to strong LoRA-Ensemble baselines. Using two rank-20 adapters, EulerLoRA requires approximately 3 million trainable adapter parameters, compared with about 10 million for a rank-8, 16-adapter LoRA-Ensemble, corresponding to roughly 69% fewer trainable parameters. These results show that useful predictive diversity can be obtained from a small number of shared adapters.

Large Language Models (LLMs) perform strongly in English medical tasks but degrade substantially in Arabic, a gap widely attributed to limited training data. We systematically investigate this assumption via tuned lens probing and causal activation patching, and find that Arabic medical knowledge is present in intermediate model representations but fails to surface at the output. This mechanistic insight motivates a targeted adaptation strategy: rather than fine-tuning the full network, we propose Targeted Low-Rank Adaptation (TLoRA), restricted to the layer window where cross-lingual representations diverge, upstream of the output layers where the failure manifests. We evaluate TLoRA on multiple-choice medical QA, where our approach outperforms full-network LoRA, zero-shot, and few-shot baselines. We further evaluate it on short-answer generation and multi-turn clinical dialogue, where it performs competitively without the need for task-specific finetuning. We additionally introduce AraClinicDialog, a clinician-constructed Arabic medical dialogue benchmark in MSA with validated variants across four Arabic dialects. Together, these contributions demonstrate that mechanistic diagnosis can serve as a practical guide for targeted adaptation in underrepresented-language medical LLMs.

Parameter-Efficient Fine-Tuning (PEFT) commonly adapts large language models using a single shared Low-Rank Adapter (LoRA). This shared optimization space often suffers from interference when adapting heterogeneous task sequences, leading to poor transfer and catastrophic forgetting. Existing approaches mainly improve adapter expressiveness by increasing parameter capacity or composing multiple adapters, yet they still rely on a shared optimization path. In this paper, we propose an optimization-path organization framework for parameter-efficient fine-tuning of large language models, implemented as an automatic multi-policy PEFT architecture. Specifically, optimization-compatible adaptation paths are automatically organized through task grouping and task sequencing under a fixed parameter budget. The organized optimization paths are implemented as independent Quantized Low-Rank Adapters (QLoRA), enabling heterogeneous tasks to be optimized in decoupled adaptation spaces while preserving positive transfer among compatible tasks. Experiments on the TRACE benchmark demonstrate that performance consistently improves from conventional single-policy PEFT to multi-policy PEFT, with the proposed automatic multi-policy framework achieving the best performance of 44.78 under the same trainable capacity. This suggests that optimization-path organization is more effective than simply increasing adapter capacity for heterogeneous parameter-efficient fine-tuning.

Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood. Existing generalization results provide upper bounds of the form O~(sqrt(rd/n)) or O~(rd/n), but a matching lower bound is missing, and the question of how to choose the LoRA rank r has no formal answer. Both gaps are closed here. A local Rademacher argument establishes an upper bound of O~(rd/n) on the excess risk of the empirical risk minimizer over rank-r LoRA, whenever the target adaptation has rank at most r. A matching minimax lower bound of Omega(rd/n) is then proved via a Fano-type packing of the rank-r subspace of R^{d x d}; the bound applies to any estimator whose output lies in the rank-r LoRA class. Combining the two yields a rank-selection dichotomy. For the constrained empirical risk minimizer, the optimal rank equals the intrinsic rank r*, and over-ranking strictly hurts. For adaptive estimators of the nuclear-norm-then-truncate type, over-ranking is harmless and the rate saturates at Theta~(r* d / n) regardless of r. Taken together, the three results characterize the statistical complexity of LoRA fine-tuning within the well-specified locally quadratic regime, and identify the empirically observed over-parameterization penalty as a property of unregularized empirical risk minimization rather than of the LoRA class itself. Predictions of the theory are verified on a synthetic trace-regression benchmark and on real LoRA fine-tuning across three (model, task) configurations covering DistilBERT and RoBERTa on SST-2 and MRPC. All configurations exhibit the predicted U-shape in validation loss, with two showing statistically significant loss inflation at large ranks (paired permutation p = 0.016).

