Low-Rank Adaptation

Discrete diffusion language model (DLM) fine-tuning inherits inexpensive diagnostics from denoising-time confidence monitors, but their PEFT-training meaning is untested. We test top-1 argmax concentration as a collapse warning. Across 816 LoRA/PEFT configurations from three DLM families, the warning fires for every configuration while logs record 0/816 actual collapses at the 200 step horizon, giving zero precision. The cause is pre-equilibrium saturation: top-1 concentration is already high before optimization and quickly becomes insensitive to final training stability. We then evaluate max LoRA gradient norm, a parameter-side signal that samples gradient routing rather than token concentration. On a pooled held-out LLaDA-family split, a train-optimized threshold identifies top-decile final-loss configurations with precision 0.68 and F1=0.79, above the all-positive top-1 baseline even at the lower split-bootstrap confidence bound. Autoregressive controls and cross-family threshold failures bound the result to short-horizon DLM-LoRA inspection rather than a universal collapse detector. Workflow: drop top-1 as a PEFT alarm, log max-gradient early in training, and calibrate thresholds per DLM family before routing runs for inspection.

Diffusion models are known to exploit unknown low-dimensional structure to accelerate sampling. However, existing convergence theory under low-dimensional data structure has largely focused on update rules with narrowly prescribed coefficient choices. This raises a fundamental question: is adaptation to low-dimensional structure sensitive to the precise choice of update coefficients? In this paper, we show that such adaptation is a robust property of diffusion models. For a broad class of update coefficients, we prove that $\widetilde{O}(k/\varepsilon)$ iterations suffice to generate an $\varepsilon$-accurate sample in total variation (TV) distance, independently of the ambient dimension. Our framework substantially broadens the class of diffusion samplers known to enjoy low dimensional adaptation and applies to several commonly used methods in practice. These results provide a theoretical justification for the empirical effectiveness of diffusion samplers across different coefficient choices when applied to structured, high-dimensional data.

As large language models (LLMs) are increasingly deployed at the network edge to provide pervasive generative AI services, decentralized federated learning (DFL) provides a vital mechanism for privacy-preserving, domain-specific fine-tuning through peer-to-peer exchanges of parameter-efficient updates. However, the dynamic nature of practical decentralized edge networks, where devices may dynamically join or leave the collaborative training process, requires the system to continuously adapt to new data while selectively removing prior contributions. This correction process remains a significant bottleneck, as individual device updates become deeply entangled within the global fine-tuned parameters. To address this challenge, we propose a priority-aware learning-unlearning correction framework based on orthogonal LoRA that can enhance the knowledge evaluation through topology adjustment. Specifically, we first design an orthogonal LoRA mechanism that yields post-training contribution coordinates, enabling history-free projection addition and deletion in response to membership changes. We then analyze the correction bottleneck and develop a priority-aware policy that selects among topology refinement, local correction, proximal damping, and synchronization scheduling according to the dominant residual term. A resource allocation algorithm is further developed to allocate limited communication across layer groups, prioritizing the primary bottlenecks within per-round wireless constraints. Experiments demonstrate that the proposed framework achieves robust post-event correction for both device join and leave events and validate that different residual regimes necessitate distinct correction actions.

Federated low-rank adaptation methods are attractive for fine-tuning large models under communication and privacy constraints, but heterogeneous client data can induce geometric misalignment between local low-rank updates. We study whether this subspace misalignment leads to destructive aggregation and slower convergence in LoRA-based federated learning. We propose a subspace-regularized federated LoRA objective that encourages local client updates to remain close to a shared global reference subspace. We present a complete empirical evaluation on two pretrained models, RoBERTa-large and SmolLM-360M, over HellaSwag in a non-IID 10-client federated setting, across 3 random seeds (42, 43, 44), yielding 24 total experimental runs (4 methods x 3 seeds x 2 models). On RoBERTa-large, Subspace-Reg achieves the strongest mean best accuracy (0.454 +/- 0.023), mean final accuracy (0.429 +/- 0.011), and lowest final loss (1.363) across all three seeds, outperforming FedAvg, SVD redistribution, and FedSVD baselines by a large margin. On SmolLM-360M, FedAvg leads on accuracy, revealing that accuracy gains are model-dependent. Crucially, Subspace-Reg achieves near-perfect basis overlap, approximately 0.9999, on both models and across all seeds, versus 0.958 to 0.991 for all baselines, providing robust support for the geometric alignment hypothesis. The code is publicly available at https://github.com/sadia-sigma-lab/Subspace-Constrained-Federated-learning-with-Lora.

Graph neural networks (GNNs) tightly couple their input-output parameters to dataset-specific feature spaces and target sets, exhibiting limited transferability across different datasets. In contrast, language models (LMs) generalize flexibly via a unified input-output interface, motivating recent attempts to adapt LMs to graph tasks. However, existing methods struggle to encode whole-graph information, leading to potential information loss and suboptimal graph understanding. In this work, we propose a novel weight-level information injection paradigm for adapting LMs to graph tasks. This paradigm injects whole-graph information by generating task-specific weight updates that interact directly with hidden representations. Instantiating this paradigm following low-rank adaptation (LoRA), we introduce GaRA, a Graph-aware LoRA generation model. GaRA constructs low-rank weight updates conditioned on the original graph structures and constrains the norm of the generated updates, thus injecting whole-graph information and avoiding the optimization bias in the weight generation. Empirical studies demonstrate that GaRA consistently outperforms baselines on zero-shot graph learning tasks.

Large multi-modal language models are increasingly deployed in high-stakes domains, making well-calibrated uncertainty essential. Traditional Bayesian methods approximate posteriors over all model weights, which becomes intractable for modern large models. For this reason, recent work instead considers Bayesian low-rank adaptation to enable tractable posterior approximation. Due to a lack of a standardized benchmark to evaluate these approaches, it remains unclear where these methods provide meaningful benefits. To fill this gap, we introduce Bayesian Adaptation Gym (BAG), a benchmark for the Bayesian adaptation of multi-modal language models. BAG provides reference implementations of classic Bayesian baselines and state-of-the-art adaptation methods, along with a multi-modal dataset and task suite designed to probe calibration, robustness under distribution shift, and decision-making under uncertainty via active learning. Using BAG, we conduct and report extensive experiments across model sizes, datasets, and tasks to highlight the successes and failures of current Bayesian adaptation approaches. To enable further research, BAG is fully open source: https://github.com/SRI-CSL/BayesAdapt.

Style-content dual-reference generation aims to synthesize an image that preserves the structure and semantics of a content reference while adopting the style of a separate style reference.Despite recent progress, this setting remains challenging because models must balance content fidelity, style alignment, and instruction following avoiding semantic leakage from the style reference.A key bottleneck is the lack of large-scale triplet data with clean content-style separation and broad long-tail style coverage.In this work, we propose FreeStyle, a scalable dual-reference generation framework based on community LoRA mining.We treat community LoRAs as compositional anchors for style and content, and design a rigorous generation and filtering pipeline to construct large-scale Style-Reference and Content-Reference triplets across multiple base models.To address content leakage, we adopt a two-stage curriculum with stage-specific disentanglement mechanisms: an attention-level enrichment constraint that suppresses style-reference leakage in the style-transfer stage, and a frequency-aware RoPE modulation strategy that targets positional-correspondence-based leakage in the harder dual-reference stage.We also introduce a benchmark covering both style-reference and dual-reference generation, with evaluations on style similarity, content preservation, aesthetics, instruction following, and leakage rejection. The benchmark incorporates a style-invariant Content Alignment Score (CAS) and introduces a calibrated VLM-based Rejection Score for evaluating generation reliability and leakage suppression.Extensive experiments show that our model achieves a strong balance among style alignment, content preservation, and leakage suppression.

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.

