Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from classification to anomaly detection. There recently has emerged number of approaches adopting pooling operation within GNNs, with goal preserve attributive and structural features during the representation learning. However, most existing operations suffer limitations relying on node-wise ...

This paper examines the assertion that partial pooling of customers is sometimes favored over complete pooling on the sole basis of demand correlation. First, the management of inventory within a supply chain is discussed, with speci2c attention paid to risk-pooling. Then, the claim that partial pooling can dominate is theoretically discussed. The conditions under which previous research found ...

This section provides additional details for some of the ablation studies reported in Section 6. Pooling type. In the context of binary networks, and because the output is restricted to 1 and -1, max-pooling might result in outputs full of 1s only. To limit this effect, we placed the activation function before the convolutional layers as proposed in [5, 9]. Additionally, we opted to replace max...

Testing large quantities of samples in order to detect one or more test-positive sample(s) is expensive and time-consuming. It is possible to optimize this process by pooling samples. Two frameworks to produce different hierarchical and non-hierarchical pooling schemes were tested and compared to standard pooling. Their efficiency and the potential savings were determined as a function of preva...

We explore which types of probabilistic updating commute with convex IP pooling (Stewart and Ojea Quintana, 2017). Positive results are stated for Bayesian conditionalization (and a mild generalization of it), imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of (precise) externally B...

In this work we compute lower Lipschitz bounds of lp pooling operators for p = 1, 2,∞ as well as lp pooling operators preceded by halfrectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the...