Bayesian LoRA

Several geometry-aware approaches to low-rank adaptation have emerged for parameter-efficient fine-tuning of large pre-trained models. These methods aim to take full advantage of the geometric structure of low-rank manifolds for improving the efficiency in subspace utilization and reducing redundancy by enforcing orthogonality constraints during optimization. The strong empirical results of these techniques have motivated further study into whether predictions from such geometry-based adaptation methods could be overconfident. In this paper, we build on the singular value decomposition factorization of adapters to develop a framework based on Stein variational gradient descent (SVGD). In this formulation, the low-rank matrices are transported along the Stiefel manifold to match the targeted distributions while retaining their crucial geometric structure. Since this geometry-aware SVGD approach provides multiple solutions during inference, it supports uncertainty quantification and produces better-calibrated adapters on the Stiefel manifold. Extensive experiments show that our method delivers strong model calibration and attains higher prediction accuracy than SVGD and related uncertainty estimation methods that are formulated in Euclidean space.

Cross-domain zero- or few-shot personalization aims to generate user-preferred responses in unseen conversational domains from only a handful of target-domain interactions. Existing adaptation methods struggle to calibrate update magnitude under sparse evidence and thus overfit, whereas history-transfer methods often entangle user preferences with source-domain artifacts, yielding unreliable personalization priors and negative transfer. To calibrate adaptation to evidence quality, we propose PAC-Bayes-regularized Meta-LoRA, which uses a meta-learned LoRA initialization as both the adaptation start and prior center, while adjusting update strength according to support-set size and predictive uncertainty. This limits overfitting under sparse or ambiguous evidence while permitting stronger personalization as evidence grows. Controlled adaptation alone does not determine which preferences should transfer across domains or how they should be expressed. We therefore functionally decompose personalization priors into user and domain components, using a human-readable prompt for stable preferences and topology-preserving soft tokens for domain-specific hidden-space conditioning. Experiments across multiple benchmarks and personalization tasks show consistent gains over strong baselines. On HiCUPID, our method reduces cross-domain win-rate degradation by 47.9% relative to the best competing baseline and improves win rate by 110.2% under unseen-user cold start.

Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.

While Low-rank adaptation (LoRA) enables highly efficient fine-tuning by constraining task-specific updates to fixed low-rank subspaces, this rigid design limits representational flexibility and often results in overconfident predictions and miscalibrated uncertainty, especially in low-data regimes. Recent Bayesian LoRA variants improve uncertainty estimation by modeling posterior distributions over adaptation parameters. However, these approaches typically rely on fixed or heuristically determined ranks, overlooking the inherently context-dependent nature of adaptation capacity. In this paper, we propose BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning. Drawing inspiration from probabilistic topic models, BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. This Bayesian formulation provides principled, data-driven capacity control, mitigating over-parameterization while preserving expressiveness. Beyond the modeling contribution, we provide a complexity-theoretic generalization analysis showing that the generalization gap of BaRA depends on the learned joint effective rank $\bar{s}_{Φ,θ}$ induced by the global-local gate, rather than the maximum rank $r$. This result explains why sparse adaptive rank allocation can reduce the effective hypothesis complexity while preserving input-dependent expressiveness. Extensive experiments on diverse natural language benchmarks demonstrate that BaRA consistently improves predictive performance, robustness, and uncertainty calibration compared to standard LoRA and existing Bayesian LoRA variants.

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.

