多面体神经网络
The Polytopal Neural Network
- Technical University of Denmark（丹麦技术大学）
- UiT The Arctic University of Norway（挪威北极大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出多面体神经网络（PNNs）框架，通过多面体结构提取分层特征，结合学习到的语料库表示与摊销单纯形推理，在性能损失极小的情况下保留潜在空间结构，为VQ深度学习训练提供新方法，助力构建更透明的AI系统。
AI中文摘要：
理解深度神经网络如何处理信息仍是核心挑战。现有可解释性方法常牺牲结构保真度、依赖预先指定的语料库或事后解释模型。我们提出多面体神经网络（Polytopal Neural Networks，PNNs），该框架通过强制采用基于多面体的结构来提取不同的分层特征，此结构可直接用于后续信息处理。我们利用学习到的语料库表示和摊销单纯形推理过程扩展该方法，并强调该框架也为向量量化（vector quantized，VQ）训练提供了直接途径。在PNNs中，观测值通过其与分层特定特征的对齐关系被明确描述。实验结果表明，对神经网络表示施加多面体约束可在潜在空间中保留有意义的结构，且性能下降极小；与无监督学习中的VQ表示相比，PNNs能生成更优的压缩表示，同时为VQ深度学习训练提供了一种高性能新方法。我们的发现表明，深度网络可强制采用可解释的基于多面体的表示，为构建更透明的AI系统提供了一条原则性路径，且性能损失极小。
英文摘要：
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.
