Educational prediction aims to estimate future learning outcomes based on students’ historical records, course performance, and behavioral features. This task is challenging because learning processes contain both long-term trends and short-term fluctuations, educational data involve hierarchical relations among students, courses, and cohorts, and many existing models provide limited explanation for their predictions. To address these issues, this study proposes a Hierarchical Temporal Graph Network for Educational Prediction (HTGN–EP). The model integrates long–short temporal modeling, hierarchical graph representation, and multi-task optimization into a unified framework to capture the temporal evolution of learning behaviors and the relational structure among students, courses, and cohorts. Experiments on real educational datasets show that HTGN–EP outperforms existing baseline methods, achieving an MAE of 0.136, an RMSE of 0.171, and an R^2 of 0.892, while maintaining stable performance across multiple prediction tasks. Further gradient-based attribution analysis indicates that prior GPA, attendance rate, and study time have strong effects on prediction outcomes, suggesting that the model can provide useful explanatory information while improving predictive accuracy. Overall, HTGN–EP effectively models temporal changes and hierarchical dependencies in educational data, offering an interpretable approach for learning outcome prediction, student risk identification, and educational management decision making.
This paper proposes a novel class of fractional-order octonion-valued fuzzy bidirectional associative memory neural networks (FOOVFBAMNNs). To address the analytical challenges arising from the inherent nonassociativity and noncommutativity of octonion algebra, we employ the Cayley–Dickson construction to decompose the original octonion-valued system into four coupled fractional-order complex-valued subsystems. Two inequalities are established in the complex-valued fuzzy logic domain, which are specifically tailored to handle complex-valued activation functions, connection weights, and state variables, providing tighter bounds for synchronization criterion derivation. A simple yet effective linear feedback controller and a properly constructed Lyapunov–Krasovskii functional (LKF) are designed for the transformed complex-valued error systems. By integrating fractional-order Lyapunov stability theory with the proposed inequalities, we derive sufficient conditions for global Mittag-Leffler synchronization of FOOVFBAMNNs under both general activation functions and linear threshold activation functions. Numerical simulations are conducted to verify the correctness and effectiveness of the obtained theoretical results.
Adaptive optimization algorithms are fundamental to modern deep learning; however, the global organization of neural-network training regimes induced by optimizer hyperparameters remains insufficiently understood. In particular, the influence of the Adam moment coefficients on the stability and qualitative behavior of the learning process has not been systematically investigated through parameter-space regime mapping. In this work, we introduce an observable-based empirical regime-mapping framework for analysing neural-network training under the Adam optimizer in the two-dimensional hyperparameter space defined by the exponential decay coefficients of the first and second gradient moments, (β1, β2). Neural-network optimization is treated as an iterative parameter-update process evolving in a high-dimensional parameter space, while its behavior is characterized through low-dimensional observable fields derived from neuron-wise training-error dynamics. Rather than relying on a single observable, the proposed framework combines seven complementary empirical descriptors that characterize regime organization, temporal stability, alignment, anisotropy, and training evolution. Experiments are performed on datasets of increasing complexity, including printed-digit patterns, Fashion-MNIST, CIFAR-10, and CIFAR-100, using multilayer neural-network architectures of varying width and depth. The resulting regime maps reveal fragmented hyperparameter landscapes containing stable, oscillatory, slow-learning, and irregular observable regimes. Increasing dataset complexity and network capacity is generally associated with smaller coherent stable regions and increased sensitivity to the Adam moment coefficients. The geometric complexity of the regime boundaries is quantified using box-counting analysis. The estimated dimensions approach D ≈ 1.9 for several investigated configurations, indicating highly irregular and nearly space-filling boundaries at the available numerical resolution. These values are interpreted as empirical measures of boundary complexity rather than as evidence of exact mathematical fractality. Additional robustness experiments performed using 300, 500, and 1000 optimizer steps demonstrate that the large-scale organization of all seven observable fields remains largely preserved, whereas the principal changes are concentrated near transition boundaries. This persistence indicates that the detected regime structures are reproducible and are not solely artifacts of short optimization histories. The proposed methodology provides an empirical computational framework for visualizing and comparing optimization regimes in the Adam hyperparameter space. It facilitates the identification of comparatively stable hyperparameter regions and offers a complementary observable-based perspective on the complex behavior of adaptive neural-network optimization.
While unsupervised skill discovery based on mutual information (MI) has shown promise for learning reusable robot behaviors, existing methods often discover static skills with limited state coverage. This can limit their usefulness in robot–object interaction settings where meaningful object-state transitions are difficult to induce through the robot’s motion. In this work, we propose DDOI (Decomposed Skill Discovery for Object Interaction) for a robot agent interacting with an object. Under the MI-based skill discovery framework, the latent skill is decomposed into an object skill and a robot skill. The object skill is learned via an object skill discriminator constrained by either a Euclidean or controllability-aware distance, encouraging far-reaching and hard-to-achieve transitions in object states. The robot skill is trained through a robot skill discriminator that conditions on both robot and object states as well as the object skill, enabling the robot to acquire behaviors that help realize desired object-state transitions. We tested DDOI in Ant, Ant-Box, and Humanoid MuJoCo environments as planar single-object interaction benchmarks, using object-state coverage as the main evaluation metric and downstream goal-reaching success rates as an additional metric. Across these environments, DDOI variants demonstrated more consistent object-state coverage and stronger downstream performance than the compared baselines.
This study explores the optimality criteria for a class of fractional optimization problems characterized by interval-valued objective functions under constraints. These problems involve curvilinear fractional integral cost functionals that are path-independent and fundamentally connected to fractional calculus, particularly through Riemann–Liouville fractional integrals. The application of fractional calculus is particularly significant in modeling complex systems exhibiting memory effects, as the fractional derivatives and integrals naturally incorporate the system’s historical behavior. An important outcome of this research is the development and demonstration of a core optimality condition—rooted in fractional calculus—ensuring that a solution locally LR-optimal for the associated variational control problem governed by PDE and PDI constraints is also globally LR-optimal. To underscore the practical relevance of these findings, an illustrative example is provided, demonstrating how fractional calculus and memory dynamics within complex systems can be effectively utilized to model and optimize real-world dynamic processes, specifically in the control of artificial neural networks.
