Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity

2026-09-30

AI Summary

This study addresses the lack of class-geometric constraints in tensor networks under label-scarce scenarios by proposing a rank-constrained tensor network method that integrates differentiable prototype rules with neuro-symbolic mechanisms. By introducing prototype regularization to embed semantic priors into the tensor decomposition process, the proposed approach effectively enhances the model's representational capacity under low-rank constraints. The method is applied to hyperspectral image classification tasks. Experimental evaluations on the Botswana dataset demonstrate an 8.82 percentage point improvement in macro F1-score for spatial assessment, validating the superiority of prototype-guided tensor networks in few-shot settings.

Abstract

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.

Problem

• tensor neural networks
• label scarcity
• rank constraint
• hyperspectral classification
• neurosymbolic learning

Innovation

• Neurosymbolic regularization
• Rank-constrained tensor neural networks
• Prototype learning
• Label scarcity
• Hyperspectral classification