Multiplex Graph Transformers
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Latest papers 35
We present Varda-single-1.0, a medium-range data-driven weather prediction system built for the Alpine domain. It provides hourly deterministic regional forecasts on a mesh of 1 km resolution and global forecasts on a 31 km mesh. The system comprises two independently trained stretched-grid Graph Transformer models with encoder-processor-decoder architecture, developed in the Anemoi framework: a 6-hourly autoregressive forecaster and a temporal downscaler reconstructing hourly forecasts between the forecaster's steps. Its training curriculum includes pre-training on ERA5 reanalysis data, followed by training on a 20-year kilometre-scale regional reanalysis, and finally fine-tuning on operational kilometre-scale analyses. Verified over one year against operational analyses and surface station observations, Varda-single is competitive with or improves on MeteoSwiss' operational numerical weather prediction baselines for most headline scores and variables. It broadly matches the skill of the high-resolution 1 km ICON-CH1-EPS control at lead times up to +33 h and generally outperforms the 2 km ICON-CH2-EPS control at lead times up to +120 h. Despite competitive aggregate scores, Varda-single underestimates some local wind maxima and produces overly smooth convective precipitation fields, consistent with the smoothing associated with squared-error training. To gain insight into the model's behaviour, we investigate three case studies beyond the aggregated headline scores, and find particular weaknesses in Varda-single's representation of local winds over complex terrain. Varda-single represents an important step in the development of high-resolution ML forecasting over complex terrain, in complementing the operational regional numerical weather prediction models of MeteoSwiss with data-driven models and in providing a pretrained model for researchers and user-specific applications.
Reinforcement Learning-Guided Graph Transformations for SpTRSV Optimization
Sparse triangular solve (SpTRSV) is a fundamental kernel in numerous scientific and engineering applications. However, the data dependencies inherent in sparse triangular matrices significantly limit the available parallelism and make efficient workload distribution challenging. Recent graph transformation techniques address these limitations by modifying the dependency graph of the input matrix to improve parallel execution. Existing graph transformation strategies, however, rely on manually designed heuristics, making their development and adaptation to different optimization objectives challenging. This work proposes a reinforcement learning-guided graph transformation framework for SpTRSV, in which graph transformation is formulated as a sequential decision-making problem and an RL agent learns matrix-dependent transformation policies. Experimental results on real-world sparse matrices demonstrate level reductions of up to 94% and reductions of up to 80% in the coefficient of variation of level costs, while modifying only 1.50% of the rows in the highest case. On average, the RL- guided graph transformation achieves a 23% reduction in the number of levels and a 29% reduction in the coefficient of variation of level costs while rewriting only 0.82% of the matrix rows. Although the heuristic strategies generally achieve more aggressive level reduction(between 31% and 46%), the RL-based approach achieves the largest average reduction in the coefficient of variation of level costs, demonstrating its ability to balance competing graph transformation objectives. The results further show that the learned policies can be transferred to previously unseen matrices through curriculum learning and fine-tuning, while zero-shot experiments provide insights into the limitations of generalizing graph transformation policies across different sparsity patterns.
Stable Transformers for Graph Generation
Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures should provide greater expressive capacity and a broader receptive field, their effectiveness can decline with depth: repeated self-attention progressively contracts node representations, impeding information flow and gradient propagation. We analyse this phenomenon from a dynamical systems perspective, focusing on how the denoiser's spectral dynamics affect graph generation. We show that standard GT denoisers become increasingly dissipative as depth grows, leading to vanishing gradients and representation collapse. To isolate the effect of these dynamics, we construct a permutation-equivariant GT with inherently stable, non-dissipative transport. We also introduce a damping mechanism that continuously interpolates between non-dissipative and increasingly contractive regimes, enabling a direct assessment of how dissipation influences generation. Experiments on synthetic and molecular graph generation benchmarks show that the gap between these regimes widens with depth: non-dissipative dynamics preserve representation diversity and gradient flow, sustaining strong generative performance, whereas greater contraction progressively impairs it. These findings identify the denoiser's dynamical regime as a key design factor for deep graph generative models.
MegaGraph: Towards Efficient Training of Large-Scale Graph Transformers with Automated Hybrid Parallelism
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 training speedup while maintaining model accuracy.