Post-training alignment in large reasoning models (LRMs) has significantly improved their adaptability to diverse safety compliance settings. However, as LRMs personalization for downstream users takes center stage, the demand for varying levels of policy compliance grows as different user-specific LRMs must adhere to distinct subsets of safety policies. Training a separate LRM for each policy subset introduces severe combinatorial overhead. While in context learning methods overcome this combinatorial overhead, they introduce additional computational challenges associated with long context generation. To address this challenge, we propose \ours, a unified adaptive hypernetwork-based framework for multi-policy compliance. In our framework, safety policies serve as customizable inputs to a LoRA adapter generator, which learns to produce policy compliant LoRA weights for downstream LRM. When added to the LRM these weights enable the generation of responses compliant with the specified policy subsets. In this work, we demonstrate that training such a hypernetwork enables on-demand policy adjustments on a single LRM without sacrificing task performance across reasoning models of different sized and different evaluation datasets. This highlights the effectiveness and practicality of adaptive hypernetwork based alignment in LRMs.

Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized. Recent schemes initialize the adapters from the downstream loss gradient: some project the raw gradient onto its top directions, while others first whiten it with an estimate of the loss curvature. We show that these seemingly distinct methods are points on a single continuum: a two-parameter family of preconditioned gradient initializations, which we call Unified LoRA (ULoRA), governed by a spectral whitening exponent and an Adam-like diagonal exponent. Sweeping this family under a full learning-rate search, we find that no single fixed preconditioning strength dominates: the best operating point is task-dependent and frequently lies strictly inside the family, away from the published endpoints. Treated as an upper bound of this family, a tuned ULoRA configuration matches or exceeds full fine-tuning on all five GLUE tasks with RoBERTa-base and is competitive with the strongest baselines on GSM8K with LLaMA-2-7B. Our deployable, search-free variant, ULoRA-Auto, selects per-layer exponents from measured spectral statistics, approaches this upper bound at no additional search cost, and ranks at or near the top among deployable LoRA methods. Our results show that a principled design space for LoRA initialization and curvature preconditioning should be treated as a tunable dimension rather than a fixed design decision.

Low-rank adaptation (LoRA) fine-tuning has made it cheap and easy to customize open-weight image generation models for specific tasks, including the production of child sexual abuse material (CSAM). Existing moderation relies on metadata or generated outputs, but metadata can be deceptive and generating outputs may itself be unacceptable or illegal. We show that a safer signal lives in the weights. The top-left singular vectors of a LoRA's updates form a compact, inference-free fingerprint ($u_1$) of its strongest learned change. Using human-subject age as a benign proxy for CSAM, we find that $u_1$ identifies what a LoRA was trained on, generalizes across base models, and abstains on unrelated benign content. The signal is robust to additive weight noise, rescaling, and precision reduction. These results indicate that harmful LoRAs could be screened directly from their weights without relying on metadata or generating harmful outputs.

Transformer adaptation is typically distributed across model depth, even when the intended change is narrow. We investigate how adaptation site shapes what a model learns, how well that learning generalizes, and how selectively it is applied. We introduce a controlled benchmark spanning five objectives (lexical binding, factual association, behavioral policy learning, causal mapping, and procedural reasoning) and define each objective's "adaptation geometry" as its profile of acquisition, transfer, and boundedness under full-stack and early-, middle-, or late-layer LoRA. The objectives exhibit distinct geometries. Lexical binding favors early-layer adaptation for acquisition and boundedness but requires broader updates for transfer; factual association favors later layers among localized adapters; behavioral learning separates late-layer action acquisition from middle-layer policy gating; and causal and procedural transfer benefit most from middle- or full-stack adaptation. These patterns largely persist under parameter-matched controls, and most corresponding directional contrasts replicate across five model families. These findings establish adaptation site as a key design variable for controlling what models learn, generalize, and leave unchanged.

