论文标题
使用热带代数的训练，修剪和执行形态神经网络的形状约束
Advances in the training, pruning and enforcement of shape constraints of Morphological Neural Networks using Tropical Algebra
论文作者
论文摘要
在本文中，我们研究了基于扩张和侵蚀的形态运算符的新兴神经网络。我们从热带几何学的角度和数学形态从数学上探索这些网络。我们的贡献是三倍。首先，我们通过征收差异编程方法检查形态网络的培训，并将二进制形态分类器扩展到多类任务。其次，我们专注于通过梯度下降算法训练的密集形态网络的稀疏性，并将其性能与繁重修剪下的线性对应物进行比较，这表明形态网络可以更好地应对，并且具有出色的压缩能力。我们的方法结合了使用的培训优化器的效果，并提供了定量和定性的解释。最后，我们研究形态网络的结构结构如何影响形状约束，重点是单调性。通过Maslov Dequantization，我们获得了已知体系结构的软化版本，并展示了这种方法如何改善培训的收敛性和性能。
In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our contributions are threefold. First, we examine the training of morphological networks via Difference-of-Convex programming methods and extend a binary morphological classifier to multiclass tasks. Second, we focus on the sparsity of dense morphological networks trained via gradient descent algorithms and compare their performance to their linear counterparts under heavy pruning, showing that the morphological networks cope far better and are characterized with superior compression capabilities. Our approach incorporates the effect of the training optimizer used and offers quantitative and qualitative explanations. Finally, we study how the architectural structure of a morphological network can affect shape constraints, focusing on monotonicity. Via Maslov Dequantization, we obtain a softened version of a known architecture and show how this approach can improve training convergence and performance.