WorldGraph: Graph-Native World Modeling
World models infer latent states of an environment to capture its underlying dynamics and predict future evolution. Many real-world environments, however, are inherently relational and observed as evolving graphs, where entities, relations, and their properties change over time. Prior graph-related world models use graph structures to organize internal states or support task-specific reasoning, rather than treating an evolving graph itself as the modeled world. We instead study graph world modeling (GWM), where graph evolution itself constitutes the world dynamics. We formulate graph world modeling over observed graph evolution, latent graph states, and heterogeneous graph-transition predictions. Based on this formulation, we construct GWM-Zero, a benchmark covering node-, edge-, and graph-level transitions over eight temporal graph datasets. We propose WorldGraph, which combines a state-aware graph transformer for multi-granularity structural and transition-conditioned evolution modeling with transition-aware GRPO using dynamic grouping and structure-aware verifiable rewards. Extensive experiments on GWM-Zero show that WorldGraph consistently outperforms representative graph representation, temporal graph learning, graph pretraining, and graph world-model baselines across all three transition granularities.
QUARTET: Quad-branch cross-Attention and Random-walk Traces for Enhancing Transformers on Relational Graphs
Relational Deep Learning (RDL) models multi-table databases as heterogeneous temporal graphs, and graph transformers currently achieve state-of-the-art performance on benchmarks like RelBench. However, the current leading model, RelGT, suffers from two key limitations: its random local sampler yields loosely connected subgraphs that hinder message passing, and its global attention module relies on a single, seed-feature-based memory that ignores broader macro-level dynamics. To overcome these limitations, we introduce QUARTET, an expressive graph transformer architecture that applies full self-attention on local subgraphs while enriching global context through cross-attention branches. Specifically, QUARTET employs a Causal Random Walk (CRW) sampler based on recency-truncated Personalized PageRank (PPR) to extract compact, hub-robust, and densely connected local subgraphs without temporal leakage. Concurrently, a quad-branch cross-attention module integrates global context from four complementary perspectives: seed feature, seed topology, temporal dynamics, and collaborative dynamics. Across the RelBench v1 classification tasks, QUARTET consistently matches or outperforms the current state-of-the-art graph transformer baselines (HGT and RelGT). Ablation studies confirm that the CRW sampler significantly enriches local neighborhood quality, while the global branches provide essential, task-specific predictive gains.
: Global Stereochemical Fields for Chiral Graph Transformers
Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar sets the direction of a relative rotation on latent query--key blocks, giving a \textbf{Chiral-RoPE} that reflection inverts rather than leaves fixed. A projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF- leads every central-ECD output and improves axial Rotation and Symbol by and over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.
Accounting Graph Transformer for Short-History Multi-KPI Forecasting in Small Businesses
Small businesses often have only 12-24 months of accounting history, yet planning and risk workflows require coordinated forecasts across financial statements. We study joint 12-month forecasting of 13 income-statement, balance-sheet, cash-flow, and working-capital key performance indicators (KPIs) from 71 monthly ledger series. We introduce the Accounting Graph Transformer (AGT), which represents each ledger series as a masked token, exchanges information through typed attention on a fixed accounting-relation graph, pools target-specific context, and fuses it with a gated three-month recency path. Across 11,993 forecast origins from 1,060 unseen companies, AGT achieves sample-weighted KPI-macro mean absolute error (MAE) over three independent seeds, compared with for the strongest baseline, LightGBM. At the pre-specified seed 42, a paired company-clustered bootstrap gives a LightGBM-minus-AGT difference of 0.0395 with 95% confidence interval (CI) . AGT is best on all 13 KPIs against LightGBM, TimeMixer, and SOFTS in the matched seed-42 comparison, while final-architecture ablations show that relational attention, accounting topology, and the recency path each improve validation and test accuracy. On 7,094 additional unseen companies with origins sampled from January-May 2025, AGT obtains 0.7548 MAE versus 0.7694 for SOFTS. A single 5.3M-parameter model produces 156 aligned forecasts without company-specific fitting, providing one forecasting layer for integrated planning, liquidity, and working-capital analysis.
