The Agile Earth Observation Satellite Scheduling Problem (AEOSSP) presents a formidable challenge in combinatorial optimization. While Deep Reinforcement Learning (DRL) offers a promising avenue for automated solution construction, the nonlinear dynamics of satellite attitude control create a critical computational bottleneck: constraint validation must be executed sequentially, precluding efficient batch parallelization and severely impeding training throughput. To overcome this, we propose the Transfer Construction Method (TCM) for fast neural policy training in AEOSSP. TCM integrates two core components: 1) Enhanced Construction Model (ECM): A lightweight yet powerful neural policy tailored for end-to-end solution generation. 2) Constraint-Consistent Transfer (CCT): A two-stage training framework. In the CCT pre-training phase, the ECM is initialized on a constraint-consistent surrogate problem, S-AEOSSP, where linearized dynamics facilitate rapid batch constraint checking while preserving the underlying constraint topology. These structural priors are subsequently transferred to the full AEOSSP for deep-training, where the model adapts to precise orbital mechanics. By explicitly decoupling structural learning from dynamic complexity, TCM dramatically accelerates convergence. Experimental evaluations demonstrate that ECM alone surpasses state-of-the-art neural policies while reducing training time by 37.8%. Under the full TCM, the required training time is further compressed to just 18.4%, alongside improvements in solution quality and generalization capability across varying scales and distributions. TCM thus establishes a new standard for efficiency in satellite scheduling, offering a scalable paradigm for neural policy optimization in highly constrained, nonlinear environments.

The large language models (LLMs) learning framework for math problem generation (MPG) mostly performs homogeneous training in different epochs on small-scale manually annotated data.This pattern struggles to provide large-scale new quality data to support continual improvement, and fails to stimulate the mutual promotion reaction between generation and reasoning ability of math problem, resulting in the lack of reliable solving process.This paper proposes a synthetic data based continual learning framework to improve LLMs ability for MPG and math reasoning.The framework cycles through three stages, "supervised fine-tuning, data synthesis, direct preference optimization", continuously and steadily improve performance.We propose a synthetic data method with dual mechanism of model self-play and multi-agent cooperation is proposed, which ensures the consistency and validity of synthetic data through sample filtering and rewriting strategies, and overcomes the dependence of continual learning on manually annotated data.A data replay strategy that assesses sample importance via loss differentials is designed to mitigate catastrophic forgetting.Experimental analysis on abundant authoritative math datasets demonstrates the superiority and effectiveness of our framework.

The quadratic unconstrained binary optimization (QUBO) is a well-known NP-hard problem that takes an $n\times n$ matrix $Q$ as input and decides an $n$-dimensional 0-1 vector $x$, to optimize a quadratic function. Existing learning-based models that always formulate the solution process as sequential decisions suffer from high computational overload. To overcome this issue, we propose a neural solver called the Value Classification Model (VCM) that formulates the solution process from a classification perspective. It applies a Depth Value Network (DVN) based on graph convolution that exploits the symmetry property in $Q$ to auto-grasp value features. These features are then fed into a Value Classification Network (VCN) which directly generates classification solutions. Trained by a highly efficient model-tailored Greedy-guided Self Trainer (GST) which does not require any priori optimal labels, VCM significantly outperforms competitors in both computational efficiency and solution quality with a remarkable generalization ability. It can achieve near-optimal solutions in milliseconds with an average optimality gap of just 0.362\% on benchmarks with up to 2500 variables. Notably, a VCM trained at a specific DVN depth can steadily find better solutions by simply extending the testing depth, which narrows the gap to 0.034\% on benchmarks. To our knowledge, this is the first learning-based model to reach such a performance.