Extended-connectivity fingerprints (ECFPs) are a ubiquitous tool in current
cheminformatics and molecular machine learning, and one of the most prevalent
molecular feature extraction techniques used for chemical prediction. Atom
features learned by graph neural networks can be aggregated to compound-level
representations using a large spectrum of graph pooling methods; in contrast,
sets of detected ECFP substructures are by default transformed into bit vectors
using only a simple hash-based folding procedure. We introduce a general
mathematical framework for the vectorisation of structural fingerprints via a
formal operation called substructure pooling that encompasses hash-based
folding, algorithmic substructure-selection, and a wide variety of other
potential techniques. We go on to describe Sort & Slice, an easy-to-implement
and bit-collision-free alternative to hash-based folding for the pooling of
ECFP substructures. Sort & Slice first sorts ECFP substructures according to
their relative prevalence in a given set of training compounds and then slices
away all but the $L$ most frequent substructures which are subsequently used to
generate a binary fingerprint of desired length, $L$. We computationally
compare the performance of hash-based folding, Sort & Slice, and two advanced
supervised substructure-selection schemes (filtering and mutual-information
maximisation) for ECFP-based molecular property prediction. Our results
indicate that, despite its technical simplicity, Sort & Slice robustly (and at
times substantially) outperforms traditional hash-based folding as well as the
other investigated methods across prediction tasks, data splitting techniques,
machine-learning models and ECFP hyperparameters. We thus recommend that Sort &
Slice canonically replace hash-based folding as the default
substructure-pooling technique to vectorise ECFPs for supervised molecular
machine learning.

推荐使用 Sort & Slice 作为将连通性指纹（ECFPs）向量化的默认技术，以替代基于哈希折叠的简单技术，该技术通过排序和切片基于训练化合物中的相对普遍性选择特定数量的亚结构，从而在预测任务、数据分割技术、机器学习模型和 ECFP 超参数中稳健地提高性能。

排序与切片：扩展连接指纹的简单且优越替代哈希折叠方法

Sort & Slice: A Simple and Superior Alternative to Hash-Based Folding  for Extended-Connectivity Fingerprints

Graph pooling methods have been widely used on downsampling graphs, achieving
impressive results on multiple graph-level tasks like graph classification and
graph generation. An important line called node dropping pooling aims at
exploiting learnable scoring functions to drop nodes with comparatively lower
significance scores. However, existing node dropping methods suffer from two
limitations: (1) for each pooled node, these models struggle to capture
long-range dependencies since they mainly take GNNs as the backbones; (2)
pooling only the highest-scoring nodes tends to preserve similar nodes, thus
discarding the affluent information of low-scoring nodes. To address these
issues, we propose a Graph Transformer Pooling method termed GTPool, which
introduces Transformer to node dropping pooling to efficiently capture
long-range pairwise interactions and meanwhile sample nodes diversely.
Specifically, we design a scoring module based on the self-attention mechanism
that takes both global context and local context into consideration, measuring
the importance of nodes more comprehensively. GTPool further utilizes a
diversified sampling method named Roulette Wheel Sampling (RWS) that is able to
flexibly preserve nodes across different scoring intervals instead of only
higher scoring nodes. In this way, GTPool could effectively obtain long-range
information and select more representative nodes. Extensive experiments on 11
benchmark datasets demonstrate the superiority of GTPool over existing popular
graph pooling methods.

我们提出了一种名为 GTPool 的图形变换汇聚方法，它引入了变换器来进行节点丢弃汇聚，以有效地捕获长程成对交互并同时进行多样化节点抽样。与现有方法相比，GTPool 在 11 个基准数据集上的广泛实验证明了其优越性。

基于多样化节点采样的分层 Transformer 汇聚用于图表示学习

Diversified Node Sampling based Hierarchical Transformer Pooling for  Graph Representation Learning

Convolutional Neural Networks (CNNs) have enabled major advances in image
classification through convolution and pooling. In particular, image pooling
transforms a connected discrete lattice into a reduced lattice with the same
connectivity and allows reduction functions to consider all pixels in an image.
However, there is no pooling that satisfies these properties for graphs. In
fact, traditional graph pooling methods suffer from at least one of the
following drawbacks: Graph disconnection or overconnection, low decimation
ratio, and deletion of large parts of graphs. In this paper, we present three
pooling methods based on the notion of maximal independent sets that avoid
these pitfalls. Our experimental results confirm the relevance of maximal
independent set constraints for graph pooling.

在图像分类中，卷积神经网络通过卷积和池化实现了重大进展；然而，对于图中的池化方法存在着一些问题，如图的断开或过连接、低减少率和删除大部分图等。本文基于最大独立集的概念提出了三种池化方法，并通过实验结果确认最大独立集约束对图池化的相关性。