原型规则神经符号正则化用于标签稀缺下的秩约束张量神经网络
Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity
- University of Macedonia（马其顿大学）
- University of Malta（马耳他大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出原型规则神经符号正则化方法，在标签稀缺下增强秩约束张量神经网络，通过训练时正则化显著提升高光谱分类性能，推理融合效果有限。
AI中文摘要：
秩约束张量神经网络减少了高阶输入的参数化，但并未显式约束学习表示中的类别几何结构。本研究探讨了可微的原型规则能否在有限监督下为Rank-R张量学习提供互补的归纳偏置。所提出的框架通过基于原型的正则化增强Rank-R目标，并可选地在推理时将原型证据与神经逻辑融合。在四种高光谱基准上，使用四种Rank-R配置，在七折分层和空间分离的折叠（以减少泄漏）下进行评估；一项独立的空间研究将类别支持预算从2个样本变化到20个样本。在空间评估下，完整的神经符号推理在Botswana上将Macro-F1分数改变了+8.82个百分点，在Indian Pines上+5.49，在Pavia University上+1.59，在Salinas上-0.62。大部分收益来自训练时的正则化，而推理融合的影响较小且依赖于数据集。
英文摘要：
Rank-constrained tensor neural networks reduce the parameterization of high-order inputs, but they do not explicitly constrain class geometry in the learned representation. This study investigates whether a differentiable prototype-rule can provide a complementary inductive bias for Rank-R tensor learning under limited supervision. The proposed framework augments the Rank-R objective with prototype-based regularization and optionally fuses prototype evidence with neural logits at inference. Four hyperspectral benchmarks are evaluated with four Rank-R configurations under both seven-fold stratification and spatially separated folds that mitigate leakage; a separate spatial study varies the class support budget from 2 to 20 samples. Under spatial evaluation, full neurosymbolic inference changes Macro-F1 score by +8.82 percentage points on Botswana, +5.49 on Indian Pines, +1.59 on Pavia University, and -0.62 on Salinas. Most of the benefit arises from training-time regularization, whereas inference fusion is small and dataset dependent.
