The difference is significant, sincesp(h) Dand the gap between the twocanbearbitrarily large.

The high-level question in this work is: If we learn a task using a sufficiently deep NN, how can we uncover the underlying hierarchical organization of sub-functions in that task?

Inparticular,standardmetricformulations as hierarchical k-center,k-means, andk-median received a lot of attention and the problems have been studied extensively in different models of computation.

To make the proof concise, we will assume matrixP is connected, otherwise we can perform the same operation inside each block. With the help of NDLS, Random Forest and XGBoost outperforms their base models by6.1% and 7.5% respectively. In these three networks, papers from different topics are considered asnodes, and the edges are citations among the papers. Industry is a short-form video graph, collected from a real-world mobile application from our industrial cooperativeenterprise. Wesampled 1,000,000 users and videos from the app, and treat these items as nodes.

Recent works reveal that feature or label smoothing lies at the core of Graph Neural Networks (GNNs).

Stochastic gradient methods have been a widespread practice in machine learning.