Fine-tuning of Large Language Models (LLMs) using Low-Rank Adaptation (LoRA) on an end-user's data offers personalized experiences while keeping data private, but faces severe memory constraints on consumer hardware. Peak memory during fine-tuning often exceeds device limits, especially for models with billions of parameters and long-context training data. This paper introduces a suite of complementary techniques to reduce memory footprint without sacrificing model quality: (1) base model quantization with on-the-fly dequantization, (2) memory-efficient checkpointing combining selective activation caching and disk offloading, (3) softmax approximation using semantically relevant token subsets, and (4) logits masking. Experiments on Llama-3.2 3B and Qwen-2.5 3B demonstrate up to $26\times$ and $28\times$ reduction in peak memory, enabling fine-tuning on resource-constrained devices.

Personal memory in a language model is two problems: content and reasoning skill. The brain keeps the two apart (a sparse, local engram in the hippocampus for each episode, a slow neocortex for the shared skills that interpret it), so a new fact need not overwrite everything else. Most personalization today keeps a user's facts outside the weights, in a natural-language memory file or a retrieval index. When facts are written into the model instead, the standard recipe is the per-user LoRA adapter, which does the opposite of the brain, folding content and skill into one global weight delta. Writing a user's facts as a LoRA contaminates text unrelated to them; writing the same facts as local Engram rows leaves it mathematically untouched, resulting in a roughly 33,000x smaller memory footprint. We therefore propose User as Engram: store a user's content as surgical edits to the hash-keyed memory table of an Engram model, and carry the reasoning skill in one shared adapter. This layered design matches per-user LoRA's direct recall while delivering 5.6x higher indirect-reasoning accuracy on average, and never makes a single user worse at reasoning than the untouched base. The edit is a glass box: writing a fact switches on its lookup at exactly the trigger, adds the value the answer needs, leaves every other position unchanged to the last bit, and fails if written into the wrong layer. Because different users' facts land in disjoint hash slots, their edits compose: many users live in one shared table at once, stacking additively and losslessly, where a per-user LoRA, a single global weight delta, admits only one. Upon retrieval, a per-user Engram table does not grow with the population the retriever must search, so past ~100 facts it overtakes a retrieval pipeline on a 2.5x larger model.

Unified multimodal models (UMMs) have recently emerged as a promising paradigm for integrating multimodal understanding and generation within a single autoregressive transformer. However, during multimodal instruction tuning, these models often exhibit pronounced modality imbalance: language gradients dominate optimization, thus leading to lower image generation quality, especially under parameter-efficient fine-tuning such as LoRA. In this work, we systematically analyze modality imbalance in LoRA-based fine-tuning of UMMs for interleaved text-image generation. We show that vision modality performance degrades substantially more than text modality performance when compared to unimodal counterparts, and that modality-specific gradients can differ by orders of magnitude across various tasks and layers. Motivated by this observation, we reformulate the multimodal instruction tuning as a bi-objective optimization problem and propose Pareto LoRA, a Pareto-optimal gradient integration strategy that balances the text and image objectives by modulating the gradient direction and strength. Experiments on the CoMM benchmark with Emu2 demonstrate that Pareto LoRA consistently improves multimodal generation balance, achieving up to 44.9% gains in perceptual image quality over vanilla LoRA while maintaining comparable text performance.

Low-Rank Adaptation (LoRA) enables efficient adaptation of large pre-trained models to downstream tasks by parameterizing weight updates with low-rank matrices. In this paper, we investigate the limitations of the LoRA parameterization from a geometric perspective. Specifically, we show that when a full fine-tuning gradient is backpropagated to the low-rank matrices, it undergoes anisotropic scaling driven by their singular values. We argue that this phenomenon is undesirable because it distorts the full fine-tuning gradient by skewing it toward dominant singular directions while suppressing others. Our analyses demonstrate that anisotropic gradient scaling reduces the effective rank of the low-rank matrices' gradients and results in suboptimal alignment between the full fine-tuning gradient and its low-rank approximation in LoRA, thereby exacerbating the gap to full fine-tuning. To address these limitations, we propose a new low-rank parameterization, SDS-LoRA, which structurally decouples singular values from the backward pass. Our method ensures that the full fine-tuning gradient backpropagates only through the orthonormal bases of the low-rank matrices' subspaces, independent of their scales. Convergence analysis demonstrates that while LoRA's convergence rate degrades with the condition number of the low-rank matrices, SDS-LoRA remains independent of it. Experimental results across natural language and vision benchmarks show that SDS-LoRA improves loss convergence and reduces the gap to full fine-tuning, significantly enhancing adaptation performance.

In the digital age, image compression is crucial for numerous applications, including web media, streaming services, high-resolution medical imaging, and connected vehicle networks, enabling efficient data storage and transmission. With the increasing demand for high-quality image communication, the need for advanced compression techniques becomes increasingly critical. Numerous Deep Image Compression (DIC) techniques have recently been introduced, showing impressive performance compared to traditional standards. However, variable-rate image compression remains an unresolved issue. Specific DIC methods deploy multiple networks to attain different compression rates, whereas others use a single model, which often results in higher computational complexity and reduced performance. This work proposes a progressive learning approach for variable-rate image compression based on the parameter-efficient fine-tuning method, the Low-Rank Adaptation (LoRA). We introduce an additional LoRA Rate-Adaptive Module (LoRAM) in DIC methods. Due to the re-parameterized merging of LoRA, our proposed method does not introduce additional computational complexity during inference. Compared to methods utilizing multiple models, comprehensive experiments demonstrate that our approach achieves competitive performance, saving 99% in parameter storage, 90% in datasets, and 97% in training steps.

Federated fine-tuning of large language models using parameter-efficient methods such as LoRA enables privacy-preserving adaptation of foundation models. Heterogeneous hardware resources introduce challenges, as clients with different adapter ranks cannot be directly aggregated. While existing methods enable aggregation under heterogeneous ranks, they fail to control how information is distributed across rank dimensions, leading to suboptimal use of shared low-rank representations. Instead, we propose PreLort: a nested low-rank formulation for federated LoRA that organizes adapter dimensions into a prefix hierarchy. Our approach ensures that lower-rank dimensions encode task-relevant information, while higher-rank dimensions capture additional capacity. Building on this, we introduce (i) a segment-wise aggregation rule that averages only over clients contributing to each rank segment, avoiding dilution from zero-padded lower-rank clients, and (ii) a prefix-nested training strategy that optimizes each adapter under multiple rank truncations, encouraging useful signal to concentrate in low-rank prefix dimensions. Together, these components encourage a consistent low-rank prefix capturing the most task-relevant information, while higher-rank dimensions learn additional capacity. This allows low-rank clients to benefit from richer information contributed by higher-rank clients, as prefix dimensions are consistently learned and aggregated. Experiments demonstrate that our method consistently outperforms prior heterogeneous federated LoRA methods in accuracy and ROUGE-L, while achieving lower or comparable perplexity across multiple base models.

Fine-tuning vision-language models to emit dense coordinate lists improves visual grounding but also changes how models serialize, repeat, and terminate structured outputs. We study this behavior as a generation and control surface. In Gemma 4 12B, high-capacity q/k/v/o LoRA raises class-aware F1@0.3 from 0.007 to 0.448 while inducing repeated-tail pressure (duplicate rate 0.080, max repeat 23). A q/v rank sweep keeps max repeat at 21-22 across ranks 4-64, showing capacity persistence. The target signal is separable: object-level repeat-stop removes exact repeated records (duplicate rate 0.000, max repeat 1) while preserving F1 (0.494 to 0.490) and stricter F1@0.5 (0.381 to 0.385). Structure-axis probes localize the effect to bbox-coordinate object lists; dense non-bbox and spatial/count JSON remain repeat-clean, including under high-capacity adapters. Qwen3-VL-8B reproduces a clean controlled endpoint (F1@0.3 0.318, duplicate rate 0.000), and COCO 2017 reproduces acquisition plus duplicate pressure. Dense coordinate-list adaptation therefore creates a structure-bound, cross-family interference surface that can be measured and controlled.

