Convergence is a critical performance metric when zeroing neural networks (ZNNs) are employed to solve time-varying problems. As an effective strategy to enhance the convergence of ZNN models, gain adjustment is widely adopted to accelerate convergence speed, with the core objective of enabling the residual error to converge to zero rapidly and accurately. However, existing gain-tuning methods are decoupled from the residual error. This decoupling may lead to oscillation when the residual error approaches zero. To address this limitation, this paper proposes a novel error-driven varying-gain scheme. In this scheme, the gain value dynamically adapts to the residual error; a large residual error triggers a large gain, while a small residual error corresponds to a small gain, ensuring the gain changes synchronously with the residual error. Theoretical analyses and experimental results collectively demonstrate that integrating this error-driven varying-gain into ZNNs yields superior convergence performance, providing a more reliable solution for time-varying problem solving with ZNNs.

Accurately modeling students’ evolving knowledge states is a core challenge in intelligent education systems. Existing knowledge tracing methods often rely on single-view representations, limiting their ability to capture high-order dependencies among questions and underlying skills. In this paper, we propose a Multi-View Question–Skill Network (MVQSN), which constructs complementary relational views from readily available data to model student knowledge states comprehensively. Specifically, we first build a question–skill bipartite graph capturing direct question–skill associations, a skill complementarity view where edges represent synergistic relationships between skills derived from co-occurrence patterns, and a question co-response view that captures hierarchical question–question associations emerging from the hierarchical patterns of aggregated student responses. Each view is independently encoded using graph neural networks, producing view-specific student knowledge embeddings. To enhance representation consistency across views while preserving unique view information, we employ a multi-view contrastive learning module that aligns embeddings from different views. The aligned embeddings are then fused through an attention-guided mechanism, generating a unified and expressive student knowledge state representation. Finally, the unified embeddings are fed into a prediction layer to estimate students’ future performance. We conduct extensive experiments on three publicly available datasets, demonstrating that MVQSN significantly outperforms state-of-the-art baselines in prediction performance.

Knowledge graphs (KGs) organize relational facts in a form that supports machine reasoning across many domains. In decentralized Internet of Things (IoT) environments, such graphs can describe interactions among distributed devices and services. However, privacy constraints, intermittent communication, and incomplete observations can leave the resulting graphs sparse and incomplete. This sparsity weakens path availability and makes missing-fact inference difficult. Multi-hop reasoning can recover unobserved links through explicit reasoning paths, but conventional hierarchical reinforcement learning (HRL) approaches may explore inefficiently when only a few valid paths are available. This paper presents attentiON exploratIon of cluster relatioN (ONION), a framework for sparse KG reasoning. ONION introduces a cluster relation augmentation (CRA) module to add cluster relation cues to the action space, together with a relation-level attention (RLA) mechanism to emphasize relations that are relevant to the query. These components guide hierarchical exploration toward more informative paths. ONION is evaluated on four public sparse-KG benchmarks, and the results show competitive performance with the clearest gains on highly sparse datasets.