Graph Machine: Exploring Edge Mechanisms as an Inductive Bias
Transformers provide a powerful architecture for global content-based matching, but reasoning problems may benefit from a stronger inductive bias toward iterative traversal of latent relations. We introduce Graph Machine, an architecture with two explicit edge-based mechanisms: Edge-augmented attention, in which edges modulate attention between nodes, and edge-centric referral, in which nodes exchange addresses to update their edges. Conceptually, this enables the model to dynamically and differentiably construct and revise relational graphs across layers. We study this inductive bias using Sudoku under controlled settings and find that Graph Machine outperforms Transformer baselines, with ablation studies and mechanistic analysis attributing the gains to the edge mechanisms. Surprisingly, we found that the model discovers a compact edge-based construction for Sudoku geometry. Our results support explicit edge mechanisms as a promising architectural design, motivating broader evaluation.
MiGHT-EHR: A Multi-task Graph Transformer for Heterogeneous Temporal Electronic Health Records
Learning from Electronic Health Records (EHRs) has gained significant attention due to its potential to improve clinical prediction. However, effective learning remains challenging because EHRs encode heterogeneous, temporally ordered clinical interactions. In particular, EHRs contain: (i) heterogeneous clinical entities, including patients, visits, diagnoses, prescriptions, and procedures, together with their heterogeneous interactions, (ii) longitudinal patient trajectories across hospital visits and (iii) shared statistical dependencies across related clinical prediction tasks. Existing EHR learning methods capture only a subset of these properties. To bridge this gap, we propose Multi-task Graph transformer for Heterogeneous Temporal EHRs (MiGHT-EHR), which jointly models all three within a unified representation learning method. MiGHT-EHR constructs a heterogeneous graph from EHRs in which nodes represent clinical entities and edges connect statistically associated entities identified via normalized point-wise mutual information. Across MIMIC-III and MIMIC-IV datasets, MiGHT-EHR outperforms state-of-the-art methods on average across four tasks: drug recommendation, prediction of length-of-stay, mortality, and readmission, with particularly strong improvements in mortality and readmission prediction. Furthermore, a post-hoc analysis of the learned representations reveals that patient neighborhoods are organized by clinical outcomes, salient medical concepts are recoverable as linear directions in the representation space, and task probabilities are well calibrated. Collectively, these findings demonstrate that MiGHT-EHR representations support diverse prediction tasks while preserving clinically interpretable structure.
Enhancing Transformer-based Routing by Encoding Distance via Relative Positional Encoding
This paper explores Relative Positional Encoding (RPE) as an additive bias in Transformer architectures to solve the Team Orienteering Problem. By embedding in the attention mechanism pairwise spatial relationships among nodes of the graph that represents the routing problem, the transformer encoder can compute a richer spatial-aware graph embedding that allows the decoder to estimate better routes. Experimental results involving instances up to 100 nodes demonstrate consistent improvements in collected rewards and optimality gaps over vanilla Transformer architectures used by other state-of-the-art works. These findings highlight that explicit relational modeling significantly enhances scalability and generalization for complex combinatorial optimization.
Topological Signatures of Context-Level Reliability in TabPFN
TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs. Despite its strong empirical performance, its internal behavior on structurally difficult tabular geometries remains poorly understood. We study this behavior using zigzag persistent homology, treating TabPFN layer representations as evolving point clouds. We construct a controlled benchmark of synthetic tabular tasks with known true probabilities and varied intrinsic topology, including warped circles, tori, spheres, Hopf links, trefoil knots, and Swiss rolls. Across these tasks, we find that the topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability; for example, the zeroth homology group fragmentation count correlates positively with mean absolute residual across controlled tasks, and this association strengthens in a high-resolution warped circle case study at large sample size. Harder geometries induce a dual topological signature: increased loop activity and increased fragmentation, while the persistence becomes shorter-lived. These descriptors correlate with Bayes error, mean absolute residuals, and overconfidence. Our results suggest that zigzag persistence diagnoses the reliability of the inferred in-context task geometry and provides a context-level view of when TabPFN operates in topologically stressed regimes.
MxGPS: Multiplex Graph Transformers for a Power Grid Foundation Model
Single-task fine-tuning of graph neural networks (GNNs) for power grid problems exhibits a systematic failure mode: models that achieve the lowest in-distribution error degrade the most under topology shift. We term this topology overfitting: the tendency of task-specific gradient signals to encode relational structure particular to the training topologies rather than the underlying physics, causing models to fail on unseen grids despite strong in-distribution performance. To expose and address this failure mode, we introduce MxGPS (Multiplex GPS), a multiplex graph transformer that runs K task-specialised GPS branches over a shared node encoder, jointly trained on Static State Estimation (SSE) and AC Power Flow (PF) via a self-supervised pre-training and multi-task fine-tuning protocol, with a cross-branch attention module evaluated in ablation. The joint SSE+PF objective forces the shared encoder to simultaneously satisfy complementary gradient signals, preventing it from overfitting to topology-specific relational structure. Under a 3-fold sliding-window cross-validation spanning four unseen topologies (14-, 24-, 162-, and 300-bus), MxGPS attains 0% boundary violation rate (BVR) on all four zero-shot Power Flow topologies. Critically, models with substantially lower in-distribution PF error degrade by 190% to 1400% under topology shift, whereas MxGPS degrades by only 39%, an inversion that directly implicates topology overfitting as the failure mechanism rather than insufficient model capacity. With only 1.6M parameters (12x fewer than the GridFM reference baseline), MxGPS demonstrates that multi-task joint training is a principled and parameter-efficient mechanism for topology-agnostic generalisation in power grid foundation models.
Higher-Order Cell Tracking Transformer
Reconstructing lineages from live-imaging microscopy requires linking cell detections across time, including through cell divisions. A common approach is to construct a candidate graph and associate cell segmentations (nodes) across frames. However, these and other existing methods overlook two structural obstacles in candidate tracking graphs: (i) cell divisions entangle distinct lineage paths in the node embedding space, and (ii) edges sharing a node have near-random label agreement, so the candidate-graph topology carries no useful information for graph neural networks to aggregate. We propose the \textbf{Higher-Order Cell Tracking Transformer} (HOCT), an edge-centric architecture in which candidate cell links attend to one another under a 3D geometric prior, resolving both issues. Evaluated on the Cell Tracking Challenge and a bacteria division benchmark, HOCT achieves state-of-the-art results without deep pre-trained image encoders. Moreover, the proposed approach is easier to fine-tune, quickly reducing tracking errors by 59% with 400 annotations in a human-in-the-loop setting, outperforming LoRA fine-tuning of competing transformer baselines (6.75% improvement).
The RG-Flow Transformer: Encoding Scale-Free Dynamics in Scarce EEG
Brain field potentials are scale-free: their power spectra follow a law whose aperiodic exponent tracks cortical state, and sleep depth in particular is a shift in . We ask whether a transformer endowed with an explicit renormalization-group (RG) inductive bias the RG-Flow Transformer, which couples ordinary self-attention to a scale-aware stream with a learnable anomalous dimension , block-spin coarse-graining, and an entropy-gated synchronization bridge has an advantage over a parameter-matched vanilla transformer on \emph{real, scarce} EEG. Using the PhysioNet Sleep-EDF corpus with a strict leakage-free by-subject hold-out, we (i) benchmark RG-Flow against a param-matched vanilla transformer and a hierarchy-only ablation on 5-class AASM sleep staging, (ii) sweep the per-subject data budget to look for the inductive-bias crossover predicted when data are scarce, and (iii) test whether RG-Flow's learned tracks the measured spectral exponent out-of-sample a quantity the vanilla model does not possess. Across subjects and seeds under leave-one-subject-out cross-validation, RG-Flow and the vanilla transformer are statistically indistinguishable on 5-class staging (77.3% vs 77.0% accuracy; paired ), and the predicted scarce-data crossover does not appear: vanilla is numerically ahead at every data-limited budget. What does separate the models is interpretability RG-Flow recovers the continuous spectral exponent out-of-sample (-recovery ), a capability the vanilla architecture has no analogue for.
