Global Communication or Graph-Specific Memory?

We investigate whether the Feed-Forward Network (FFN) sublayer in a decoder-only transformer can be replaced by an explicit learned memory graph while preserving the surrounding autoregressive architecture. The proposed Graph Memory Transformer (GMT) keeps causal self-attention intact, but replaces the usual per-token FFN transformation with a memory cell that routes token representations over a learned bank of centroids connected by a learned directed transition matrix. In the base GMT v7 instantiation studied here, each of 16 transformer blocks contains 128 centroids, a 128 * 128 edge matrix, gravitational source routing, token-conditioned target selection, and a gated displacement readout. The cell therefore returns movement from an estimated source memory state toward a target memory state, rather than a retrieved value. The resulting model is a fully decoder-only language model with 82.2M trainable parameters and no dense FFN sublayers, compared with a 103.0M-parameter dense GPT-style baseline used in the evaluation. The base v7 model trains stably and exposes centroid usage, transition structure, and source-to-target movement as directly inspectable quantities of the forward computation. It remains behind the larger dense baseline in validation loss and perplexity (3.5995/36.58 vs. 3.2903/26.85), while showing close zero-shot benchmark behavior under the evaluated setting. These results are not intended as a state-of-the-art claim; they support the viability and structural interpretability of replacing dense within-token transformation with graph-mediated memory navigation. Broader scaling, optimized kernels, and more extensive benchmark evaluation are left for subsequent work.

Graph Transformers (GTs) offer superior representation capabilities by overcoming the depth limitations and over-smoothing issues of traditional Graph Neural Networks (GNNs). However, scaling GTs to large graphs poses critical bottlenecks. Specifically, the attention score matrix and its associated topology-aware bias matrix jointly incur significant per-layer memory overhead, and heavy graph embedding layers result in severe workload imbalances. These characteristics are unique to GT training and are not addressed by parallelism techniques designed for either conventional GNNs or Transformers, making a dedicated solution necessary. This paper introduces MegaGraph, the first automated hybrid parallelism framework designed for efficient GT training. MegaGraph designs three specialized strategies, namely graph-aware context parallelism, heterogeneous pipeline parallelism, and hybrid data parallelism, to support efficient training on large-scale graphs. However, coordinating these three parallelism strategies yields an exponentially large configuration space. To address this complexity, an automatic search engine leverages precise cost models via a Profile - Model - Search workflow to identify the optimal parallelism configuration. Evaluations demonstrate that MegaGraph enables training on large-scale graphs where state-of-the-art baselines fail due to out-of-memory (OOM) errors. The framework reduces per-device peak memory by up to 77.8% and achieves up to 4.51$\times$ training speedup while maintaining model accuracy.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.