Identifying conditions that a certain drug takes therapeutic effect on a target disease is crucial for clinical decision-making support. However, most existing biomedical information extraction methods have focused on identifying only relations between drugs and diseases, while largely overlooking the context-specific conditions where such relations can apply. To address this problem, we introduce the task of applicability condition extraction for therapeutic drug-disease relations from biomedical research literature. We create the first dataset that has manually annotated triples of drugs, diseases, and applicability conditions on biomedical paper abstracts with 1,119 drug-disease pairs. Using this dataset, we systematically evaluate the performance of a range of existing methods. In addition, we propose a new method that enhances LoRA to consider relations between drugs and diseases. Our method consistently outperforms strong baselines across different evaluation settings.

While personalizing Image-to-Video (I2V) diffusion models with specific visual effects is increasingly demanded for high-end generation, current practice requires training a separate Low-Rank Adaptation (LoRA) module for each effect, incurring substantial data curation and iterative optimization costs that hinder interactive control. We present Prompt2Effect, a weight-driven hypernetwork that amortizes per-effect training by directly synthesizing effect-specific LoRA weights in a single forward pass. Unlike prior hypernetworks that regress adapter weights purely from semantics, Prompt2Effect is explicitly conditioned on the frozen base model weights, grounding prediction in the structural geometry of each layer. Furthermore, instead of predicting raw LoRA matrices, we introduce an SVD-canonicalized parameterization that resolves factorization ambiguity and stabilizes large-scale synthesis. Extensive experiments demonstrate that Prompt2Effect achieves on-par or superior video quality and effect alignment compared to conventional LoRA fine-tuning, while reducing the computational cost from 56 GPU training hours to 3.3 seconds of hypernetwork inference. When used as initialization for subsequent fine-tuning, our predicted weights further improve final performance and accelerate optimization by approximately 10x.

Diffusion-based style transfer must balance inference efficiency with stylization fidelity. Adapter-based methods are efficient, but they inject style as an external condition and can either weaken reference-specific appearance or copy reference semantics into the generated image. Optimization-based personalization methods such as LoRA internalize style more effectively, but require a separate training process for every new style. We introduce i2L (image-to-LoRA), a framework that amortizes style LoRA training into a single forward pass. Given one or more reference images, i2L predicts LoRA weights for a text-to-image model, enabling immediate style instantiation without per-style optimization. The architecture combines an image encoder, learnable LoRA queries, and compressed decoding heads that generate adapted matrices. Training on semantically diverse style pairs encourages the predictor to preserve appearance cues while suppressing reference-content copying. Experiments on Z-Image, FLUX.2, and Hidream-O1 show that i2L improves style fidelity, prompt alignment, and perceptual quality over existing baselines. Because i2L produces explicit LoRA weights, it also supports asymmetric classifier-free guidance, multi-reference style fusion, and composition with controllable-generation modules.

Low-rank adaptation (LoRA) and its variants provide a memory- and compute-efficient alternative to full fine-tuning of pre-trained models. However, questions remain about the comparative generalizability of these approaches and how the structural restrictions on low-rank updates preserve effective adaptation performance. We present a historical framing, covering the past (full fine-tuning and original LoRA), the present (different variants of LoRA), and propose simpler, cheaper, parameter-efficient extensions by inducing sparsity within existing LoRA variants: Cheap LoRA (cLA), training a single low-rank factor with the other fixed (deterministically or, in its randomized variant, stochastically), and the chained circulant variant, ${c}^3$LA. We frame cLA as a structured instance of asymmetric LoRA, serving as a controlled column-subspace restriction of full fine-tuning. We derive information-theoretic generalization error bounds for these variants, marking one of the first endeavors in this area. Empirically, we evaluate 11 fine-tuning methods across 10 pre-trained models and 14 datasets, analyzing the fine-tuned models' performance and generalization using tools such as loss landscapes and spectral analysis. Despite the sensitivity of fine-tuned models to the pre-trained model, datasets, and other factors, our study suggests that restricting LoRA-based PEFT methods' adaptation to a sparse, structured column space remains competitive across tasks with their parameter-matched baselines while reducing up to 10% training time and peak GPU memory up to 15%, even with a naïve, non-optimized, sparse implementation. Our theoretical and empirical generalization measures provide a more consistent and principled approach to their cost-effective adaptation than commonly used analytical tools. Overview and code are available at: https://elicaden.github.io/Beyond_LoRA/.

Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines. We derive LoRA-Muon by applying the Muon optimizer's spectral steepest-descent rule to the low-rank setting. Along with our split weight-decay rule, our main claim is that LoRA-Muon is a good low-rank proxy for full-rank Muon and Shampoo-family optimizers. Its optimal learning rates transfer across rank, width, depth, and factor-rescaling. In our compute-matched TinyShakespeare study, a rank-$2$ proxy recovers the dense best tested learning rate, and a rank-$32$ LoRA-Muon run attains lower mean validation loss than the dense baseline in the seed-averaged sweep. We further show that the Spectron optimizer depends on arbitrary factor scaling, so it would likely be a poor fit when finetuning starts from badly imbalanced factors, and that LoRA-RITE's simplified QR-coordinate core implements the same spectral update. LoRA-Muon computes that update without QR-decomposition and avoids storing second moments, making it more accelerator-friendly and memory-efficient.

In Low-Rank Adaptation (LoRA), the scaling factor $α$ is often treated as a mere complement to the learning rate, yet its role in optimization remains poorly understood. In this paper, we reveal that the scaling factor $α$ and the learning rate function differently, with $α$ emerging as the dominant driver of effective optimization, delivering gains that cannot be replicated by learning rate scaling alone. Through the synergy of extensive empirical analysis and a theoretical Signal-Drift framework, we uncover three findings into LoRA's scaling mechanism: First, LoRA's spectral suppression smooths the optimization landscape, rendering standard hyperparameters overly conservative and creating an optimization gap. Second, when leveraging this smoothness to accelerate convergence, $α$ outperforms the learning rate by amplifying the task signal without increasing the drift ratio. Third, the optimal scaling factor follows a sublinear relationship with the rank, well characterized by a square-root law with an unexpectedly large coefficient, revealing the insufficient scaling of existing rank-tied heuristics. Based on these insights, we propose LoRA-$α$, a minimalist framework that restores $α$ to its principled regime, making LoRA compatible with standard small learning rates. Extensive evaluations across diverse tasks demonstrate that LoRA-$α$ consistently improves performance while streamlining hyperparameter search, unleashing the learning potential of LoRA.

Recent efforts to extend large language models (LLMs) to speech inputs typically rely on cascaded ASR-LLM pipelines, end-to-end speech-language models, or bridge/distillation-based adaptation. While these routes respectively reuse strong pretrained components, enable native speech-language interaction, or offer lightweight adaptation, they often suffer from transcript-interface latency, costly multimodal training, or sequential speech-language coupling. To address these limitations, we present AuRA, a method that distills audio encoding capability into the LLM. Specifically, AuRA feeds the same speech input to an ASR encoder (as a teacher) and a LoRA-adapted LLM (as a student) through a lightweight audio embedding layer, and uses layer-wise distillation to align the student's hidden states with corresponding teacher representations, thereby internalizing speech representations into lightweight LLM-side adaptations. Compared with cascaded and serial bridge methods, AuRA enables tighter speech-language joint modeling and efficient parallel end-to-end inference, while also reusing pretrained speech and language models rather than requiring large-scale multimodal training. On multiple speech-language benchmarks, AuRA consistently outperforms cascaded systems, speech-to-LLM adaptation baselines, and large-scale speech-language and multimodal models in both effectiveness and efficiency.

