THGFM: Dual-Branch Temporal Heterogeneous Graph Fusion Model

Temporal heterogeneous graphs offer a natural abstraction for dynamic relational systems in which diverse node and relation types co-exist and evolve over time. Learning on such graphs requires jointly modeling cross-type structural heterogeneity and the temporal dynamics of interactions, yet existing methods still struggle to reconcile parameter-efficient cross-type transfer with relation-aware specialization, and typically inject time only as additive features outside the attention kernel. We propose \textbf{THGFM}, a web-scale temporal heterogeneous graph fusion model that addresses both limitations within a unified dual-path architecture. THGFM couples a \textit{Shared-Space Temporal Attention} branch for parameter-efficient cross-type transfer with a \textit{Relational Type-Partitioned Temporal Attention} branch for relation-aware specialization, and integrates them through \textit{Dual-Path Relational--Shared Fusion}, instantiated with \textit{Type-Conditioned Non-Competitive Gated Sum Fusion}: a adaptive mechanism that assigns independent, type-conditioned feature-wise gates to the shared and specialized branches, allowing both to be amplified or suppressed without zero-sum competition. To directly incorporate relative time into the attention score, THGFM further introduces \textit{Rotary Temporal Attention}, which rotates queries and keys by half-phases of relative time before matching. THGFM consistently outperforms baseline graph transformer models on academic graphs benchmarks, delivering a $+3.25\%$ six-task mean gain, with peak relative gains of $+12.37\%$ on OAG-CS PV, $+4.87\%$ on PF-$L_2$, and $+1.18\%$ on PF-$L_1$, and $+4.24\%$, $+3.73\%$, and $+4.61\%$ on OGBN-MAG, HTAG-ArXiv, and HTAG-DBLP, respectively.

Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att

Communicability-Inspired Positional Encoding (CIPE)

Positional encodings (PEs) are essential for Transformers. Yet designing effective PEs for non-Euclidean graphs remains challenging. Such encodings should ideally induce an Attention-Compatible Geometry for self-attention: not merely describing graph structure, but defining a geometry whose inner products reflect meaningful structural relatedness. To realize this geometry, we propose Communicability-Inspired Positional Encoding (CIPE), built from communicability, a measure between pairs of nodes that aggregates contributions from paths of all lengths. By construction, CIPE inner products recover communicability, converting global multi-path connectivity into an attention-ready similarity geometry. For practical Transformer training, we introduce dimensionality alignment, mapping graph-size-dependent CIPE representations to prescribed dimensions while faithfully preserving the induced geometry. Empirically, CIPE improves structure-agnostic Transformers by 35.5% on average across seven benchmarks, outperforming representative PEs; it also consistently improves structure-biased graph Transformers, where competing PEs often yield only marginal benefits. These results position CIPE as a principled framework for attention-compatible graph positional encodings.

Graph Cascades: Contagion-Based Mesoscopic Rewiring for Structure-Aware Graph Machine Learning

We introduce Graph Cascades, a mesoscopic rewiring strategy for Graph Neural Networks (GNNs) and Graph Transformers (GTs) that captures intermediate-scale graph structure beyond purely local edges or fully global attention. Using contagion-based diffusion processes, Graph Cascades constructs, in O(|V|+|E|) time, an auxiliary graph where node pairs supported by repeated multi-hop reinforcement are promoted to direct neighbors. We theoretically characterize when reinforcement-based rewiring helps: sufficient conditions under which reinforcement-based edge selection is more label-aligned than direct adjacency, an SBM witness in which two-hop reinforcement is perfectly homophilic, and a formalization of mesoscopic connectivity via graph effective resistance. Empirically, across node-classification benchmarks, Graph Cascades improves multiple GNN and sparse-GT backbones, with the most reliable gains observed on heterophilic and moderate- to high-degree homophilic graphs. The theoretical conditions also identify regimes where mesoscopic rewiring is unlikely to be beneficial -- low-degree regular graphs and graphs with structural bottlenecks -- and these predictions match the observed failures. We additionally observe tight correlations between performance and structural properties in the rewired graphs.