Parameter-efficient adaptation has made LLMs practical for domain prediction, but standard LoRA still relies on a static low-rank update and does not expose the latent interactions that often drive scientific labels. We introduce iLoRA. To our knowledge, it is the first Bayesian graph-conditioned LoRA framework. It infers a latent interaction graph from the input and uses it to generate input-conditioned LoRA updates. As a result, iLoRA learns prediction and latent interaction structure jointly, rather than training a predictor and applying interaction analysis only post hoc. We instantiate this idea for microbiome diagnosis, where disease state can depend on both species-level abundance and microbe-microbe cross-talk, and evaluate it in two complementary settings: interactive QA with human-annotated graphs, which tests latent structure recovery, and multi-cohort IBD diagnosis, which tests biomedical utility. Across both settings, iLoRA improves over strong LoRA and Bayesian adaptation baselines, recovers graphs aligned with human annotations and cohort-level microbiome associations, and provides calibrated uncertainty with moderate graph-branch overhead.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

Low-Rank Adaptation (LoRA) reparameterizes a weight update as a product of two low-rank factors, but the Jacobian $J_{G}$ of the generator mapping the factors to the weight matrix is rank-deficient, so the factor-space preconditioner $J_{G}^* {F}_t J_{G}$ induced by any ${W}$-space preconditioner ${F}_t$ is singular, and consequently the standard chain rule cannot be uniquely inverted to map a preconditioned ${W}$-space direction back to a factor-space update. We cast existing LoRA optimizers in a unified framework parameterized by two choices: (i) which invertible surrogate for $J_{G}^* {F}_t J_{G}$ to use, and (ii) which ${F}_t$ on ${W}$ to use. Existing methods occupy four families along these axes: factor-space adaptive updates, block-diagonal surrogates for $J_{G}^* J_{G}$, Frobenius-residual pseudoinverse methods, and Riemannian manifold constraint. Within this design space, a gradient-statistics-aware ${F}_t$ paired with a closed-form factor-space solve at ${O}((m+n)r)$ memory remains underexplored. We propose \textbf{AdaPreLoRA}, which fills this gap by adopting the Adafactor diagonal Kronecker preconditioner ${H}_t$ on ${W}$ and selecting from the resulting factor-space solution family the element minimizing an ${H}_t$-weighted imbalance between the two factor contributions; by construction, the resulting factor update is the closest LoRA approximation to the preconditioned ${W}$-space direction under the ${H}_t$-weighted norm. Across GPT-2 (E2E), Mistral-7B and Qwen2-7B (GLUE, ARC, GSM8K), and diffusion-model personalization, AdaPreLoRA is competitive with or improves over a representative set of LoRA optimizers while keeping peak GPU memory at the LoRA optimizer level.

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks mechanisms for uncertainty quantification, leading to overconfident and poorly calibrated models. Bayesian variants of LoRA address this limitation, but at the cost of a significantly increased number of trainable parameters, partially offsetting the original efficiency gains. Additionally, these models are harder to train and may suffer from unstable convergence. In this work, we propose a novel framework for parameter-efficient Bayesian fine-tuning, demonstrating that effective uncertainty quantification can be achieved in very low-dimensional parameter spaces. The proposed method achieves strong performance with improved calibration and generalization while maintaining computational efficiency. Our empirical findings show that, with the appropriate projection of the weight space uncertainty can be effectively modeled in a low-dimensional space, and weight covariances exhibit low ranks.

Parameter-efficient fine-tuning methods like Low-Rank Adaptation (LoRA) have become essential for deploying large language models, yet their static parameter allocation remains suboptimal for inputs of varying complexity. We present Flexi-LoRA, a novel framework that dynamically adjusts LoRA ranks based on input complexity during both training and inference. Through empirical analysis across question answering, mathematical reasoning, and speech tasks, we demonstrate that maintaining consistency between training and inference dynamics is important for effective adaptation, particularly for sequential reasoning tasks. Our findings reveal that input-dependent parameter allocation achieves higher performance with fewer parameters by optimally matching rank configurations to question complexity. Furthermore, task-specific dependency on rank dynamics varies, with mathematical reasoning tasks exhibiting higher dependency than QA tasks. Successful adaptation manifests not only in correctness but also in reasoning quality and instruction adherence. Flexi-LoRA consistently outperforms static LoRA while using fewer parameters, with performance gains more pronounced on tasks requiring strict reasoning chains. Our approach realizes key benefits of mixture-of-experts frameworks through a more streamlined implementation, reducing parameter redundancy while improving model capabilities. We provide comprehensive empirical studies across diverse tasks, establishing a basis for future work in input-adaptive and efficient fine-tuning approaches.