Parameter-efficient fine-tuning (PEFT) and low-bit quantization are now standard tools for adapting language models under tight compute budgets, yet their interaction is most often studied on billion-parameter models where the design space is expensive to explore. We ask a complementary question: on a specific, fully reproducible 60M-parameter encoder-decoder model (T5-small) and a single-table text-to-SQL benchmark (WikiSQL), how much task accuracy does each efficiency knob actually cost? We run a controlled, single-variable study over (i) LoRA rank r in {2, 4, 8, 16, 32}, (ii) the set of adapted modules, and (iii) numerical precision. We report task accuracy alongside system-level metrics including trainable parameters, peak training memory, inference latency, and throughput, and frame adaptation as a constrained trade-off rather than an accuracy-only objective. Our results show that LoRA with r=16 recovers within 11.6 percentage points of full fine-tuning accuracy (59.6% vs. 71.2% exact-match) while training fewer than 1% of parameters and consuming 31% less peak GPU memory. Within this setting, rank beyond r=16 yields no measurable accuracy gain. QLoRA with INT8 and NF4 quantization achieves comparable accuracy (52.8% and 53.2%) at dramatically lower memory cost (0.60 GB each), demonstrating a compelling trade-off for memory-constrained deployments. All code, configurations, and logs are released for full reproducibility.

Degraded images not only reduce visual quality but also impair downstream high-level vision tasks. Task-driven image restoration (TDIR) addresses this issue by jointly optimizing restoration quality and task performance. Recent works show that pretrained diffusion priors benefit TDIR, yet diffusion-based restoration is inherently stochastic, as the sampling process depends on a random noise term, which can undermine task consistency. In this paper, we show that a deterministic, noise-free one-step forward pass with pretrained diffusion priors can substantially improve TDIR, but the benefit critically depends on the adaptation module: LoRA yields consistent gains, whereas ControlNet-style conditioning does not. This enables one-step forwarding that surpasses conventional multi-step diffusion TDIR baselines. Furthermore, we introduce a task-preserving GAN training strategy that improves perceptual quality without sacrificing task performance. Extensive experiments on classification, segmentation, and detection demonstrate consistent gains over prior TDIR methods, and we further validate generalization on real-world degraded images and OCR.

Optimization over the Stiefel manifold plays a significant role in various machine learning tasks. Existing methods either use the retraction operators, requiring costly orthonormalization for large-scale matrices, or employ landing methods that rely on careful step size selection and penalty parameter tuning. To address these challenges, we propose a retraction-free and penalty parameter-free algorithm that directly lands on the manifold. By leveraging the strongly-convex-like property of the quadratic penalty function and the proximal smoothness of the Stiefel manifold, we establish global convergence guarantees with the best-known iteration complexities under both constant and diminishing step sizes. Then, we reformulate the low-rank adaptation (LoRA) fine-tuning problem for large language models as a manifold optimization problem, introducing Manifold-LoRA for geometry-accelerated adaptation. This approach employs the proposed landing technique and a carefully designed step size strategy to accelerate the training process. Numerical experiments on benchmark datasets demonstrate the efficiency and strong downstream performance of the proposed method.

LoRA fine-tuning can create intruder dimensions: new leading singular vectors of the updated weight matrix $W+BA$ that are nearly orthogonal to all pretrained singular vectors and that drive catastrophic forgetting. Since their discovery, no theory has predicted, layer by layer on measured spectra, when they appear. We derive a per-layer critical update strength $s^\ast=\barθ/(γσ_1(BA))$, computed from the measured spectrum of $W$ alone through the rectangular spiked-deformation transform, together with an exact secular-equation characterization of the updated spectrum, with no fitted parameters. In a pre-specified study spanning four dense Transformer families, a state-space model, a mixture-of-experts model, and an encoder-decoder (18 adapters, 9{,}840 layer scans), the law localizes the empirical threshold within a factor of two on $82\%$ of layers, separates intruder-bearing from intruder-free layers at deployment with a mean AUC of $0.89$, holds unchanged on six third-party adapters, and predicts where WikiText-2 perplexity begins to degrade; a combination of the two pre-specified edge evaluations reaches $98\%$ and is confirmed out-of-bag on the external adapters ($0.997$). Full fine-tuning disperses its update far below the threshold of every layer, which resolves the asymmetry between LoRA and full fine-tuning. Norm-matched interventions confirm that threshold-crossing layers, rather than update magnitude, carry the forgetting, and a spike-budget rule derived from the thresholds, requiring one SVD and no validation sweeps, reduces forgetting by $62\%$ on the most fragile model at no task cost.