a-TMFG: Scalable Triangulated Maximally Filtered Graphs via Approximate Nearest Neighbors

Graph convolutional networks (GCNs) have demonstrated significant success in capturing complex user-item relationships for collaborative filtering (CF). However, due to their reliance on extensive model training, training-free graph filtering (GF)-based CF methods have emerged as a promising alternative, offering computational efficiency by smoothing graph signals via matrix operations. In particular, polynomial GF-based approaches demonstrate improved accuracy through their ability to design more expressive and flexible filtering functions. Despite these advantages, existing GF methods suffer from a critical memory bottleneck: they necessitate storing the full item similarity graph, incurring prohibitive memory costs for large-scale datasets, which limits their practical applicability. To tackle this challenge, we propose Mem-GF (Memory-efficient GF), a new GF-based CF method that departs from conventional designs by principally leveraging the structure of Krylov subspaces as a core mechanism for approximating polynomial graph filters without explicitly storing the item similarity graph. We theoretically analyze the minimum Krylov subspace size that guarantees lossless approximation. Through extensive experiments, we demonstrate that Mem-GF achieves up to 5.74$\times$ lower memory usage and 4.38$\times$ speedup in runtime, while consistently exceeding the recommendation accuracy of state-of-the-art GF and GCN-based methods. Mem-GF robustly scales to datasets with tens of millions of interactions, establishing itself as a practically viable and theoretically grounded solution for efficient CF.

Graph neural networks (GNNs) excel at representation learning on Knowledge Graphs (KGs), achieving stateof-the-art performance on tasks like link prediction or entity classification. However, their high computational complexity, inherent to their user-defined message passing (MP) algorithm, still prohibits their widespread adoption, especially for large KGs. Current efforts to mitigate the scalability bottlenecks of GNNs on KGs, such as subgraph sampling, are often task- and model-specific, and do not reliably guarantee lossless (if applicable) runtime/space reductions. To address this, we extend Relational Sparse Matrix Multiplication (RSPMM), originally designed to losslessly lower the space complexity of composition-based MP with pointwise composition functions, to support more expressive functions (e.g., 2x2 block-diagonal matrix multiplication, Givens rotation, circular correlation). Our method delivers significant task-independent reductions in runtime and space for current GNNs on KGs and facilitates efficient re-implementations of GNNs that maintain near state-of-the-art performance on challenging KG tasks, for a fraction of computational costs.

Temporal graph neural networks (TGNNs) have shown strong performance on dynamic graph learning tasks by continuously updating node memories from evolving interactions (i.e., events) and leveraging these memories for downstream predictions. As graphs grow rapidly in modern applications, training requires processing an increasing number of events; meanwhile, each event can update node memories used by later events, creating dependencies that constrain parallel execution and limit the benefits of additional computing resources. These costs motivate an upstream question: Are all events, and the dependencies they introduce, necessary for learning? We investigate this question through two roles of temporal events: prediction targets and historical events sampled as inputs. We observe that targets involving stable node memories tend to exhibit lower prediction loss, while filtering historical events associated with stable memories can retain similar training-loss trajectories in several evaluated settings. Together, these observations suggest an opportunity to identify input redundancy through changes in node memories. Building on this opportunity, we propose RAFT, a redundancy-aware input-filtering framework for TGNN training. RAFT tracks memory changes during training and uses them to guide two filters: a root-event filter removes selected prediction targets before training, and a support-event filter excludes selected historical context during sampling. Filtering inputs before their downstream preparation and processing reduces the work they trigger. Across three TGNN models and five datasets, RAFT reduces training inputs by 35.23% on average and up to 97.11%, while reducing recorded training time by up to 52.56% with negligible changes to model precisions.