Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Pooling through the Lens of Optimal Transport   Pooling is one of the most significant operations in many machine learning
models and tasks, whose implementation, however, is often empirical in
practice. In this paper, we develop a novel and solid algorithmic pooling
framework through the lens of optimal transport. In particular, we demonstrate
that most existing pooling methods are equivalent to solving some
specializations of an unbalanced optimal transport (UOT) problem. Making the
parameters of the UOT problem learnable, we unify most existing pooling methods
in the same framework, and accordingly, propose a generalized pooling layer
called \textit{UOT-Pooling} for neural networks. Moreover, we implement the
UOT-Pooling with two different architectures, based on the Sinkhorn scaling
algorithm and the Bregman ADMM algorithm, respectively, and study their
stability and efficiency quantitatively. We test our UOT-Pooling layers in two
application scenarios, including multi-instance learning (MIL) and graph
embedding. For state-of-the-art models of these two tasks, we can improve their
performance by replacing conventional pooling layers with our UOT-Pooling
layers.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex