This paper presents a relation-centric algorithm for solving arithmetic word problems (AWPs) by synergizing a syntax-semantics extractor for extracting explicit relations, and a neural network miner for mining implicit relations. This is the first algorithm that has a specific component to acquire implicit knowledge items for solving AWPs. This paper proposes a three-phase scheme to decompose the challenging task of designing an algorithm for solving AWPs into three smaller tasks. The first phase proposes a state-action paradigm; the second phase instantiates the paradigm into a relation-centric approach; and the third phase implements a relation-centric algorithm for solving AWPs. There are two main steps in the proposed algorithm: problem understanding and symbolic solver. By adopting the relation-centric approach, problem understanding becomes a task of relation acquisition. For conducting the task of relation acquisition, a relaxed syntax-semantics method first extracts a group of explicit relation candidates. In parallel, a neural network miner acquires implicit relation candidates. The miner computes the vectors encoded by BERT to determine which implicit relations should be added. Thus, problem understanding can acquire both explicit relations and implicit relations, which addresses the challenge of building a problem understanding method that can acquire all the knowledge items to find the solution. In the subsequent step of symbolic solver, a fusion procedure forms a distilled set of relations from all the candidates by discarding unnecessary relations. Experimentation on nine benchmark datasets validates the superiority of the proposed algorithm that outperforms the state-of-the-art algorithms.

The rapid advancement of artificial intelligence relies on massive high-quality data, yet increasingly stringent data privacy regulations have exacerbated the problem of data silos. Federated learning enables collaborative training under privacy protection by exchanging model parameters rather than transmitting raw data. Nevertheless, its traditional centralized architecture still suffers from limitations such as single points of failure, lack of trust, and insufficient incentives. The integration of blockchain and federated learning opens new pathways for decentralized, auditable, and secure machine learning systems. This paper systematically reviews research progress in blockchain-enabled federated learning, analyzing technological evolution from three perspectives: system architecture, incentive mechanisms, and privacy enhancement. It further explores critical challenges including efficiency bottlenecks, storage overhead, and the inherent tension between transparency and privacy, while identifying key research directions for building scalable, efficient, and trustworthy decentralized learning systems.

Word annotation has been adopted as a crucial preprocessing step in developing algorithms for solving arithmetic word problems (AWPs). This paper proposes a mathematical concepts enhanced annotation (MONA) model for Chinese arithmetic word problems (AWPs), consisting of two modules: mathematical Chinese word segmentation and mathematical part-of-speech tagging. The MONA model utilizes mathematical concepts to enhance the training tasks of both modules, improving their capabilities to ensure high-quality AWPs annotations. The mathematical Chinese word segmentation module is trained on an AWP corpus segmented based on mathematical concepts, resulting in higher accuracy in identifying mathematical concepts compared to general segmentation models. The mathematical part-of-speech tagging module redefines part-of-speech categories into seven classes according to mathematical concepts and trains the MONA model on the redefined part-of-speech tags, allowing more suitable part-of-speech tagging for acquiring math relations when solving AWPs. Experimental results show the proposed MONA model outperforms baseline models on benchmark AWP datasets.

Developing Arithmetic Word Problem (AWP) -solving algorithms has recently become one of the hottest research areas because it can simultaneously advance general artificial intelligence and the application of AI technology in education. This paper presents a novel algorithm for solving AWPs by synergizing Large Language Models (LLMs) with the Scene-Aware Syntax–Semantics ($S^2$) method. The innovation of this algorithm lies in leveraging the LLM to divide problems into multiple scenes, thereby enhancing the relation-flow approach in the processes of relation extraction and reasoning. Our algorithm consists of three components: scene decomposer, relation extractor, and symbolic solver. In the scene decomposer, we propose the Chain-Of-Scene (COS) method. It dynamically constructs prompts for the LLM using a retrieval-augmented strategy, thus enabling the chain-formed generation of scenes from the input problem. In the relation extractor, we introduce the Scene-Aware $S^2$ method, which utilizes syntax–semantics models to match the text within each scene and convert it into relations. This allows for the efficient and accurate extraction of explicit and implicit relations. Finally, a symbolic solver is employed to reason through the set of relations to derive the solution. Experimental results on six authoritative datasets demonstrate that the proposed algorithm achieves an average solving accuracy of 90.4%, outperforming the State-Of-The-Art (SOTA) algorithm by 1.1%. The case study further illustrates that it outputs more reliable solutions than baseline algorithms. These findings have significant implications for promoting smart education and developing personalized intelligent tutoring systems.