Task vectors, LoRA, activation steering, and random search around pretrained weights all suggest that learned behaviour can be controlled by linear directions. We ask which linear structures actually exist and on what scale. In a synthetic multitask transformer and LoRA adapters on DistilGPT-2 / GPT-2 we find strong local low-rank task-gradient structure but reject the fixed-task-plane hypothesis: static bases miss the recovery direction, and the useful basis drifts substantially within 100 steps. However, the first recovery updates form a trajectory-prefix basis capturing 77% of the LoRA recovery displacement. We develop random search theory with a Gaussian local-linear theorem that justifies the effectiveness of random parameter search even in very high dimensions. We also study the relation between parameter perturbations and activation steering: a single gradient step produces an activation shift with 0.58 cosine to a labelled-contrast CAA steering vector, with a similar steering effect on Qwen-0.5B BoolQ statements. We validate our results with experiments on synthetic Transformers and LLMs. Our results suggest that linear structures in trained networks are not global task directions, but evolving local geometries that partially persist across parameter and activation spaces.

Low-Rank Adaptation (LoRA) merging can efficiently combine diverse generative capabilities from multiple trained LoRAs for a diffusion model. However, existing LoRA merging techniques often suffer from severe parameter interference, causing destructive collisions in the shared parameter space. To address this, we propose Subspace Signal Routing (SSR), which resolves interference by routing internal signals instead of performing parameter-space merge. Specifically, SSR first constructs a unified subspace by concatenating candidate LoRAs along the rank dimension. Next, SSR employs an inverse correlation matrix to decorrelate mixed signals within this space. Finally, a directional guide matrix steers these purified signals into their respective task-specific subspaces. We provide a rigorous theoretical analysis proving that SSR aligns with the Ordinary Least Squares (OLS) solution, thereby ensuring mathematical optimality. We utilize the additivity of sufficient statistics to design a streaming algorithm. This enables on-the-fly updates that significantly reduce memory overhead and computation time. Extensive experiments validate that SSR significantly outperforms state-of-the-art methods while maintaining comparable efficiency. Code is available at https://github.com/nagara214/SSR-Merge.

We investigate whether commonly available LoRA variants have an advantage over basic LoRA in multilingual instruction tuning. Experiments involving LoRA and four other variants on two datasets across diverse target languages show that there is no significant advantage in using more complex LoRA variants instead of basic LoRA, with respect to balancing cross-lingual transfer and knowledge retention. An analysis of hidden embeddings reveal that layer-wise language representation remains largely similar across LLMs fine-tuned with different LoRA techniques, suggesting that architectural novelty of LoRA techniques may not translate into better cross-lingual adaptation.

Financial named-entity recognition (NER) is essential for translating unstructured financial reports and news into structured knowledge graphs. However, general-purpose large language models (LLMs) often misclassify financial entities or ignore domain-specific patterns. This paper investigates the use of DeepSeek-R1-8B, a recent open-source large language model, combined with Low-Rank Adaptation (LoRA) and Noisy Embedding Fine-Tuning (NEFTune) for financial NER. Each annotated sentence in our corpus of 1693 samples is converted into an instruction-input-output triple. We insert lightweight LoRA matrices into the Transformer layers and apply NEFTune to improve generalisation by adding uniform noise to embedding vectors during training. Experiments show that the LoRA-adapted DeepSeek-R1-8B achieves a micro-F1 of 0.901 on seven entity types (Company, Date, Location, Money, Person, Product and Quantity), and adding NEFTune further boosts the micro-F1 to 0.912, outperforming Llama3-8B, Qwen3-8B, Baichuan2-7B, T5 and BERT-Base baselines.

Low-Rank Adaptation (LoRA) enables efficient federated fine-tuning of segmentation foundation models for medical imaging. However, most federated LoRA methods adopt a uniform aggregation rule, which breaks under the encoder-decoder asymmetry in medical segmentation: the encoder is dominated by appearance shifts, while the decoder is dominated by supervision variations. This mismatch entangles shared anatomy with site-specific biases and harms generalization. To address this, we propose Inverse Asymmetric Tuning (IAT). IAT aligns adaptation with heterogeneity sources by personalizing module-specific components in the encoder to absorb appearance shifts and in the decoder to accommodate site-dependent supervision, while retaining a shared pathway for transferable consensus. However, structural separation alone is insufficient under LoRA's bilinear parameterization, where multiplicative coupling can still cause site-specific updates to leak into the shared direction. We therefore introduce a Subspace Orthogonality Regularizer that penalizes shared-local collinearity in the effective update space, mitigating leakage without extra communication. Experiments show consistent improvements over strong federated LoRA and parameter-efficient FL baselines.

Merchant information extraction turns noisy financial transaction descriptors into structured fields at production scale. Our deployed LoRA-fine-tuned LLaMA3.1-8B reaches 96.95% F1, but its memory and throughput motivate smaller replacements. We evaluate 23 retained fine-tuning runs plus a separately trained production reference, spanning Gemma3 (270M--4B), Qwen3.5 (0.8B--4B), Aya3.35B, and LLaMA3.1-8B across LoRA ranks, prompts, training templates, and serving environments. A rank-8 LLaMA fine-tune reaches 96.75% F1, only 0.20 points below the rank-32 production reference. Qwen3.54B with JSON-Only prompting reaches 96.60% F1 and strict record-level exact match of 91.67%, with a $3.8\times$ lower inverse-throughput time estimate than the rank-8 8B model. Qwen3.5~0.8B reaches 94.75% F1, and Qwen Think and Nothink templates differ by less than 0.004 F1. Across 14 Databricks endpoints, mean F1 change from local evaluation is $-0.0081$; Aya is the only family with a 2.7--5.1 point decline. These results show that compact fine-tuned models can preserve most extraction accuracy, but model selection must account for prompt choice, throughput, and serving-stack behavior.

Vision-Language-Action (VLA) models are emerging as a promising paradigm for robotic manipulation, enabling general-purpose policies trained from large corpora of demonstrations and action labels. However, adapting these models to new tasks still typically requires task-specific demonstrations, action annotations, and additional fine-tuning, making deployment costly and difficult to scale. We propose WIZARD, a weight-space meta-learning framework that sidesteps task-specific fine-tuning by generating task-specific LoRA parameters for a frozen VLA policy. Given only a language instruction and a short demonstration video, WIZARD predicts the corresponding adaptation weights in a single forward pass, without target-task action labels or test-time optimization. During meta-training, WIZARD learns to map task evidence directly to expert LoRA updates, capturing relationships between tasks in weight space. Experiments on LIBERO show that WIZARD improves performance by up to ~2x on unseen dataset collections and up to ~14x on unseen tasks. On a Franka Emika Panda, WIZARD consistently improves over a real-domain adapted baseline, showing that generated adapters provide task-level specialization beyond simulation.

Image tokenizers, from 2D grids to recent 1D sequences, typically encode every image with the same fixed number of tokens. Yet visual complexity is highly heterogeneous, so a uniform budget overspends on simple inputs and underserves complex ones. Existing elastic tokenizers expose variable-length reconstructions, but often leave token length as a deployment-time operating point, a search target, or an external prediction rather than an output of the tokenizer itself. In this work, we ask whether a discrete visual tokenizer can budget itself in one pass. Our central finding is that actionable elasticity requires a representation--allocation co-design: prefixes must remain decodable across budgets, and the tokenizer must learn which prefix each image needs. We propose AdaTok, a self-budgeting discrete 1D tokenizer. AdaTok combines Prioritized Representation Learning, which orders tokens with nested tail masking and resolves budget-dependent semantic shift through Multi-Head LoRA decoder heads, with Adaptive Token Allocation, which trains a lightweight deterministic-group GRPO policy over candidate budgets. Dynamic Pareto Weighting balances fidelity and efficiency during policy training without manual trade-off sweeps. On ImageNet-1K, AdaTok-Full reaches rFID 1.31 at 256 tokens, while AdaTok-Adaptive attains rFID 1.50 using only ~118 tokens on average, outperforming discrete 1D baselines at comparable budgets. In autoregressive image generation, the shorter adaptive representation yields ~2.1x throughput over a fixed 256-token decode, suggesting that visual token count can be learned as a content-conditioned output rather than set as a fixed hyperparameter.

