提出新型深层形态网络，实现高效通用逼近且可训练。
Training Deep Morphological Neural Networks as Universal Approximators
- 在形态层间引入受限线性激活与平均化极值单元
- 仅每层需O(N)可学习参数，即可实现通用逼近
- 结构紧凑且训练稳定，适合资源受限场景
我们研究深层形态神经网络（DMNNs），分析代数结构变化对深层架构表达能力与可训练性的影响。尽管形态操作具有固有非线性，现有深层形态网络无法成为通用逼近器，并存在梯度稀疏、信息量低的问题。为此，我们提出新架构：在形态层间引入受限线性激活，以及平均最大-加和最小-加的神经元。每层仅需O(N)个可学习参数（对应大小为N的层），其余参数受形态操作约束。我们证明该架构无需显著增加参数量即可实现通用逼近。残差连接与权重丢弃进一步提升泛化性能。实验表明，尽管结构受限，所提网络仍具备可训练性和紧凑性。
原文摘要 · Abstract (English)
We investigate deep morphological neural networks (DMNNs), studying how changes in algebraic structure affect the expressivity and trainability of deep architectures. We show that despite the inherent non-linearity of morphological operations, existing deep morphological architectures fail to be universal approximators and exhibit optimization limitations related to sparse and uninformative gradients. To address these issues, we introduce architectures incorporating constrained "linear" activations between morphological layers and averaging max-plus and min-plus neurons. Only O(N) parameters (or learnable parameters) per layer of size N belong to the activations, with the remaining parameters constrained to morphological operations. We prove universal approximation results for the proposed architectures without requiring substantially larger parameter counts than comparable linear networks. Residual connections and weight dropout further improve generalization. Our experiments show that our networks are trainable and compact, despite the imposed architectural restrictions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。