aiqbench analysis
This research introduces a neurosymbolic regularization technique specifically designed to improve rank-constrained tensor neural networks when training data is scarce. By leveraging prototype rules to constrain class geometry, the method achieves significant gains in Macro-F1 scores on hyperspectral benchmarks without relying on large labeled datasets. The findings highlight that the primary performance boost comes from training-time inductive bias rather than inference-stage fusion, offering a practical path forward for low-data regimes in high-order input modeling.
Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity
arXiv:2609.40131v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
arXiv:2609.40131 [cs.LG]
(or arXiv:2609.40131v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.40131 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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