Federated fine-tuning of foundation models using Low-Rank Adaptation (LoRA) offers a communication efficient solution for distributed learning. However, existing federated LoRA methods suffer from two fundamental limitations: (1) structural aggregation bias, where independently averaging low rank factors fails to approximate the true combined update, and (2) client side initialization lag, as clients repeatedly reinitialize LoRA parameters across communication rounds, slowing convergence. We propose HyperLoRA, a unified framework that addresses both issues through amortized federated adaptation through hypernetwork-driven LoRA generation and product space aggregation. Instead of iterative per-client optimization, HyperLoRA employs a learned generator that maps client distribution signatures to LoRA initializations, effectively amortizing per client adaptation. On the server side, we introduce a learned aggregation module that directly synthesizes updates in the low-rank product space, eliminating the inconsistencies of factor-wise averaging. A lightweight residual correction module further improves stability under heterogenous (non-IID) client distributions.By replacing iterative optimization and heuristic averaging with learned operators, HyperLoRA jointly enables efficient personalization, unbiased aggregation, and faster convergence. Experiments on federated vision and vision-language benchmarks show that HyperLoRA achieves improved convergence speed, greater robustness to distribution shift, and stronger personalization performance compared to prior federated LoRA methods.

We develop a high-dimensional statistical theory of low-rank adaptation (LoRA) in attention models, capturing the interplay between pre-training and fine-tuning. We introduce a solvable framework in which a single-head attention layer is first pre-trained on a data-abundant task and subsequently adapted via a rank-one LoRA update on limited data. In the high-dimensional limit, both stages admit a sharp asymptotic characterization in terms of a finite set of order parameters, yielding explicit predictions for test errors and representation alignment. Our analysis shows that the impact of pre-training on LoRA is summarized by an effective noise term, from which we derive prescriptions for the optimal pre-training procedure. We also demonstrate a regime with a mismatch between the value of the test error and representation quality, and propose an application of our theory to active fine-tuning.

We propose GLASS, a framework for composable acoustic style control in zero-shot autoregressive text-to-speech (TTS) that learns controls from post-generation rewards rather than style labels. In zero-shot TTS, a speaker prompt often entangles speaker identity with prosodic attributes such as speaking rate and pitch, making it difficult to change style without changing the prompt itself. GLASS instead treats each acoustic attribute as a reward-defined control direction. For each control axis, GLASS freezes the TTS backbone and trains one lightweight LoRA adapter with Group Relative Policy Optimization (GRPO), using speech-token length and mean F0 as style rewards and WER as an intelligibility anchor. Because each control is represented as a LoRA weight update, independently trained adapters can be swapped, interpolated, and composed through linear LoRA arithmetic without retraining the backbone. Experiments on speaking rate and pitch control show targeted style shifts while preserving naturalness, speaker similarity, and intelligibility, and demonstrate smooth interpolation and multi-axis composition across independently trained adapters.

T2I models cannot effectively capture sentiment from various types of text, including diaries, as they primarily focus on visual object-related patterns rather than contextual emotional understanding. This paper proposes an emotion-aware text-to-image pipeline that generates children's hand drawing style images from short Korean diary entries. The proposed pipeline employs Qwen3-8B for recognising implicit sentiment from short diaries, and Stable Diffusion 3.5 Medium fine-tuned with LoRA on children's drawing images with emotion-based trigger words for image generation. Additionally, this paper presents experiments examining the effect of emotion trigger words on generated images and discusses the limitations of CLIP Score as an evaluation metric for emotion-aware image generation.

Deploying frontier large language models (LLMs) for domain-specific structured evaluation tasks incurs prohibitive latency, cost, and data-privacy overhead. We present a hybrid framework that fine-tunes a small language model (LLaMA 3.1 8B, 2.05% trainable parameters via LoRA) on only 219 curated examples and couples it with a deterministic rule-based postprocessing layer. Applied to multi-label compliance evaluation of conversational transcripts (18 heterogeneous output fields), our system achieves 100% JSON structural validity, 83.0% human-validated overall accuracy, and 100% accuracy on the most critical classification field in blind evaluation on 53 unseen production transcripts. On a single NVIDIA A100 GPU, inference completes in $\sim$2 seconds -- 2--5x faster than frontier APIs -- at USD 0.013 per evaluation versus USD 0.025--0.055 for proprietary alternatives, yielding 46--76% cost savings. We introduce targeted hard-negative augmentation for critical decision boundaries and formalize the hybrid neural-symbolic decomposition, demonstrating that domain-adapted small language models with postprocessing can match frontier model accuracy while dramatically reducing operational cost, latency, and privacy risk.

Parametric retrieval augmentation encodes document information into lightweight, document-specific modules such as LoRA adapters, reducing the need to include all evidence as input context. However, it remains unclear how this parameter-side memory interacts with context-side memory stored in the KV cache. We study this interaction in document-level question answering by progressively evicting document key-value states and measuring when a document LoRA contributes beyond the retained context. We find that document LoRA adds little when the KV cache is largely intact, but becomes increasingly useful under aggressive compression, recovering 13-21 ROUGE-L points when no document context remains. The gain is largest when the base model encodes the document, and the adapter is applied only during answer generation, suggesting that document LoRA is better understood as decoding-time parametric memory than as a document encoder. Finally, QA-style supervision produces substantially stronger adapters than raw-context next-token-prediction. These results position document LoRA as a complementary memory channel whose value emerges precisely when context-side evidence is scarce.

Combining a task LoRA adapter with a domain LoRA adapter into a single unified model is a practical yet largely unexplored challenge. Existing methods treat both adapters as symmetric peers, applying uniform weights across all layers. We argue that task and domain adapters exhibit a consistent depth-dependent asymmetry across transformer architectures. Domain dominance increases with layer depth, while shallower layers retain stronger task-relevant signals. Motivated by this observation, we propose $\textbf{TaDA}$ ($\textbf{Ta}$sk-$\textbf{D}$omain LoR$\textbf{A}$ Merging), a training-free algorithm that exploits this structure through calibrated probe-guided per-layer gating and per-component subspace-aware merging. The gating assigns individual weights per layer and projection type using a probe signal proved invariant to adapter weight magnitude. The merging discards conflicting singular directions before combining the remaining components. $\textbf{TaDA}$ produces a standard rank-$r$ LoRA adapter with zero inference overhead. On six scientific QA benchmarks with Llama-2-7B, TaDA achieves an average accuracy of 0.452, outperforming DARE-TIES by +3.6 percentage points and obtaining the best result on all six benchmarks. On six image classification benchmarks with ViT-L/16, TaDA reaches 85.9% average accuracy, improving over the strongest merging baseline while leading in three of the six individual benchmarks.

Custom diffusion models (CDMs) have garnered significant interest owing to their remarkable capacity for generating personalized concepts. However, the majority of CDMs unrealistically presume that the user's collection of personalized concepts is static and incapable of incremental growth over time. Furthermore, they exhibit significant catastrophic forgetting and concept neglect of previously learned concepts when incrementally learning a sequence of new ones. To resolve the above challenges, we develop a novel Continually Customizable Diffusion Model (CCDM), enabling users to perform concept-incremental versatile customization. Specifically, we design an attribute-decoupled LoRA (AD-LoRA) module and a relevance-guided AD-LoRA aggregation strategy to mitigate catastrophic forgetting. They can preserve concept-specific attributes of each task and leverage beneficial inter-task correlations to enhance the continual learning of new customization tasks. Additionally, to address the challenge of concept neglect, we propose a controllable regional context synthesis strategy that performs multi-concept composition in alignment with user-provided conditions. This strategy enhances the overall consistency in multi-concept synthesis by guaranteeing semantic independence between user-defined regions and their smooth boundary transitions. Experiments show our CCDM exhibits significant improvements over baseline methods.

