Heterogeneous graph neural networks (HGNNs) have demonstrated strong capability in modeling complex semantics across multi-type nodes and relations. However, their scalability to large-scale graphs remains challenging due to structural redundancy and high-dimensional node features. Existing graph condensation approaches, such as GCond, are primarily developed for homogeneous graphs and rely on gradient matching, resulting in considerable computational, memory, and optimization overhead. We propose HGC-Herd, a training-free condensation framework that generates compact yet informative heterogeneous graphs while maintaining both semantic and structural fidelity. HGC-Herd integrates lightweight feature propagation to encode multi-hop relational context and employs a class-wise herding mechanism to identify representative nodes per class, producing balanced and discriminative subsets for downstream learning tasks. Extensive experiments on ACM, DBLP, and Freebase validate that HGC-Herd attains comparable or superior accuracy to full-graph training while markedly reducing both runtime and memory consumption. These results underscore its practical value for efficient and scalable heterogeneous graph representation learning.

Water quality monitoring is a core component of ecological environmental protection. However, due to sensor failure or other inevitable factors, data missing often exists in long-term monitoring, posing great challenges in water quality analysis. This paper proposes a Neural Tucker Convolutional Network (NTCN) model for water quality data imputation, which features the following key components: a) Encode different mode entities into respective embedding vectors, and construct a Tucker interaction tensor by outer product operations to capture the complex mode-wise feature interactions; b) Use 3D convolution to extract fine-grained spatiotemporal features from the interaction tensor. Experiments on three real-world water quality datasets show that the proposed NTCN model outperforms several state-of-the-art imputation models in terms of accuracy. In advancing the modernization drive for harmonious coexistence between humans and nature, water quality monitoring plays an irreplaceable role [1]-[7].

Air turbulence refers to the disordered and irregular motion state generated by drastic changes in velocity, pressure, or direction during airflow. Various complex factors lead to intricate low-altitude turbulence outcomes. Under current observational conditions, especially when using only wind profile radar data, traditional methods struggle to accurately predict turbulence states. Therefore, this paper introduces a NeuTucker decomposition model utilizing discretized data. Designed for continuous yet sparse three-dimensional wind field data, it constructs a low-rank Tucker decomposition model based on a Tucker neural network to capture the latent interactions within the three-dimensional wind field data. Therefore, two core ideas are proposed here: 1) Discretizing continuous input data to adapt to models like NeuTucF that require discrete data inputs. 2) Constructing a four-dimensional Tucker interaction tensor to represent all possible spatio-temporal interactions among different elevations and three-dimensional wind speeds. In estimating missing observations in real datasets, this discretized NeuTucF model demonstrates superior performance compared to various common regression models.

Spectral Graph Neural Networks offer a principled approach to graph filtering but face a fundamental "Stability-vs-Adaptivity" trade-off. This trade-off is dictated by the choice of spectral domain. Filters in the finite [-1, 1] domain (e.g., ChebyNet) are numerically stable at high polynomial degrees (K) but are static and low-pass, causing them to fail on heterophilic graphs. Conversely, filters in the semi-infinite [0, infty) domain (e.g., KrawtchoukNet) are highly adaptive and achieve SOTA results on heterophily by learning non-low-pass responses. However, as we demonstrate, these adaptive filters can also suffer from numerical instability, leading to catastrophic performance collapse at high K. In this paper, we propose to resolve this trade-off by designing a hybrid-domain GNN, HybSpecNet, which combines a stable `ChebyNet` branch with an adaptive `KrawtchoukNet` branch. We first demonstrate that a "naive" hybrid architecture, which fuses the branches via concatenation, successfully unifies performance at low K, achieving strong results on both homophilic and heterophilic benchmarks. However, we then prove that this naive architecture fails the stability test. Our K-ablation experiments show that this architecture catastrophically collapses at K=25, exactly mirroring the collapse of its unstable `KrawtchoukNet` branch. We identify this critical finding as "Instability Poisoning," where `NaN`/`Inf` gradients from the adaptive branch destroy the training of the model. Finally, we propose and validate an advanced architecture that uses "Late Fusion" to completely isolate the gradient pathways. We demonstrate that this successfully solves the instability problem, remaining perfectly stable up to K=30 while retaining its SOTA performance across all graph types. This work identifies a critical architectural pitfall in hybrid GNN design and provides the robust architectural solution.

Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on "heterophilic" graphs and 2) performance collapse at high polynomial degrees (K), known as over-smoothing. Both issues stem from the static, low-pass nature of standard filters. In this work, we propose `KrawtchoukNet`, a GNN filter based on the discrete Krawtchouk polynomials. We demonstrate that `KrawtchoukNet` provides a unified solution to both problems through two key design choices. First, by fixing the polynomial's domain N to a small constant (e.g., N=20), we create the first GNN filter whose recurrence coefficients are \textit{inherently bounded}, making it exceptionally robust to over-smoothing (achieving SOTA results at K=10). Second, by making the filter's shape parameter p learnable, the filter adapts its spectral response to the graph data. We show this adaptive nature allows `KrawtchoukNet` to achieve SOTA performance on challenging heterophilic benchmarks (Texas, Cornell), decisively outperforming standard GNNs like GAT and APPNP.

Graph Neural Networks (GNNs) based on spectral filters, such as the Adaptive Orthogonal Polynomial Filter (AOPF) class (e.g., LaguerreNet), have shown promise in unifying the solutions for heterophily and over-smoothing. However, these single-filter models suffer from a "compromise" problem, as their single adaptive parameter (e.g., alpha) must learn a suboptimal, averaged response across the entire graph spectrum. In this paper, we propose DualLaguerreNet, a novel GNN architecture that solves this by introducing "Decoupled Spectral Flexibility." DualLaguerreNet splits the graph Laplacian into two operators, L_low (low-frequency) and L_high (high-frequency), and learns two independent, adaptive Laguerre polynomial filters, parameterized by alpha_1 and alpha_2, respectively. This work, however, uncovers a deeper finding. While our experiments show DualLaguerreNet's flexibility allows it to achieve state-of-the-art results on complex heterophilic tasks (outperforming LaguerreNet), it simultaneously underperforms on simpler, homophilic tasks. We identify this as a fundamental "Flexibility-Stability Trade-off". The increased parameterization (2x filter parameters and 2x model parameters) leads to overfitting on simple tasks, demonstrating that the "compromise" of simpler models acts as a crucial regularizer. This paper presents a new SOTA architecture for heterophily while providing a critical analysis of the bias-variance trade-off inherent in adaptive GNN filter design.

Spectral Graph Neural Networks (GNNs) operating in the canonical [-1, 1] domain (like ChebyNet and its adaptive generalization, L-JacobiNet) face a fundamental Flexibility-Stability Trade-off. Our previous work revealed a critical puzzle: the 2-parameter adaptive L-JacobiNet often suffered from high variance and was surprisingly outperformed by the 0-parameter, stabilized-static S-JacobiNet. This suggested that stabilization was more critical than adaptation in this domain. In this paper, we propose \textbf{GegenbauerNet}, a novel GNN filter based on the Gegenbauer polynomials, to find the Optimal Compromise in this trade-off. By enforcing symmetry (alpha=beta) but allowing a single shape parameter (lambda) to be learned, GegenbauerNet limits flexibility (variance) while escaping the fixed bias of S-JacobiNet. We demonstrate that GegenbauerNet (1-parameter) achieves superior performance in the key local filtering regime (K=2 on heterophilic graphs) where overfitting is minimal, validating the hypothesis that a controlled, symmetric degree of freedom is optimal. Furthermore, our comprehensive K-ablation study across homophilic and heterophilic graphs, using 7 diverse datasets, clarifies the domain's behavior: the fully adaptive L-JacobiNet maintains the highest performance on high-K filtering tasks, showing the value of maximum flexibility when regularization is managed. This study provides crucial design principles for GNN developers, showing that in the [-1, 1] spectral domain, the optimal filter depends critically on the target locality (K) and the acceptable level of design bias.

