  Graph neural networks (GNNs) are a powerful solution for various structure
learning applications due to their strong representation capabilities for graph
data. However, traditional GNNs, relying on message-passing mechanisms that
gather information exclusively from first-order neighbours (known as positive
samples), can lead to issues such as over-smoothing and over-squashing. To
mitigate these issues, we propose a layer-diverse negative sampling method for
message-passing propagation. This method employs a sampling matrix within a
determinantal point process, which transforms the candidate set into a space
and selectively samples from this space to generate negative samples. To
further enhance the diversity of the negative samples during each forward pass,
we develop a space-squeezing method to achieve layer-wise diversity in
multi-layer GNNs. Experiments on various real-world graph datasets demonstrate
the effectiveness of our approach in improving the diversity of negative
samples and overall learning performance. Moreover, adding negative samples
dynamically changes the graph's topology, thus with the strong potential to
improve the expressiveness of GNNs and reduce the risk of over-squashing.
