Low-rank adaptations (LoRA) are widely used to fine-tune large models across various domains for specific downstream tasks. While task-specific LoRAs are often available, concerns about data privacy and intellectual property can restrict access to training data, limiting the acquisition of a multi-task model through gradient-based training. In response, LoRA merging presents an effective solution by combining multiple LoRAs into a unified adapter while maintaining data privacy. Prior works on LoRA merging primarily frame it as an optimization problem, yet these approaches face several limitations, including the rough assumption about input features utilized in optimization, massive sample requirements, and the unbalanced optimization objective. These limitations can significantly degrade performance. To address these, we propose a novel optimization-based method, named IterIS: 1) We formulate LoRA merging as an advanced optimization problem to mitigate the rough assumption. Additionally, we employ an iterative inference-solving framework in our algorithm. It can progressively refine the optimization objective for improved performance. 2) We introduce an efficient regularization term to reduce the need for massive sample requirements (requiring only 1-5% of the unlabeled samples compared to prior methods). 3) We utilize adaptive weights in the optimization objective to mitigate potential unbalances in LoRA merging process. Our method demonstrates significant improvements over multiple baselines and state-of-the-art methods in composing tasks for text-to-image diffusion, vision-language models, and large language models. Furthermore, our layer-wise algorithm can achieve convergence with minimal steps, ensuring efficiency in both memory and computation.

Transductive learning is a popular setting in statistic learning theory, reasoning from observed, specific training cases to specific test cases, which has been widely used in many fields such as graph neural networks and semi-supervised learning. Existing results provide fast rates of convergence based on the traditional local techniques, which need the surrogate function that upper bounds the uniform error within a localized region to be ``sub-root''. We derive new version of concentration inequality for empirical processes in transductive learning and apply generic chaining technique to relax the assumptions and gain tighter results in empirical risk minimization. Furthermore, we concentrate on the generalization of moment penalization algorithm. We design a novel estimator based on the second moment (variance) penalization and derive its learning rates, which is the first theoretical generalization analysis considering variance-based algorithms.

One of the central problems of statistical learning theory is quantifying the generalization ability of learning algorithms within a probabilistic framework. Algorithmic stability is a powerful tool for deriving generalization bounds, however, it typically builds on a critical assumption that losses are bounded. In this paper, we relax this condition to unbounded loss functions with subweibull diameter. This gives new generalization bounds for algorithmic stability and also includes existing results of subgaussian and subexponential diameters as specific cases. Furthermore, we provide a refined stability analysis by developing generalization bounds which can be $\sqrt{n}$-times faster than the previous results, where $n$ is the sample size. Our main technical contribution is general concentration inequalities for subweibull random variables, which may be of independent interest.

Cross-validation (CV) is a ubiquitous model-agnostic tool for assessing the error of machine learning. However, it has high complexity due to the requirement of multiple times of learner training especially in multimedia tasks with huge amounts of data. In this paper, we provide a unified framework to approximate the CV error for various common multimedia tasks such as supervised, semi-supervised and pairwise learning which requires training only once. Moreover, we study the theoretical performance of the proposed approximate CV and provide an explicit finite-sample error bound. Experimental results on several datasets demonstrate that our approximate CV has no statistical discrepancy from the original CV, but can significantly improve the efficiency, which is a great advantage in model selection.