Existing memory-augmented LLM agents store past experience exclusively in prompt space, as textual summaries or retrieved passages, while keeping model parameters frozen throughout a rollout. Such agents can \emph{look up} what they have seen but cannot \emph{learn from} it: their policy is unchanged by experience, and any information dropped from the context is permanently lost. We introduce \texttt{TMEM}, a self-evolving parametric memory framework in which the agent not only compresses history into explicit memory but also absorbs distilled supervision into fast LoRA weights $Δ_t$ via lightweight online updates, genuinely altering its future behavior within a single episode. We formalize this as an agentic decision process with fast-weight rollout dynamics: actions are sampled from $π_{θ_0+Δ_t}$, while extraction actions produce supervision that updates $Δ_t$ for subsequent decisions. This view makes the extraction policy directly optimizable by RL: training $θ_0$ improves not only task actions but also the quality of the data used for online LoRA adaptation. We further propose SVD-based initialization of the LoRA subspace to accelerate online convergence. Experiments on LoCoMo, LongMemEval-S, multi-objective search, and CL-Bench show that \texttt{TMEM} consistently outperforms summary-based and retrieval-based baselines across different model scales.

Low-Rank Adaptation (LoRA) is a popular parameter-efficient fine-tuning (PEFT) method that restricts weight updates to low-rank adapters, introducing a fixed low-rank inductive bias by optimizing in a low-dimensional subspace. In this work, we question whether a fixed-rank constraint is the most effective inductive bias for parameter-efficient fine-tuning. We introduce Learnable Rank LoRA (LR-LoRA), a PEFT method in which the adapter rank is learned during the training process. Instead of prescribing a uniform rank for all adapter layers, LR-LoRA allows the optimizer to determine the appropriate rank for each layer. Using this approach, we find substantial layer-wise variation in the learned ranks, with the attention and MLP layers in the transformer models exhibiting systematically different rank preferences. Across a range of language understanding and commonsense reasoning benchmarks, LR-LoRA achieves state-of-the-art performance in most settings and consistently outperforms strong PEFT baselines, demonstrating that a learnable rank provides a more flexible and effective inductive bias than fixed-rank adaptations.

Low-Rank Adaptation (LoRA) successfully enables personalization in text-to-image generation by adapting pre-trained diffusion models to specific visual concepts and styles. However, extending such models to multi-concept customization remains challenging. Naively combining multiple LoRA weights or their outputs often leads to interference among concepts, resulting in degraded visual quality and reduced fidelity to the reference images of individual concepts. This paper proposes a simple yet effective approach for multi-concept customization by optimally combining the outputs of multiple LoRA modules. We leverage the relative importance of each concept during generation, as inferred from its corresponding prompt tokens and introduce two methods, W-Switch and W-Composite, that employ a prompt-aware importance weighting strategy in which each LoRA is weighted according to the semantic influence of its trigger words in the target prompt. In addition, we extend existing quantitative evaluation metrics by proposing a new image-based similarity evaluation framework that assesses image fidelity and identity preservation through comparisons between real-world reference images and automatically segmented concept regions from generated images. We evaluate our approach on the ComposLoRA testbed and demonstrate consistent improvements over existing state-of-the-art methods in terms of visual quality, identity preservation and compositionality. Qualitative evaluations, including a Large Language Model (LLM) based assessment and a user study, further validate the effectiveness of the proposed methods and align with the newly introduced quantitative image-based metrics. Our code is available at https://github.com/GeorgeTsoumplekas/Prompt-Aware-Multi-LoRA-Composition.

Low-rank adaptation (LoRA) enables parameter-efficient specialization of foundation models, but the proliferation of task-specific adapters fragments capabilities across many adapters, complicating reuse and deployment. We study the problem of merging $T$ LoRAs into a single rank-$r$ LoRA, thereby preserving the benefits of low-rank structure. Existing Merge-then-Compress pipelines treat the rank constraint as an afterthought: they merge adapters in the full parameter space, then compress the merged result to rank $r$ via truncated SVD. However, full-parameter merging may destroy the low-rank structure, making it difficult for subsequent compression to recover an effective rank-$r$ LoRA. We propose Compress-then-Merge (CtM), a reversed pipeline that enforces the rank-$r$ bottleneck before merging: CtM computes shared $r$-dimensional subspaces using only the LoRA weights to capture cross-adapter common structure, projects each adapter into the shared subspaces to obtain $r\times r$ coordinates, and then applies standard merging rules in this reduced space. CtM guarantees a rank-$r$ LoRA by construction, avoiding post-hoc truncation, and enables efficient computation in the core space spanned by concatenated LoRA factors. Experiments across multiple models and tasks show that CtM consistently outperforms existing single-LoRA-output baselines while narrowing the performance gap to full-parameter merging methods.

Continual industrial anomaly detection with diffusion models suffers from historical normality prior drift and catastrophic forgetting. Existing continual diffusion methods preserve previous knowledge through replay or constrained optimization, but they lack an explicit mechanism for isolating and protecting category-specific normality priors during sequential adaptation. Although low-rank adaptation provides modular residual updates, standard LoRA neither freezes historical normality subspaces nor prevents new adapters from interfering with previous ones. To address this issue, we propose a normality-preserving continual anomaly detection framework based on two modules: History Frozen Orthogonal LoRA Bank (HF-OLB) and Hierarchical Novelty Adaptive Bank Growth module (HNABG). HF-OLB freezes both the pre-trained U-Net backbone and the learned LoRA banks, and constrains new task-specific normality residuals to the orthogonal complement of historical LoRA subspaces. HNABG further allocates layer-dependent residual capacity and expands the bank only when the residual normality novelty exceeds the expressive capacity of existing banks. Extensive experiments on MVTec and VisA demonstrate the effectiveness of the proposed method. On the challenging VisA 2x6 setting, our method achieves 83.6/91.8 image and pixel level A-AUROC with 3.8/3.9 FM, improving pixel level A-AUROC over the state of the art by 3.2 points while reducing pixel level FM by 1.3. These results show that our method effectively preserves historical normality priors in long horizon continual category sequences.

Blind image quality assessment (BIQA) predicts perceived image quality without access to a pristine reference and is fundamental to applications such as image compression, transmission, and restoration. Recent BIQA methods increasingly rely on large vision-language models (VLMs). Although frozen VLMs provide an efficient alternative to computationally expensive full fine-tuning, it remains unclear how much performance is sacrificed by not adapting the backbone and, more importantly, under what conditions such adaptation is truly beneficial. Answering this question, however, is complicated by the widespread use of image-level splitting on synthetic-distortion benchmarks, where distorted versions of the same reference image can appear in both training and test partitions. This content overlap artificially inflates the apparent performance of frozen representations, masking their true generalization ability and potentially leading to incorrect conclusions about the value of backbone adaptation. We therefore address these two issues jointly. We develop an efficient BIQA framework that fuses a natural-scene-statistics descriptor with frozen SigLIP and CLIP-H embeddings through a lightweight regression head, and then apply parameter-efficient Low-Rank Adaptation (LoRA) to the SigLIP backbone, training only $0.23\%$ of its parameters. Evaluating both frozen and adapted models across six datasets under image-level and reference-level protocols, we find that image-level splitting inflates frozen-feature SROCC by up to $0.44$ and masks wide variation in true difficulty, which reference-level evaluation reveals. Under this content-independent protocol, LoRA adaptation recovers performance in proportion to the exposed difficulty, with the largest gains where frozen features generalize poorly (up to $+0.357$ SROCC on TID2013) and little benefit where they are already strong.

