Message Passing Graph Neural Networks (MPGNNs) have emerged as the preferred method for modeling complex interactions across diverse graph entities. While the theory of such models is well understood, their aggregation module has not received sufficient attention. Sum-based aggregators have solid theoretical foundations regarding their separation capabilities. However, practitioners often prefer using more complex aggregations and mixtures of diverse aggregations. In this work, we unveil a possible explanation for this gap. We claim that sum-based aggregators fail to "mix" features belonging to distinct neighbors, preventing them from succeeding at downstream tasks. To this end, we introduce Sequential Signal Mixing Aggregation (SSMA), a novel plug-and-play aggregation for MPGNNs. SSMA treats the neighbor features as 2D discrete signals and sequentially convolves them, inherently enhancing the ability to mix features attributed to distinct neighbors. By performing extensive experiments, we show that when combining SSMA with well-established MPGNN architectures, we achieve substantial performance gains across various benchmarks, achieving new state-of-the-art results in many settings. We published our code at \url{https://almogdavid.github.io/SSMA/}

Graph neural networks (GNNs) have become a powerful tool for processing graph-structured data but still face challenges in effectively aggregating and propagating information between layers, which limits their performance. We tackle this problem with the kernel regression (KR) approach, using KR loss as the primary loss in self-supervised settings or as a regularization term in supervised settings. We show substantial performance improvements compared to state-of-the-art in both scenarios on multiple transductive and inductive node classification datasets, especially for deep networks. As opposed to mutual information (MI), KR loss is convex and easy to estimate in high-dimensional cases, even though it indirectly maximizes the MI between its inputs. Our work highlights the potential of KR to advance the field of graph representation learning and enhance the performance of GNNs. The code to reproduce our experiments is available at https://github.com/Anonymous1252022/KR_for_GNNs