Scientific symbol input assistant leveraging LLM-augmented hybrid neural prediction model

Although recent advances in artificial intelligence (AI) have greatly accelerated automated problem solving, most existing systems still rely heavily on manual symbol input, which is inefficient for complex or symbol-intensive tasks. To address this limitation, this paper introduces scientific symbol prediction as a novel and practically oriented research task. Given a natural language problem description, the system proactively recommends relevant symbols for reasoning and solution development, enabling users to select appropriate ones and thereby reducing repetitive manual input. This task requires bridging natural language semantics and symbolic representations that are not explicitly aligned and often necessitate implicit reasoning. Unlike conventional machine learning tasks that depend solely on observed sample features, symbol prediction demands additional external knowledge to establish effective mappings between problem texts and symbolic notations. To this end, we propose a hybrid framework that combines semantic representations with the nonlinear interaction modeling capabilities of neural collaborative filtering, augmented by content-based knowledge derived from large language models (LLMs) and human expertise. To maintain a lightweight design, we utilize only LLM-generated embeddings rather than full model parameters, enabling efficient training, rapid deployment, and scalability. Based on the proposed approach, a full-stack prototype symbol recommendation system has been developed, demonstrating its practical potential in scientific and educational applications.