Research and applications in artificial intelligence have recently shifted with the rise of large pretrained models, which deliver state-of-the-art results across numerous tasks. However, the substantial increase in parameters introduces a need for parameter-efficient training strategies. Despite significant advancements, limited research has explored parameter-efficient fine-tuning (PEFT) methods in the context of transformer-based models for instance segmentation. Addressing this gap, this study investigates the effectiveness of PEFT methods, specifically adapters and Low-Rank Adaptation (LoRA), applied to two models across four benchmark datasets. Integrating sequentially arranged adapter modules and applying LoRA to deformable attention--explored here for the first time--achieves competitive performance while fine-tuning only about 1-6% of model parameters, a marked improvement over the 40-55% required in traditional fine-tuning. Key findings indicate that using 2-3 adapters per transformer block offers an optimal balance of performance and efficiency. Furthermore, LoRA, exhibits strong parameter efficiency when applied to deformable attention, and in certain cases surpasses adapter configurations. These results show that the impact of PEFT techniques varies based on dataset complexity and model architecture, underscoring the importance of context-specific tuning. Overall, this work demonstrates the potential of PEFT to enable scalable, customizable, and computationally efficient transfer learning for instance segmentation tasks.

Visual Prompting (VP) has emerged as an efficient paradigm for adapting large-scale pre-trained vision models to downstream tasks by incorporating learnable prompts at the input level. However, existing VP methods typically employ dense pixel-level prompts, which often suffer from redundant perturbations, limited generalization and energy inefficiency. To overcome these limitations, we propose to integrate brain-inspired spiking learning into visual prompt learning tasks. As we know that spiking neuron can perform inexpensive information processing by transmitting the input data into discrete spike trains and return sparse outputs. Inspired by this, we propose \textbf{Lo}w-\textbf{R}ank visual \textbf{S}pike \textbf{P}rompting (LoRSP), a novel framework that learns dynamic low-rank sparse visual prompts naturally via a Spiking neuron learning mechanism. The core idea of LoRSP is to exploit the brain-inspired sparse firing mechanism of spiking neurons to generate pixel-level sparse prompt for each instance. To be specific, we first construct a series of prompt factors via low-rank factorization to capture distinct prompt subspaces. These prompt factors are then fed into an SNN architecture, which performs the integrate-and-fire process to emit spikes. As a result, our LoRSP generates a \emph{sparse} visual prompt while maintaining the low-rank constraint. This design enables instance-specific selective prompting, leading to more compact and robust adaptation across diverse downstream tasks. Extensive experiments on five heterogeneous vision backbones and multiple benchmarks demonstrate that LoRSP achieves competitive performance while requiring fewer tunable parameters compared to existing VP methods.

Agentic language model systems alternate between two structurally distinct step types: structured tool calls (short, deterministic, low perplexity) and open-ended planning/reasoning steps (long, complex, high perplexity). Despite this heterogeneity, current inference systems apply identical compute to every step. We introduce LayerRoute, a lightweight adapter that learns to selectively skip transformer blocks on a per-input basis. LayerRoute augments each of the 24 transformer blocks in Qwen2.5-0.5B-Instruct with: (1) a per-layer router (~897 parameters, Linear(896,1)) that outputs a hard binary gate via the straight-through estimator, and (2) LoRA adapters (rank 8, ~1.08M parameters) on the Q/K/V/O attention projections. The backbone weights remain frozen. A single end-to-end training pass on agentic data (Hermes, Glaive, GSM8K, Turing) with a gate regularisation term forces the system to discover which blocks are skippable per input type. After 3,000 steps (6.4 minutes on an A100 40GB), LayerRoute achieves a 12.91% skip differential: tool calls skip 15.25% of FLOPs while planning steps skip only 2.34%, using only 1.10M trainable parameters (0.22% of the 494M backbone). Quality improves over the base model due to LoRA adaptation, with perplexity delta of -1.29 on tool calls and -1.30 on planning.

Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form $W\approx Q+LR$. In this paper, we study this low-precision plus low-rank representation through the layer-wise reconstruction objective $\|XW-X(Q+LR)\|_F^2$, where $X$ is a calibration matrix. We establish, to our knowledge, the first information-theoretic lower bounds for this problem under finite-alphabet and bounded low-rank compensation constraints. We then propose GPTQ-intrinsic LoRA, a training-free algorithm that incorporates the low-rank correction directly into a GPTQ-style quantization pass by appropriately augmenting the calibration Hessian. For the choice $L=V_r$, where $V_r$ contains the top right singular vectors of $X$, we prove layer-wise reconstruction error bounds in which the usual GPTQ dependence on $\|X\|_F^2$ is replaced by the rank-$r$ residual $\|X-X_r\|_F^2$, up to regularization terms. Under natural structural assumptions, these bounds match the information-theoretic lower bounds in their dominant scaling, up to constants and mild factors. We also introduce Bid-Up, a fixed-grid quantization refinement step that can be alternated with optimal low-rank compensation with guaranteed non-increasing layer-wise reconstruction error. Experiments on Qwen3 language models and DeiT vision transformers show that GPTQ-intrinsic LoRA improves over GPTQ and GPTQ followed by low-rank compensation, with additional gains from refinement loops.

Large language models often improve on difficult tasks by spending inference-time compute on a reasoning trace before producing the final answer. That extra computation can be useful, but it also raises latency, token cost, and deployment complexity. We introduce \textbf{ThinkSwitch}, a low-compute procedure for co-training paired instruct and thinking checkpoints. Starting from compatible Qwen3-4B instruct and thinking models, each iteration asks the thinking checkpoint to generate answers, removes the reasoning trace, distills the answer-only pairs into the instruct checkpoint with QLoRA, and reconstructs a thinking checkpoint with spherical weight interpolation. The only human-supplied inputs are task prompts; the labels are generated by the model itself. On a 30-question AIME 2026 evaluation, ThinkSwitch improves the instruct checkpoint from 10/30 to 20/30 and the thinking checkpoint from 14/30 to 22/30. On a 30-question PubMedQA subset, it improves the instruct checkpoint from 13/30 to 18/30 and the thinking checkpoint from 18/30 to 25/30. The complete experiment uses 15 training prompts per domain and costs $2.86 on a single cloud RTX 3070. The results are small-scale, but they indicate that targeted distillation loops can move part of the benefit of explicit reasoning into weights while preserving a separate thinking mode.

Applying differential privacy (DP) via DP-SGD to Low-Rank Adaptation (LoRA) is a natural approach for privacy-preserving fine-tuning. However, LoRA's low-rank parameterization poses a fundamental challenge. In LoRA, each trainable update is represented as a low-rank matrix $Z = AB^\top$, but this factorization is inherently non-identifiable: many factor pairs $(A,B)$ represent the same update $Z$. As a result, applying DP-SGD directly to the factors induces gauge-dependent perturbations on $Z$, and we show that this naive DP-LoRA can lead to unbounded noise amplification. We propose PRISM, an intrinsic DP mechanism for LoRA that is gauge invariant by construction, avoids bilinear noise amplification, and admits an efficient low-dimensional noise sampler. Moreover, PRISM yields a closed-form characterization of the effective intrinsic noise induced on $Z$, enabling stable privacy-utility trade-offs through bounded, gauge-invariant perturbations. We establish standard $(ε,δ)$-DP guarantees for PRISM and introduce a DP-aware, gauge-invariant adaptive update rule that prevents adaptive optimization from amplifying injected privacy noise, improving numerical stability in practice.

Subliminal learning is a phenomenon where language models can transmit behavioral traits to other models through seemingly innocuous data (Cloud et al., 2025). In subliminal learning, a teacher model with a behavioral trait (e.g. obsession with cats) can transmit this cat obsession to a student model finetuned only on numerical sequences generated by the teacher. In this paper, we ask: how does this unexpected behavioral transmission occur? We show that subliminal learning is a LoRA artifact. When subliminal learning occurs, transmission has an inverted U-shaped relationship with LoRA rank; it also disappears with full finetuning. We show that subliminal learning is highly dependent on the context seen during finetuning and evaluation. For example, a Qwen model with the default system prompt during finetuning ("You are Qwen, created by Alibaba Cloud. You are a helpful assistant.") does not show subliminal learning during generation when no system prompt is included. We further demonstrate that subliminal behavior is localized to computation at tokens seen during both finetuning and evaluation (e.g. the model's default system prompt, the standard chat template tokens, etc.). Overall, subliminal learning seems to be a fragile artifact of LoRA hyperparameters and finetuning context, making it an unstable channel for behavioral transmission.