On Preserving Geometrical Invariance for Superpixel Image Classification using Graph Transformer
Convolutional Neural Network (CNN) and Vision Transformer (ViT) for image classification exploit a dense grid of pixels containing redundant information. Consequently, for a larger image dataset, CNNs and ViTs face deployability challenges due to high computational complexity. Representing images as graphs of superpixels offers an efficient alternative that preserves key information while eliminating pixel-level redundancy. Graph Neural Networks (GNNs) have been utilized on such graphs to perform image classification. However, GNNs are known to struggle with capturing long-range dependencies which is important in the domain of image classification. Furthermore, a majority of these superpixel-based image classification approaches do not explicitly preserve translation/rotation invariance. Nevertheless, preserving translation/rotation invariance is important for robust image classification. Thus, this paper proposes SuperGT, a Graph Transformer-based framework for image classification, which captures the long range dependencies, along with a pre-processing scheme that preserves translation/rotation invariance. We evaluate SuperGT on CIFAR-10 dataset and observe that it performs significantly better than many baselines. Furthermore, we note that the overall performance of SuperGT is comparable to the previous state-of-the-art model, namely, ShapeGNN, without relying on coordinates of the boundary points of each superpixel required by ShapeGNN.
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.
Universal Encoders for Modular Relational Deep Learning
Relational Deep Learning (RDL) models multi-tabular databases as temporal heterogeneous graphs for end-to-end representation learning. While RDL is evolving rapidly, existing approaches face significant generalization obstacles. They are either schema-specific, requiring training from scratch for every new database, or they rely on monolithic architectures that entangle feature encoding with graph message-passing. Analyzing these limitations, we establish four core pillars for building foundational relational models: semantic granularity, structural topology, temporal causality, and unified optimization. Addressing these pillars, we propose a modular approach that decouples row encoding from graph message-passing. We introduce the Universal Row Encoder, a transformer-based module that integrates raw cell data with schema metadataincluding column semantics, table names, and global distribution statisticsto produce table-width invariant row embeddings. By explicitly feeding global statistics to an intra-row self-attention mechanism, the encoder natively contextualizes unseen features and handles sparse data. Serving as a flexible "backend" for any downstream graph architecture, our pretrained encoder enhances cross-database knowledge transfer on the established RelBench benchmarks while improving learning convergence and memory footprint.
Graph Set Transformer
We introduce the Graph Set Transformer (GST), a neural network architecture for learning on sets of graphs, designed for tasks in which per-element predictions depend on set-wide context as well as local structure. Existing architectures, including DeepSets and SetTransformer, require pre-encoded graph embeddings from a separate GNN, creating a bottleneck between feature extraction and set-level contextualisation. In contrast, GST interleaves node-level feature propagation and cross-graph contextual modelling at every layer, fusing the two levels of information through a gating mechanism. We evaluate GST on a controlled synthetic suite designed to isolate set-conditional structural reasoning and on three real-data benchmarks spanning per-atom reaction-centre identification, reaction yield prediction, and image classification. Under matched parameter budgets, GST performs better than the baselines across these settings. An architectural ablation strongly suggests that the interleaving of local and set context contributes substantially to this advantage.
RelGT-AC: A Relational Graph Transformer for Autocomplete Tasks in Relational Databases
Relational databases underpin modern enterprise, scientific, and healthcare systems, yet predictive machine learning on such data remains challenging due to their multi-table, heterogeneous, and temporal structure. Relational Deep Learning (RDL) addresses this by representing databases as heterogeneous graphs and applying graph neural networks (GNNs) directly. RelBench v2 recently introduced autocomplete tasks -- a practically motivated task type where the goal is to predict an existing column value from relational context, analogous to an intelligent form-filling assistant. We propose RelGT-AC (Relational Graph Transformer for Autocomplete), extending the RelGT architecture with three targeted contributions: (1) a column masking strategy that prevents trivial solutions by masking the target column during subgraph encoding; (2) a unified task head supporting binary classification, multiclass classification, and regression autocomplete tasks within a single model; and (3) a TF-IDF text encoder that automatically detects and encodes free-text columns, recovering strong lexical signal that categorical encoders discard. Across 7 tasks spanning 3 RelBench v2 datasets (rel-trial, rel-f1, rel-stack), RelGT-AC outperforms the GraphSAGE baseline on all 3 regression autocomplete tasks and achieves up to +10 AUROC points on text-heavy eligibility tasks via the TF-IDF encoder.
