This paper advances the theory of reproducing kernel Banach spaces (RKBSs) by investigating the general $\ell^p$ regularization framework, with a particular focus on the non-convex regime $0<p<1$. While our preceding work established the foundation for RKBSs with the $\ell^1$ norm, the pursuit of stronger sparsity---closer to the $\ell^0$ pseudo-norm---naturally motivates this exploration into $\ell^p$ quasi-norms. For $0<p<1$, we construct reproducing kernel quasi-Banach spaces (RKQBSs) with $\ell^p$ quasi-norms and establish existence and sparsity results for interpolation and regularized learning under appropriate assumptions. We characterize the linear and relaxed representer theorems in terms of a generalized Lebesgue constant and derive bounds under kernel decay, sample spacing, and stability assumptions. For $p>1$, we construct RKBSs using a fixed countable dictionary, establish minimizer existence, and identify the optimal relaxed representer factor through an off-sample coefficient operator. These results reveal fundamental differences between the regimes $0<p<1$, $p=1$, and $p>1$. Numerical experiments compare the accuracy and sparsity of solutions for these three cases.
Qijian Zheng, Wanqing Lin, Yuanfang Wang, Yijun Ge, Jordan Bate, Katie Aafjes-van Doorn, Feng Liu
Facilitative Interpersonal Skills (FIS) is a performance-based assessment method that provides a structured framework for evaluating the interpersonal competencies of mental health professionals. However, existing FIS assessment relies heavily on human observer ratings, making the evaluation process labor-intensive, costly, and difficult to scale. Progress toward automated FIS assessment has also been constrained by the lack of publicly available professional data in psychotherapy settings. To address this limitation, we introduce Therapy-FIS, a dataset for automated FIS assessment in standardized psychotherapy tasks. To our knowledge, Therapy-FIS is the first publicly available dataset in this domain. It contains facial, acoustic, and textual signals derived from standardized therapist responses to standardized mock patient stimulus clips, based on 890 therapist video recordings and 8 patient videos, and is rated with eight FIS subscale ratings and an overall FIS score. Built on Therapy-FIS, we further establish a benchmark with two downstream tasks: Therapist Performance Rating and Joint Therapist--mock-Patient Performance Rating. We also introduce a competitive baseline, DyadicFIS, with gated fusion and routed readout under therapist-only and dyadic settings. DyadicFIS obtains the best macro CCC(Concordance Correlation Coefficient) scores on both tasks (0.2807 and 0.3299). Therapy-FIS offers a reproducible resource for data-driven automated assessment of therapeutic interpersonal skills in mental health.
Outcome prediction from event sequence data requires effective use of information at two distinct semantic levels: attributes of individual events and attributes of the complete sequence. Although graph models can explicitly represent temporal relations between events, existing approaches commonly rely on predefined representations and manually configured architectures, with limited consideration of how event and sequence information should be incorporated at their corresponding GNN levels or how GNN models should be fitted to different datasets without manual tuning. We propose HGCN(O), an end to end self tuning graph toolkit for hierarchical information representation and automated model configuration. Its core T-GCN architecture processes event information at the node level and sequence information at the graph level, while O-GCN provides a one level reference for early integration of sequence attributes. TP-GCN and TE-GCN extend T-GCN with a pseudo informative duration embedding and a learned activity embedding, respectively. HGCN(O) integrates these architecture specific designs with hypermodel optimization to jointly determine model structure and training configuration. The core T-GCN achieves F1 scores of 1.0000 on two balanced benchmarks and a weighted F1 of 0.8639 on a highly imbalanced dataset, compared with 0.8318 for GAT and 0.8453 for TransformerConv. Prefix and ablation analyses further demonstrate its effectiveness for outcome prediction from incomplete sequences and quantify the contributions of temporal edge weights and graph level sequence attributes.
Vision-Language-Action (VLA) models have shown great promise for robotic manipulation by mapping multi-modal semantics to physical actions. However, this mapping inherently struggles to align these coarse-grained semantics with fine-grained temporal execution. It leaves VLA models with limited generalization and insufficient robustness in cluttered environments. To overcome this issue, we propose ActionUNet, an efficient multi-scale fine-tuning framework that enhances pre-trained VLA models with minimal computational cost. ActionUNet first constructs a lightweight temporal U-Net within the temporal-aligned action feature space to fuse hierarchical structural priors, effectively bridging the scale gap between semantics and temporal executions. Recognizing that multi-scale modeling can disrupt microscopic temporal continuity and cause mechanical oscillations, ActionUNet then employs a conditional SIREN as a continuous action decoder. Equipped with explicit second-order smoothness constraints, this decoder guarantees temporal continuity and reduces high-frequency motion jitter. By smoothing temporal discontinuities from multi-scale fusion, this continuous formulation reduces mechanical execution failures while preserving the base VLA model's generalization and manipulation robustness. Extensive experiments on RoboTwin 2.0 and LIBERO-Plus benchmarks, together with real-world hard evaluations, demonstrate that ActionUNet significantly improves π0.5 success rates by absolute 9.8%, 6.1%, and 11.4%, respectively, while also generalizing to the regression-based OpenVLA-OFT backbone, highlighting its effectiveness and efficiency as a fine-tuning strategy. Code and implementation details are available at https://github.com/Di-Zhu123/ActionUNet.