Haotian Lin

Haotian Lin, Matthew Reimherr

We study the transfer learning (TL) for the functional linear regression (FLR) under the Reproducing Kernel Hilbert Space (RKHS) framework, observing that the TL techniques in existing high-dimensional linear regression are not compatible with the truncation-based FLR methods, as functional data are intrinsically infinite-dimensional and generated by smooth underlying processes. We measure the similarity across tasks using RKHS distance, allowing the type of information being transferred to be tied to the properties of the imposed RKHS. Building on the hypothesis offset transfer learning paradigm, two algorithms are proposed: one conducts the transfer when positive sources are known, while the other leverages aggregation techniques to achieve robust transfer without prior information about the sources. We establish asymptotic lower bounds for this learning problem and show that the proposed algorithms enjoy a matching upper bound. These analyses provide statistical insights into factors that contribute to the dynamics of the transfer. We also extend the results to functional generalized linear models. The effectiveness of the proposed algorithms is demonstrated via extensive synthetic data as well as real-world data applications.

Haotian Lin, Matthew Reimherr

Many existing mechanisms to achieve differential privacy (DP) on infinite-dimensional functional summaries often involve embedding these summaries into finite-dimensional subspaces and applying traditional DP techniques. Such mechanisms generally treat each dimension uniformly and struggle with complex, structured summaries. This work introduces a novel mechanism for DP functional summary release: the Independent Component Laplace Process (ICLP) mechanism. This mechanism treats the summaries of interest as truly infinite-dimensional objects, thereby addressing several limitations of existing mechanisms. We establish the feasibility of the proposed mechanism in multiple function spaces. Several statistical estimation problems are considered, and we demonstrate one can enhance the utility of sanitized summaries by oversmoothing their non-private counterpart. Numerical experiments on synthetic and real datasets demonstrate the efficacy of the proposed mechanism.

Wenli Xiao, Haotian Lin, Andy Peng et al.

Supervised fine-tuning (SFT) has become the de facto post-training strategy for large vision-language-action (VLA) models, but its reliance on costly human demonstrations limits scalability and generalization. We propose Probe, Learn, Distill (PLD), a three-stage plug-and-play framework that improves VLAs through residual reinforcement learning (RL) and distribution-aware data collection. In Stage 1, we train lightweight residual actors to probe failure regions of the VLA generalist. In Stage 2, we use a hybrid rollout scheme that aligns collected trajectories with the generalist's deployment distribution while capturing recovery behaviors. In Stage 3, we distill the curated trajectories back into the generalist with standard SFT. PLD achieves near-saturated 99% task success on LIBERO, over 50% gains in SimplerEnv, and 100% success on real-world Franka and YAM arm manipulation tasks. Ablations show that residual probing and distribution-aware replay are key to collecting deployment-aligned data that improves both seen and unseen tasks, offering a scalable path toward self-improving VLA models.

Xiaoning Liu, Zongwei Wu, Ao Li et al.

This paper reviews the NTIRE 2024 low light image enhancement challenge, highlighting the proposed solutions and results. The aim of this challenge is to discover an effective network design or solution capable of generating brighter, clearer, and visually appealing results when dealing with a variety of conditions, including ultra-high resolution (4K and beyond), non-uniform illumination, backlighting, extreme darkness, and night scenes. A notable total of 428 participants registered for the challenge, with 22 teams ultimately making valid submissions. This paper meticulously evaluates the state-of-the-art advancements in enhancing low-light images, reflecting the significant progress and creativity in this field.

Haotian Lin, Matthew Reimherr

Many existing two-phase kernel-based hypothesis transfer learning algorithms employ the same kernel regularization across phases and rely on the known smoothness of functions to obtain optimality. Therefore, they fail to adapt to the varying and unknown smoothness between the target/source and their offset in practice. In this paper, we address these problems by proposing Smoothness Adaptive Transfer Learning (SATL), a two-phase kernel ridge regression(KRR)-based algorithm. We first prove that employing the misspecified fixed bandwidth Gaussian kernel in target-only KRR learning can achieve minimax optimality and derive an adaptive procedure to the unknown Sobolev smoothness. Leveraging these results, SATL employs Gaussian kernels in both phases so that the estimators can adapt to the unknown smoothness of the target/source and their offset function. We derive the minimax lower bound of the learning problem in excess risk and show that SATL enjoys a matching upper bound up to a logarithmic factor. The minimax convergence rate sheds light on the factors influencing transfer dynamics and demonstrates the superiority of SATL compared to non-transfer learning settings. While our main objective is a theoretical analysis, we also conduct several experiments to confirm our results.

Yixiao Wang, Mingxiao Huo, Zhixuan Liang et al. · berkeley

Pretrained vision foundation models (VFMs) advance robotic learning via rich visual representations, yet individual VFMs typically excel only in specific domains, limiting generality across tasks. Distilling multiple VFMs into a unified representation for policy can mitigate this limitation but often yields inflexible task-specific feature selection and requires costly full re-training to incorporate robot-domain knowledge. We propose VER, a Vision Expert transformer for Robot learning. During pretraining, VER distills multiple VFMs into a vision expert library. It then fine-tunes only a lightweight routing network (fewer than 0.4% of parameters) to dynamically select task-relevant experts from the pretrained library for downstream robot tasks. We further introduce Patchwise Expert Routing with Curriculum Top-K Annealing to improve both flexibility and precision of dynamic expert selection. Moreover, VER supports parameter-efficient finetuning for scalable expert utilization and adaptive robot-domain knowledge integration. Across 17 diverse robotic tasks and multiple policy heads, VER achieves state-of-the-art performance. We find that VER reduces large-norm outliers in task-irrelevant regions (e.g., background) and concentrates on task-critical regions. Visualizations and codes can be found in https://yixiaowang7.github.io/ver_page/.

Haotian Lin, Matthew Reimherr

When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or pre-trained models from similar source domains. While existing generalization analyses of kernel-based transfer learning typically rely on correctly specified models, we present a transfer learning procedure that is robust against model misspecification while adaptively attaining optimality. To facilitate our analysis and avoid the risk of saturation found in classical misspecified results, we establish a novel result in the misspecified single-task learning setting, showing that spectral algorithms with fixed bandwidth Gaussian kernels can attain minimax convergence rates given the true function is in a Sobolev space, which may be of independent interest. Building on this, we derive the adaptive convergence rates of the excess risk for specifying Gaussian kernels in a prevalent class of hypothesis transfer learning algorithms. Our results are minimax optimal up to logarithmic factors and elucidate the key determinants of transfer efficiency.