Prior-Guided Multi-Omic Transformers for Single-Cell Gene Regulatory Network Inference
Gene regulatory networks (GRNs) capture transcription factor-target interactions and are central to understanding cell-state regulation and disease. Reconstructing GRNs from paired single-cell transcriptomic and chromatin accessibility data is promising but challenging: scATAC is extremely sparse, and most methods rely on fixed peak-to-gene links and weak supervision. We present EpiAwareNet, a prior-guided multi-omic Transformer framework that reconstructs GRNs from paired single-cell data using only lightweight biological priors. In Stage 1, EpiAwareNet learns joint gene-peak representations with a gene-peak cross-attention module, enabling data-driven, gene-specific aggregation of accessibility signals rather than hard-coded peak-to-gene assignments. In Stage 2, EpiAwareNet incorporates a bulk-derived GRN prior as noisy positive edges to provide weak supervision under label scarcity, refining regulatory scores while remaining robust to prior noise. In our experiments, EpiAwareNet improves GRN reconstruction over representative single- and multi-omic baselines and yields GRNs with greater biological plausibility, such as improved recovery of known regulatory interactions, suggesting that lightweight biological priors from bulk data can effectively guide single-cell GRN inference when combined with adaptive cross-modal representation learning. Code and data will be available at https://github.com/tianyang-x/EpiAwareNet_pub.
Spatiotemporal Multi-Task Graph Transformer for Trip-Level Transit Prediction
Passenger count data from public transit systems reveals urban mobility patterns and is essential for planning, operation, and optimisation. However, non-linear spatiotemporal interdependencies across stops and lines make modelling and prediction challenging. Existing approaches often rely on fixed temporal, spatial, or stop-level formulations, limiting their ability to capture within-trip evolution and network context. This study proposes SMT-GraphFormer, a spatiotemporal multi-task graph transformer that frames trip-level transit prediction as sequence-to-sequence modelling. Given a line's stop sequence and trip-level context, the model predicts successive boarding and alighting counts, with delay and dwell time treated as encoder-side surrogate tasks. Key components include graph embeddings for multi-relational stop similarity, a context encoder for weather and temporal information, and a multi-gate mixture-of-experts module that produces task-specific decoder representations for boarding and alighting predictions. Evaluation on public bus transit data from Trondheim, Norway, shows that SMT-GraphFormer outperforms stop-level tabular benchmarks, with ablation studies examining each component's contribution. The sequential formulation yields substantial gains on alighting prediction (0.24 in ) and consistent improvements on boarding, delay, and dwell, confirming the value of explicit trip-level sequential bias and inter-target dependencies. These findings demonstrate the potential of transformer-based sequence modelling for capturing complex spatiotemporal dynamics in public transit and underscore the value of architectures tailored to transit data rather than off-the-shelf tabular models. The proposed framework provides a horizon-agnostic basis for scenario analysis in digital twin environments, supporting informed decision-making by planners and transit operators.
GraphARC: A Comprehensive Benchmark for Graph-Based Abstract Reasoning
Relational reasoning lies at the heart of intelligence, but existing benchmarks are typically confined to formats such as grids or text. We introduce GraphARC, a benchmark for abstract reasoning on graph-structured data. GraphARC generalizes the few-shot transformation learning paradigm of the Abstraction and Reasoning Corpus (ARC). Each task requires inferring a transformation rule from a few input-output pairs and applying it to a new test graph, covering local, global, and hierarchical graph transformations. Unlike grid-based ARC, GraphARC instances can be generated at scale across diverse graph families and sizes, enabling systematic evaluation of generalization abilities. We evaluate state-of-the-art language models on GraphARC and observe clear limitations. Models can answer questions about graph properties but often fail to solve the full graph transformation task, revealing a comprehension-execution gap. Performance further degrades on larger instances, exposing scaling barriers. More broadly, by combining aspects of node classification, link prediction, and graph generation within a single framework, GraphARC provides a promising testbed for future graph foundation models.
Lost in Tokenization: Fundamental Trade-offs in Graph Tokenization for Transformers
Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this work, we show that this choice is a fundamental component of transformer expressivity. We examine three tokenizations that serve as building blocks for many existing graph tokenizations: spectral, random-walk, and adjacency tokenizations. We prove that different tokenizations induce distinct depth regimes: the same graph computation may be realizable by a shallow transformer under one tokenization, while requiring substantially larger depth under another. For example, we prove that random-walk tokenization is lossy for any walk length, making it impossible in general to recover the graph from it, and that while spectral tokenization is lossless, it is ill-conditioned for local tasks. We further show that although both random-walk and spectral tokenizations are derived from adjacency information, it is impossible for a limited-depth transformer to convert between tokenization families in general. In particular, we establish lower bounds and impossibility results showing that unfavorable tokenizations may preclude the efficient recovery of more suitable structural representations. Finally, we complement our theory with controlled experiments on synthetic and real-world tasks, validating the predicted separations and showing that different tasks favor different structural views, and combining complementary tokenizations allows the transformer to leverage distinct signals from each representation.
Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction
Precise measurement of the kinematic Sunyaev-Zel'dovich (kSZ) effect - a probe of the large-scale distribution of baryonic matter, a key observable for cosmological inference - requires accurate reconstruction of galaxy velocities from spectroscopic surveys. The signal-to-noise ratio (SNR) of kSZ measurements scales directly with the correlation coefficient between reconstructed and true velocities. We introduce Velocityformer, an equivariant graph transformer architecture designed to match the specific symmetry of the observational data. While the underlying physics is equivariant with respect to translations and rotations, observational effects break this symmetry due to the preferred line-of-sight direction. Matching the model's inductive bias to the data's broken symmetry consistently improves performance across all model sizes and training volumes, with Velocityformer improving by 35% over the standard linear theory baseline and outperforming ML baselines at every data volume. By matching the model's inductive bias to the data and conditioning on the physics-based long-wavelength solution, Velocityformer is highly data-efficient, training to high accuracy on as few as 4 low-fidelity simulations, and generalises zero-shot across input geometry, cosmological parameters, and galaxy sample. On high-fidelity simulated galaxy catalogues, this yields a 30% improvement in over the physical baseline, directly translating to the same SNR gain on observational data.
Function graph transformers universally approximate operators between function spaces
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function is represented by its graph measure , with finite tokens being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers, a graph-preserving subclass of measure-theoretic transformers that maps graph measures to graph measures, which is to say that outputs remain single-valued functions. Crucially, this additional structure does not reduce generality: we prove that the resulting graph-preserving maps can be approximated by finite compositions of standard softmax self-attention layers and pointwise MLPs, yielding universal approximation results for broad classes of nonlinear operators. Unlike existing theoretical approaches to operator learning with transformers, the measure-theoretic framework also accommodates regularized negative-order Sobolev inputs for which discretization invariance is particularly challenging, as well as query points on different output domains. Overall, function graph transformers provide a continuum viewpoint and mathematical toolkit for transformer-based operator learning, clarifying the roles of positional encodings, graph structure, regularization, and ensuring consistency across discretizations.
Attention Dispersion in Dynamic Graph Transformers: Diagnosis and a Transferable Fix
Transformer-based architectures have become the dominant paradigm for Continuous-Time Dynamic Graph (CTDG) learning, yet their performance remains limited on temporally shifted datasets. In this work, we identify attention dispersion as a shared failure mode of dynamic graph Transformers under temporal distribution shift. Through controlled ablation contrasting structurally and temporally distinguished historical neighbors against random ones, we show that prediction depends on a class of critical nodes that carry consistently more predictive signal than arbitrary neighbors. However, existing Transformers fail to focus on these nodes even when they are present in the input, as temporal shift weakens attention contrast and produces overly dispersed attention distributions. This diagnosis suggests a simple and transferable fix: replace standard attention with differential attention, which suppresses common-mode attention and amplifies distinctive token-level signals. When added to three representative CTDG Transformer baselines, differential attention consistently improves performance, with gains concentrated on high-shift datasets. Attention-level measurements further confirm the mechanism, showing reduced attention entropy and increased attention mass on critical nodes. Building on these findings, we introduce DiffDyG, a reference implementation combining differential attention with standard input encodings. Across 9 benchmarks and three negative sampling protocols, DiffDyG achieves SOTA performance, with especially large gains on the most shifted datasets.
