Polytopal Neural Network：用多胞体结构实现可解释的神经网络表示

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Abstract:Understanding how deep neural networks process information remains a central challenge. Existing interpretability methods often compromise structural fidelity, rely on prespecified corpora, or explain models post-hoc. We propose Polytopal Neural Networks (PNNs), a framework that extracts distinct layer-wise aspects by enforcing a polytope-based structure that is used directly in subsequent information processing. We scale our approach using learned corpus representations and an amortized simplex inference procedure and highlight how the framework also gives a direct route to vector quantized (VQ) training. In PNNs, observations are explicitly described by their alignment with layer-specific aspects. Empirical results show that imposing polytopal constraints on neural network representations preserves meaningful structures in the latent space with minimal degradation in performance, favorable compressed representations when compared to VQ representations in unsupervised learning, while also providing a performant new approach to VQ deep learning training. Our findings suggest that deep networks can enforce interpretable polytope-based representations, offering a principled path toward more transparent AI systems with minimal performance compromise.

Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:	arXiv:2610.12004 [cs.LG]
	(or arXiv:2610.12004v1 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2610.12004 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Anna Emilie Jennow Wedenborg [view email]
[v1] Thu, 8 Oct 2026 14:08:53 UTC (4,393 KB)