Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Advances in the training, pruning and enforcement of shape constraints
  of Morphological Neural Networks using Tropical Algebra   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.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg