摘要： 认知诊断（Cognitive Diagnosis，CD）旨在根据学生在在线教学平台中的作答记录，精准识别其在不同知识点上的掌握状态，是个性化学习推荐、学习路径规划和教学干预的重要基础。然而，真实教育数据普遍存在明显的长尾分布特征：少数头部学生拥有丰富的答题交互，能够为模型提供充分监督信号；而大量尾部学生仅具有少量作答记录，其认知状态难以被稳定估计，容易出现表征混叠、均值回归甚至表征坍塌问题。现有认知诊断模型大多依赖学生ID嵌入和有限交互记录，对头部学生中较为完备的认知模式利用不足，难以有效缓解尾部学生的冷启动与表征稀疏问题；同时，部分模型未充分区分答题正确与错误行为背后的认知语义差异，导致稀疏交互中的判别信息挖掘不充分。针对上述问题，本文提出一种基于条件流形增强与正误双视图对比学习的学生认知诊断框架CFECD。 在方法设计上，CFECD首先引入语义增强特征初始化模块，融合习题文本语义、知识点信息与ID嵌入，以提升稀疏场景下节点表示的泛化能力；随后，利用LightGCN编码学生、习题和知识点之间的高阶交互关系，获得结构化认知表征。在此基础上，构建条件流形增强模块，通过全局记忆库存储头部学生的高质量认知表征，并利用流形的可逆映射能力，在连续概率空间中对尾部学生进行逆向投影、潜空间插值和正向生成，实现尾部学生稀疏表征的分布补全与特征校准。为进一步提高增强特征的可靠性，模型融合原始图特征、流形生成特征、同伴参考特征和上下文交互特征，形成多源协同的尾部学生表示。同时，针对答题正误行为所反映的不同认知含义，本文构建正误双视图对比学习机制，将交互图解耦为正向掌握视图和负向缺陷视图，通过对比约束增强隐空间中不同认知状态的可分性。最后，模型设计带缩放因子的诊断预测函数，对学生能力与习题难度之间的边际差异进行适度放大，并结合自适应损失权重生成网络动态平衡预测损失、排序损失、一致性损失和对比学习损失，以提升联合优化过程的稳定性。在ASSIST2009、Junyi和XES3G5M三个公开教育数据集上的实验结果表明，CFECD在预测精度和排序能力方面均优于多种基线模型，尤其对于尾部学生有明显提升。消融实验和参数敏感性分析进一步表明，条件流形增强能够有效补全尾部学生表征，正误双视图对比学习能够提升隐空间语义判别性，适度的流形约束、网络深度、对比学习权重和缩放因子有助于在表征增强与主任务预测之间取得平衡。 综上，CFECD能够在长尾在线教学场景中生成更加稳定、可解释的学生知识掌握画像，尤其适用于低活跃学生、新注册学生和交互记录不足学生的早期诊断。模型输出可进一步服务于薄弱知识点识别、个性化习题推荐、学习路径规划、教师教学预警和班级学情分析。实验结果验证了所提方法在长尾学生认知诊断任务中的有效性、鲁棒性和实际教学应用潜力。

Abstract: Cognitive diagnosis ( CD ) aims to accurately identify students ' mastery of different knowledge points based on their response records in online teaching platforms. It is an important basis for personalized learning recommendation, learning path planning and teaching intervention. However, the real education data generally have obvious long tail distribution characteristics : a small number of head students have rich answer interaction, which can provide sufficient supervision signals for the model ; however, a large number of tail students only have a small number of answering records, and their cognitive state is difficult to be stably estimated, which is prone to representational aliasing, mean regression and even representational collapse. Most of the existing cognitive diagnosis models rely on student ID embedding and limited interaction records, and the relatively complete cognitive models in head students are not fully utilized, which is difficult to effectively alleviate the cold start and sparse representation of tail students. At the same time, some models do not fully distinguish the cognitive semantic differences behind the correct and wrong answers, resulting in insufficient mining of discriminative information in sparse interaction. In view of the above problems, this paper proposes a student cognitive diagnosis framework CFECD based on conditional manifold enhancement and positive and negative two-view contrastive learning. In the design of the method, CFECD first introduces the semantic enhancement feature initialization module, which integrates the semantics of the exercise text, knowledge point information and ID embedding to improve the generalization ability of node representation in sparse scenes. Then, LightGCN is used to encode the high-order interaction between students, exercises and knowledge points to obtain structured cognitive representations. On this basis, the conditional manifold enhancement module is constructed to store the high-quality cognitive representation of the head students through the global memory library, and the reverse projection, latent space interpolation and forward generation of the tail students in the continuous probability space are carried out by using the reversible mapping ability of the manifold to realize the distribution completion and feature calibration of the sparse representation of the tail students. In order to further improve the reliability of the enhanced features, the model combines the original graph features, manifold generation features, peer reference features and context interaction features to form a multi-source collaborative tail student representation. At the same time, aiming at the different cognitive meanings reflected by the correct and wrong behaviors of the answers, this paper constructs a positive and negative dual-view contrastive learning mechanism, decouples the interaction graph into a correct-response mastery view and an incorrect-response deficiency view, and enhances the separability of different cognitive states in the hidden space by comparing the constraints. Finally, the model designs a diagnostic prediction function with scaling factor to moderately enlarge the marginal difference between students ' ability and the difficulty of exercises, and combines the adaptive loss weight to generate the network dynamic balance prediction loss, sorting loss, consistency loss and contrast learning loss to improve the stability of the joint optimization process. The experimental results on the three public education datasets of ASSIST2009, Junyi and XES3G5M show that CFECD is superior to various baseline models in terms of prediction accuracy and ranking ability, especially for tail students. The ablation experiment and parameter sensitivity analysis further show that the conditional manifold enhancement can effectively complement the tail student representation, the positive and negative two-view contrast learning can improve the semantic discrimination of the hidden space, and the moderate manifold constraint, network depth, contrast learning weight and scaling factor help to achieve a balance between representation enhancement and main task prediction. In summary, CFECD can generate more stable and interpretable portraits of students ' knowledge mastery in the long-tail online teaching scene, especially for the early diagnosis of low-active students, newly registered students and students with insufficient interactive records. The model output can further serve the identification of weak knowledge points, personalized exercise recommendation, learning path planning, teacher teaching early warning and class learning situation analysis. The experimental results verify the effectiveness, robustness and practical teaching application potential of the proposed method in the cognitive diagnosis task of long tail students.