A simple way to improve the performance of almost any machine learning model is not to train a single but several models with diverse algorithms which will make slightly distinct kinds of predictions and errors on the same data, and thus improve the average predictions and robustness. However, making predictions using a whole ensemble of models is cumbersome and computationally too expensive to allow deployment to a large number of users, especially if the models are large neural nets. In response to this, we introduce a layer and point wise projection mapping, which maps student and teacher representations into an aligned high-dimensional embedding space during training process. The proposed approach combined with LoRA injection reduces the student model trainable parameters to less than 1% of the teacher model, while significantly improving word error rate (WER) compared to other distillation methods, as demonstrated in ablation studies. Unlike a mixture of experts, our method can be trained rapidly and in parallel.

Post-Training Quantization (PTQ) and Low-Rank Adaptation (LoRA) constitute the standard pipeline for efficient Large Language Model (LLM) deployment. However, applying them sequentially poses a problem: PTQ often leaves behind random noise that is spread out (across the model's weights) in a way LoRA can't easily fix, meaning that LoRA ends up wasting its limited capacity trying to fix uncorrectable noise instead of improving task performance. In this paper, we propose \textbf{ProjQ}, a novel framework for constraining quantization noise to the low-rank manifold via orthogonal subspace projection. We derive an efficient alternating algorithm that shapes the quantization noise into a low-rank structure, effectively offloading dominant error components to the subsequent adapter while minimizing the residual error in the orthogonal "uncorrectable" subspace. Our theoretical analysis demonstrates that ProjQ preserves strictly greater model plasticity for downstream tasks compared to standard PTQ. Extensive experiments on LLaMA-2, Qwen2.5 and Qwen3 confirm that ProjQ consistently outperforms existing methods in both quantization error compensation and downstream task fine-tuning, achieving up to $2\times$ lower evaluation loss for compensation and matching the performance of standard 4-bit baselines on language modeling tasks with only 3 bits. The code is available on https://github.com/yy9301/ProjQ .

Low-rank adapters are usually compared by sweeping a small set of ranks, but the rank also fixes the resolution of the parameter budget. For a $2048{\times}2048$ OPT attention projection, increasing LoRA by one rank stores $4096$ trainable scalars, leaving large gaps between feasible low-budget adapter sizes. This paper asks whether a tensorized adapter with finer capacity increments changes the observed accuracy--budget trade-off. We instantiate this question with fixed-component canonical polyadic (CP) tensor adapters. Under a $32{\times}64{\times}32{\times}64$ tensorization, one normalized CP component stores $193$ trainable scalars per projection, about $21$ times smaller than one LoRA rank step. We compare CP adapters and LoRA on OPT-1.3B across SST-2, RTE, and BoolQ under matched target modules, training protocol, data caps, and seed schedules. CP trains stably and fills the gaps between LoRA ranks, but the effect is task-dependent: SST-2 reaches an early low-budget plateau, BoolQ benefits from additional CP components before saturating slightly below LoRA, and RTE remains LoRA-favored. Finer parameter steps are therefore useful for diagnosing PEFT budget sensitivity, but they do not by themselves guarantee a better accuracy--budget curve.

Training strong large language models (LLMs) requires high-quality supervision, which is often scarce. Recent work shows that paired preference data from weak-weaker model pairs (e.g., Qwen3 4B over 1.7B), despite the limited quality of individual responses, can provide an effective supervision signal through relative quality deltas, which we term a "weak" signal. This motivates a key research question: can multiple "weak" signals be constructively aggregated for improving strong models (e.g., Qwen3 8B)? To this end, we propose Preference Delta Aggregation (PDA), the first framework that derives a preference delta from each weak-weaker model pair, instantiates it as a LoRA adapter learned through preference optimization, and aggregates the resulting deltas via LoRA merging. To further mitigate directional interference during LoRA merging, we introduce Geometric Alignment Merging (GAM), a geometry-aware merging method that aligns adapter subspaces before aggregation, enabling more robust composition of diverse deltas. Evaluations on knowledge reasoning and agentic search benchmarks show that aggregating multiple "weak" signals pushes performance beyond any single signal, with further gains as additional signals are incorporated. Correspondingly, PDA with GAM improves the strong model by 6.8 and 7.3 points on average for knowledge reasoning and agentic search, respectively. It outperforms all single-delta and multi-delta baselines, exceeding the best single-delta baseline by 2.1 and 4.3 points. Further analysis attributes these gains to the effective composition of complementary capabilities encoded across distinct preference deltas.

Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models. Notably, LoRA is inherently overparameterized: multiple pairs of low-rank factors can yield the same adapted weight matrix. We show--both theoretically and empirically--that these pairs exhibit significantly different condition numbers. As a result, converging to different loss minimizers directly impacts the convergence rate of LoRA. Building on this observation, we introduce Balanced Low-Rank Adaptation (BaLoRA), a variant of LoRA that projects iterates onto a balanced manifold. This manifold improves the conditioning of the loss landscape while preserving the adapted matrix. The projection step is computationally lightweight and integrates seamlessly into existing fine-tuning pipelines. Empirically, BaLoRA converges faster than standard LoRA and achieves superior performance across a range of fine-tuning tasks.

State-of-the-art GRPO-style methods for speech-aware large language model post-training suffer from coarse credit assignment, broadcasting the same terminal-reward advantage to every token in a response. This ignores useful structure within rollout batches, where speech-conditioned completions often share prefixes before diverging at important decisions. We propose Low-rank Exploration with Adaptive Forking (LEAF), a retrospective tree-based RL method that recovers this structure without online branching or additional decoding. LEAF samples complete responses, selects high-surprisal boundaries, groups responses by shared prefixes, and assigns span-level advantages using descendant rewards. We theoretically justify LEAF's span-level credit assignment and boundary-selection design. Empirically, LEAF improves over GRPO across speech question answering and speech translation benchmarks under the same rollout and low-rank adaptation budget. Notably, smaller LEAF-trained models outperform current state-of-the-art, full-parameter baselines.

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.

While finetuning effectively adapts foundation models to specialized downstream tasks, it can degrade nontarget capabilities acquired during pretraining. Existing forgetting aware methods typically seek safer updates through specialized initialization or fixed constraints, but do not regulate the adaptation preservation trade-off during training. We propose Foundation Preserving LoRA (FoLoRA), a forgetting aware optimization framework. Guided by a first order preservation condition, FoLoRA defines a forgetting penalty over pretraining-proxy activations and a task utility over downstream task activations. It then scores update directions by task utility per unit forgetting penalty via a generalized Rayleigh quotient. The resulting spectral coordinate system enables direction wise gated Adam updates, attenuating low utility to penalty directions during training. To estimate the forgetting penalty, FoLoRA constructs pretraining proxy calibration data by sampling from the pretrained model rather than relying on a single proxy dataset. Experiments on math, code, and instruction following adaptation show that FoLoRA achieves the strongest preservation adaptation balance over baselines, improving target task performance with best aggregate preservation of non target capabilities.

Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on qualitative downstream evaluations, leaving the quantitative capacity limits and underlying dynamics of exact parametric memory largely unexplored. To bridge this gap, we employ LoRA as a controlled memory capacity probe within the latent space to systematically quantify exact parametric memory. We introduce the Parametric Memory Law, a robust power law linking loss reduction Delta L to effective parameters and sequence length. At the token level, fine-grained analysis reveals a deterministic phase transition, demonstrating that a prediction probability of p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Driven by these insights, we introduce MemFT, a threshold-guided optimization strategy that dynamically redistributes the training budget toward sub-threshold tokens. Empirical evaluations demonstrate that MemFT can enhance memory fidelity and efficiency. Code will be released at https://github.com/zjunlp/ParametricMemoryLaw.