Matrix multiplication (MM) is pivotal in fields from deep learning to scientific computing, driving the quest for improved computational efficiency. Accelerating MM encompasses strategies like complexity reduction, parallel and distributed computing, hardware acceleration, and approximate computing techniques, namely AMM algorithms. Amidst growing concerns over the resource demands of large language models (LLMs), AMM has garnered renewed focus. However, understanding the nuances that govern AMM's effectiveness remains incomplete. This study delves into AMM by examining algorithmic strategies, operational specifics, dataset characteristics, and their application in real-world tasks.

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale organization, yet their extension to hypergraphs involves a trade-off between expressive power and computational complexity. A recent simplification, a single-order model, mitigates this complexity by assuming a single affinity pattern governs interactions of all orders. This universal assumption, however, may overlook order-dependent structural details. Here, we propose a framework that relaxes this assumption by introducing a multi-order block structure, in which different affinity patterns govern distinct subsets of interaction orders. Our framework is based on a multi-order stochastic block model and searches for the optimal partition of the set of interaction orders that maximizes out-of-sample hyperlink prediction performance. Analyzing a diverse range of real-world networks, we find that multi-order block structures are prevalent. Accounting for them not only yields better predictive performance over the single-order model but also uncovers sharper, more interpretable mesoscale organization. Our findings reveal that order-dependent mechanisms are a key feature of the mesoscale organization of real-world higher-order networks.

Faced with saturation of Moore's law and increasing size and dimension of data,

However, the existing literature on parallel inference almost exclusively focuses on Euclidean data and parameters.

However, the over-reliance on input topology diminishes the efficacy of message passing and restricts the ability of GNNs.

However, the existing literature on parallel inference almost exclusively focuses on Euclidean data and parameters.

It should be noted that we only made a little modification to the GraphTrans model. For NTREE, we set GA T as its basic block with a 0.2 dropout probability between layers.

Graph neural networks (GNNs) leverage the connectivity and structure of real-world graphs to learn intricate properties and relationships between nodes. Many real-world graphs exceed the memory capacity of a GPU due to their sheer size, and training GNNs on such graphs requires techniques such as mini-batch sampling to scale. The alternative approach of distributed full-graph training suffers from high communication overheads and load imbalance due to the irregular structure of graphs. We propose a three-dimensional (3D) parallel approach for full-graph training that tackles these issues and scales to billion-edge graphs. In addition, we introduce optimizations such as a double permutation scheme for load balancing, and a performance model to predict the optimal 3D configuration of our parallel implementation -- Plexus. We evaluate Plexus on six different graph datasets and show scaling results on up to 2048 GPUs of Perlmutter, and 1024 GPUs of Frontier. Plexus achieves unprecedented speedups of 2.3-12.5x over prior state of the art, and a reduction in time-to-solution by 5.2-8.7x on Perlmutter and 7.0-54.2x on Frontier.

Expressivity theory, characterizing which graphs a GNN can distinguish, has become the predominant framework for analyzing GNNs, with new models striving for higher expressivity. However, we argue that this focus is misguided: First, higher expressivity is not necessary for most real-world tasks as these tasks rarely require expressivity beyond the basic WL test. Second, expressivity theory's binary characterization and idealized assumptions fail to reflect GNNs' practical capabilities. To overcome these limitations, we propose Message Passing Complexity (MPC): a continuous measure that quantifies the difficulty for a GNN architecture to solve a given task through message passing. MPC captures practical limitations like over-squashing while preserving the theoretical impossibility results from expressivity theory, effectively narrowing the gap between theory and practice. Through extensive validation on fundamental GNN tasks, we show that MPC's theoretical predictions correlate with empirical performance, successfully explaining architectural successes and failures. Thereby, MPC advances beyond expressivity theory to provide a more powerful and nuanced framework for understanding and improving GNN architectures.

Strategies to improve the predicting performance of Message-Passing Neural-Networks for molecular property predictions can be achieved by simplifying how the message is passed and by using descriptors that capture multiple aspects of molecular graphs. In this work, we designed model architectures that achieved state-of-the-art performance, surpassing more complex models such as those pre-trained on external databases. We assessed dataset diversity to complement our performance results, finding that structural diversity influences the need for additional components in our MPNNs and feature sets. In most datasets, our best architecture employs bidirectional message-passing with an attention mechanism, applied to a minimalist message formulation that excludes self-perception, highlighting that relatively simpler models, compared to classical MPNNs, yield higher class separability. In contrast, we found that convolution normalization factors do not benefit the predictive power in all the datasets tested. This was corroborated in both global and node-level outputs. Additionally, we analyzed the influence of both adding spatial features and working with 3D graphs, finding that 2D molecular graphs are sufficient when complemented with appropriately chosen 3D descriptors. This approach not only preserves predictive performance but also reduces computational cost by over 50%, making it particularly advantageous for high-throughput screening campaigns.