In this paper, we propose a novel pooling layer for graph neural networks based on maximizing the mutual information between the pooled graph and the input graph. Since the maximum mutual information is difficult to compute, we employ the Shannon capacity of a graph as an inductive bias to our pooling method. More precisely, we show that the input graph to the pooling layer can be viewed as a representation of a noisy communication channel. For such a channel, sending the symbols belonging to an independent set of the graph yields a reliable and error-free transmission of information. We show that reaching the maximum mutual information is equivalent to finding a maximum weight independent set of the graph where the weights convey entropy contents. Through this communication theoretic standpoint, we provide a distinct perspective for posing the problem of graph pooling as maximizing the information transmission rate across a noisy communication channel, implemented by a graph neural network. We evaluate our method, referred to as Maximum Entropy Weighted Independent Set Pooling (MEWISPool), on graph classification tasks and the combinatorial optimization problem of the maximum independent set. Empirical results demonstrate that our method achieves the state-of-the-art and competitive results on graph classification tasks and the maximum independent set problem in several benchmark datasets.
Towards Fine-grained Visual Representations by Combining Contrastive Learning with Image Reconstruction and Attention-weighted Pooling
Bayer AG（拜耳股份公司）
本文介绍了对比重建，ConRec -一种自监督学习算法，通过联合优化对比和自重建损失来获得图像表示。我们展示了最先进的对比学习方法（例如Simplified）在其表示中捕获细粒度视觉特征方面存在缺陷。ConRec通过添加（1）自我重建任务和（2）对比学习任务中的注意力机制扩展了Simplified框架。这是通过应用具有两个头的简单编码器-解码器架构来实现的。我们表明，这两个扩展有助于改善图像的矢量表示与细粒度的视觉特征。结合这些概念，ConRec在细粒度分类数据集上的性能优于Simplified和Simplified with Attention-Pooling。
Path Integral Based Convolution and Pooling for Graph Neural Networks
Princeton University（普林斯顿大学）；University of Technology Sydney（悉尼科技大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；University of New South Wales（新南威尔士大学）；Zhejiang Normal University（浙江师范大学）；University of Cambridge（剑桥大学）
Hierarchical Pooling and Explainability in Graph Neural Networks for Tumor and Tissue-of-Origin Classification Using RNA-seq Data
Institute of Informatics（信息学院）；Universidade Federal do Rio Grande do Sul（鲁汶联邦大学）；Bioinformatics Core（生物信息学核心）；Hospital de Clínicas de Porto Alegre（波多利亚临床医院）
Barycentric Neural Networks and Length-Weighted Persistent Entropy Loss: A Green Geometric and Topological Framework for Function Approximation
Department of Applied Mathematics I, University of Seville（应用数学I系，塞维利亚大学）；Department of Computer Science and Artificial Intelligence, University of Seville（计算机科学与人工智能系，塞维利亚大学）