Low-Rank Adaptation (LoRA) has become the standard for fine-tuning large pre-trained models at reduced computational cost. However, its low-rank point-estimate updates limit expressiveness, leave a persistent gap relative to full fine-tuning accuracy, and provide no built-in uncertainty quantification, limiting its applicability in settings where reliability matters as much as accuracy. We introduce BaLoRA, a Bayesian extension of LoRA with a novel input-adaptive Bayesian parameterization of LoRA matrices that adds minimal parameters and compute. Surprisingly, not only does the Bayesian extension yield well-calibrated uncertainty estimates, but the adaptive noise injection underlying our approach also significantly improves prediction accuracy, narrowing the gap with full fine-tuning across both natural language reasoning and vision tasks. When applied to band gap prediction in metal-organic frameworks, BaLoRA produces zero-shot test-time uncertainty estimates that correlate more strongly with model error than a trained ensemble of LoRA models, and improve monotonically with compute without sacrificing accuracy.

Large pre-trained language models are increasingly adapted to downstream tasks using parameter-efficient fine-tuning (PEFT), but existing PEFT methods are typically deterministic and unimodal, making them poorly suited for low-resource multimodal settings where predictive uncertainty and cross-modal reliability both matter. We introduce CALIBER (Context-Aware Low-rank Inference with Bayesian Embedding Regularization), a multimodal uncertainty-aware PEFT framework for audio-text learning. CALIBER extends Bayesian low-rank adaptation by conditioning the variational posterior in the adapter space on per-layer, token-level text-audio cross-attention. Specifically, text-derived low-rank features attend to frame-level audio embeddings to produce localized acoustic context, which then modulates the mean and variance of a compact stochastic latent matrix within the rank-$r$ adapter space. This design treats audio not only as an additional feature source, but as a contextual reliability signal that shapes both adaptation and confidence. By confining stochasticity to a low-dimensional latent component, CALIBER retains the computational efficiency and scalability of PEFT while enabling heteroscedastic multimodal uncertainty estimation. Experimental results across diverse text and audio backbones show that CALIBER consistently matches or improves upon text-only Bayesian PEFT and conventional multimodal transfer-learning baselines, with token-level cross-attention yielding the most consistent gains. Our findings demonstrate that localized cross-modal conditioning is an effective and lightweight mechanism for uncertainty-aware multimodal adaptation.

We introduce CoCo-LoRA, a multimodal, uncertainty-aware parameter-efficient fine-tuning method for text prediction tasks accompanied by audio context. Existing PEFT approaches such as LoRA are efficient but typically deterministic, while recent Bayesian low-rank adapters model uncertainty in a lightweight way yet remain largely unimodal and condition uncertainty primarily on internal text features. This leaves them poorly equipped to reflect uncertainty driven by external acoustic factors such as background noise, channel variability, or speaking style, which can materially affect reliability in speech-centered applications. CoCo-LoRA addresses this gap by conditioning a contextual variational posterior in the low-rank space on both local text-derived adapter features and an audio-derived context signal. A pooled audio embedding is projected once into a shared context space and then adapted through lightweight layer-wise heads, enabling global-to-local, depth-specific modulation of the adapter uncertainty and update without high-dimensional multimodal fusion. Stochasticity is confined to a compact latent component in the rank space, preserving PEFT scalability while producing audio-sensitive, heteroscedastic uncertainty. Based on our evaluations across diverse tasks and backbone combinations, CoCo-LoRA consistently matches or outperforms text-only PEFT and conventional feature-fusion transfer baselines, particularly on high-coverage labels where reliable adaptation is critical. The results indicate that using audio as a contextual uncertainty signal, rather than as a fused feature stream, provides a robust and parameter-efficient alternative for multimodal low-resource prediction.

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