Positive--Unlabeled (PU) learning considers settings in which only positive and unlabeled data are available, while negatives are missing or left unlabeled. This situation is common in real applications where annotating reliable negatives is difficult or costly. Despite substantial progress in PU learning, the multi-class case (MPU) remains challenging: many existing approaches do not ensure \emph{unbiased risk estimation}, which limits performance and stability. We propose a cost-sensitive multi-class PU method based on \emph{adaptive loss weighting}. Within the empirical risk minimization framework, we assign distinct, data-dependent weights to the positive and \emph{inferred-negative} (from the unlabeled mixture) loss components so that the resulting empirical objective is an unbiased estimator of the target risk. We formalize the MPU data-generating process and establish a generalization error bound for the proposed estimator. Extensive experiments on \textbf{eight} public datasets, spanning varying class priors and numbers of classes, show consistent gains over strong baselines in both accuracy and stability.

Abstract--Imitation learning (IL) aims to learn a policy from expert demonstrations and has been applied to various applications. By learning from the expert policy, IL methods do not require environmental interactions or reward signals. However, most existing imitation learning algorithms assume perfect expert demonstrations, but expert demonstrations often contain imperfections caused by errors from human experts or sensor/control system inaccuracies. T o address the above problems, this work proposes a filter-and-restore framework to best leverage expert demonstrations with inherent noise. Our proposed method first filters clean samples from the demonstrations and then learns conditional diffusion models to recover the noisy ones. We evaluate our proposed framework and existing methods in various domains, including robot arm manipulation, dexterous manipulation, and locomotion. The experiment results show that our proposed framework consistently outperforms existing methods across all the tasks. Ablation studies further validate the effectiveness of each component and demonstrate the framework's robustness to different noise types and levels. These results confirm the practical applicability of our framework to noisy offline demonstration data. MIT A TION learning [1]-[13] aims to learn a policy from expert demonstrations and has been applied to various applications, including robotics [8], industrial automation, strategy board games, video games, etc [14]-[19]. Compared to reinforcement learning (RL), acquiring a policy in a trial-and-error manner, which can be unsafe or expensive, imitation learning (IL) algorithms can learn without environmental interactions. Furthermore, while designing sophisticated RL reward functions is often difficult and tedious [20], [21], IL methods learn from expert demonstrations and do not require reward signals. Despite the wide applicability, most existing imitation learning algorithms assume perfect (i.e., optimal and clean) expert demonstrations, which can be challenging and expensive to collect. Specifically, expert demonstrations often contain imperfections caused by errors from human experts or sensor and control system inaccuracies.

Spiking neural networks (SNNs), recognized as an energy-efficient alternative to traditional artificial neural networks (ANNs), have advanced rapidly through the scaling of models and datasets. However, such scaling incurs considerable training overhead, posing challenges for researchers with limited computational resources and hindering the sustained development of SNNs. Data pruning is a promising strategy for accelerating training by retaining the most informative examples and discarding redundant ones, but it remains largely unexplored in SNNs. Directly applying ANN-based data pruning methods to SNNs fails to capture the intrinsic importance of examples and suffers from high gradient variance. To address these challenges, we propose a novel spike-aware data pruning (SADP) method. SADP reduces gradient variance by determining each example's selection probability to be proportional to its gradient norm, while avoiding the high cost of direct gradient computation through an efficient upper bound, termed spike-aware importance score. This score accounts for the influence of all-or-nothing spikes on the gradient norm and can be computed with negligible overhead. Extensive experiments across diverse datasets and architectures demonstrate that SADP consistently outperforms data pruning baselines and achieves training speedups close to the theoretical maxima at different pruning ratios. Notably, SADP reduces training time by 35% on ImageNet while maintaining accuracy comparable to that of full-data training. This work, therefore, establishes a data-centric paradigm for efficient SNN training and paves the way for scaling SNNs to larger models and datasets. The source code will be released publicly after the review process.