Ruikai Yang

Zhengbao He, Ruiqi Ding, Zhehao Huang et al.

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.

Xinwen Cheng, Zhehao Huang, Wenxin Zhou et al.

Machine unlearning (MU) is to forget data from a well-trained model, which is practically important due to the ``right to be forgotten''. The unlearned model should approach the retrained model, where the forgetting data are not involved in the training process and hence do not contribute to the retrained model. Considering the forgetting data's absence during retraining, we think unlearning should withdraw their contribution from the pre-trained model. The challenge is that when tracing the learning process is impractical, how to quantify and detach sample's contribution to the dynamic learning process using only the pre-trained model. We first theoretically discover that sample's contribution during the process will reflect in the learned model's sensitivity to it. We then practically design a novel method, namely MU-Mis (Machine Unlearning by Minimizing input sensitivity), to suppress the contribution of the forgetting data. Experimental results demonstrate that MU-Mis can unlearn effectively and efficiently without utilizing the remaining data. It is the first time that a remaining-data-free method can outperform state-of-the-art (SoTA) unlearning methods that utilize the remaining data.

Ruikai Yang, Fan He, Mingzhen He et al.

Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random features on different nodes are identical. However, in many applications, data on different nodes varies significantly on the number or distribution, which calls for adaptive and data-dependent methods that generate different RFs. To tackle the essential difficulty, we propose a new decentralized KRR algorithm that pursues consensus on decision functions, which allows great flexibility and well adapts data on nodes. The convergence is rigorously given and the effectiveness is numerically verified: by capturing the characteristics of the data on each node, while maintaining the same communication costs as other methods, we achieved an average regression accuracy improvement of 25.5\% across six real-world data sets.

Ruikai Yang, Mingzhen He, Zhengbao He et al.

Machine unlearning (MU) is to make a well-trained model behave as if it had never been trained on specific data. In today's over-parameterized models, dominated by neural networks, a common approach is to manually relabel data and fine-tune the well-trained model. It can approximate the MU model in the output space, but the question remains whether it can achieve exact MU, i.e., in the parameter space. We answer this question by employing random feature techniques to construct an analytical framework. Under the premise of model optimization via stochastic gradient descent, we theoretically demonstrated that over-parameterized linear models can achieve exact MU through relabeling specific data. We also extend this work to real-world nonlinear networks and propose an alternating optimization algorithm that unifies the tasks of unlearning and relabeling. The algorithm's effectiveness, confirmed through numerical experiments, highlights its superior performance in unlearning across various scenarios compared to current state-of-the-art methods, particularly excelling over similar relabeling-based MU approaches.

Ruikai Yang, Fan He, Mingzhen He et al.

Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows that the pursuit of better classification can guide the data imputation process. While some works consider using label information to assist in this task, their simplistic utilization of labels lacks flexibility and may rely on strict assumptions. In this paper, we propose a new framework that effectively leverages supervision information to complete missing data in a manner conducive to classification. Specifically, this framework operates in two stages. Firstly, it leverages labels to supervise the optimization of similarity relationships among data, represented by the kernel matrix, with the goal of enhancing classification accuracy. To mitigate overfitting that may occur during this process, a perturbation variable is introduced to improve the robustness of the framework. Secondly, the learned kernel matrix serves as additional supervision information to guide data imputation through regression, utilizing the block coordinate descent method. The superiority of the proposed method is evaluated on four real-world data sets by comparing it with state-of-the-art imputation methods. Remarkably, our algorithm significantly outperforms other methods when the data is missing more than 60\% of the features