Gaussian Relational Graph Transformer
Relational graph learning enables predictive modeling over relational databases by directly capturing dependencies across interconnected tables. While relational graph Transformers extend the receptive field beyond local message passing, a larger receptive field does not necessarily provide more useful information: sampling must preserve relational structure without introducing excessive semantically irrelevant nodes, while attention must account for the temporal relevance of the retained information. We propose GelGT, a Gaussian relational graph transformer that explicitly addresses these challenges. GelGT introduces a structure-semantic collaborative sampling strategy to preserve structural connectivity while filtering irrelevant semantic information, and incorporates a Gaussian graph attention mechanism with a learnable Gaussian bias on the sampled subgraphs to dynamically encode temporal dependencies. We provide theoretical analysis characterizing the structural preservation, semantic refinement, and temporal discrimination of these mechanisms. Experiments on \textbf{7} real-world relational datasets covering \textbf{21} prediction tasks show that GelGT consistently outperforms existing relational graph learning methods, with improvements of up to \textbf{13.8%}.
Teaching LLMs to See Graphs: Unifying Text and Structural Reasoning
Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich textual attributes into solitary tokens, creating a significant semantic bottleneck. In this paper, we introduce the Graph Transformer Language Model (GTLM), a novel architecture that enables pretrained LLMs to natively process graph topologies while entirely eliminating this compressive bottleneck. GTLM is exceptionally parameter-efficient: by injecting graph-aware attention biases directly into the LLM's attention modules, it introduces only 0.015% additional parameters relative to the base model. We theoretically prove that our bidirectional attention prefix preserves node permutation equivariance while maintaining exact backward compatibility with the pretrained base model. Extensive evaluations demonstrate that a 1B-parameter GTLM matches or exceeds the performance of 7B-parameter state-of-the-art models on standard Text-Attributed Graph benchmarks, while significantly surpassing baselines on GraphQA. Finally, we demonstrate that GTLM attention heads implicitly learn to simulate message passing, explaining its superior performance on algorithmic tasks. This paradigm shift enables true algorithmic reasoning within LLMs and provides a scalable foundation for next-generation GraphRAG and relational deep learning.
CTQWformer: A CTQW-based Transformer for Graph Classification
Graph Neural Networks (GNN) and Transformer-based architectures have achieved remarkable progress in graph learning, yet they still struggle to capture both global structural dependencies and model the dynamic information propagation. In this paper, we propose CTQWformer, a hybrid graph learning framework that integrates continuous-time quantum walks (CTQW) with GNN. CTQWformer employs a trainable Hamiltonian that fuses graph topology and node features, enabling physically grounded modeling of quantum walk dynamics that captures rich and intricate graph structure information. The extracted CTQW-based representations are incorporated into two complementary modules:(i) a Graph Transformer module that embeds final-time propagation probabilities as structural biases in the self-attention mechanism, and (ii) a Graph Recurrent Module that captures temporal evolution patterns with bidirectional recurrent networks. Extensive experiments on benchmark graph classification datasets demonstrate that CTQWformer outperforms graph kernel and GNN-based methods, demonstrating the potential of integrating quantum dynamics into trainable deep learning frameworks for graph representation learning. To the best of our knowledge, CTQWformer is the first hybrid CTQW-based Transformer, integrating CTQW-derived structural bias with temporal evolution modeling to advance graph learning.
STLGT: A Scalable Trace-Based Linear Graph Transformer for Tail Latency Prediction in Microservices
Accurate end-to-end tail-latency forecasting is critical for proactive SLO management in microservice systems. However, modeling long-range dependency propagation and non-stationary, bursty workloads while maintaining inference efficiency at scale remains challenging. We present STLGT (Scalable Trace-based Linear Graph Transformer), a per-API predictor that encodes traces as span graphs for multi-step p95 tail-latency forecasting. STLGT uses a structure-aware linear graph Transformer to propagate cross-service dependencies with inference time linear in span graph size, and a decoupled temporal module to capture workload dynamics. Across a personalized education microservice application, DeathStarBench, and Alibaba traces, STLGT improves forecasting accuracy over PERT-GNN by 8.5% MAPE on average and achieves up to 12x faster CPU inference at N=32, matching the maximum span graph size after preprocessing the Alibaba traces. Ablation studies further demonstrate the effectiveness of each component, especially under bursty traffic.
Graph Memory Transformer (GMT)
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.
Distance-Misaligned Training in Graph Transformers and Adaptive Graph-Aware Control
Graph Transformers can mix information globally, but this flexibility also creates failure modes: some tasks require long-range communication while others are better served by local interaction. We study this through a synthetic node-classification benchmark on contextual stochastic block model graphs, where labels are generated by a controllable mixture of local and far-shell signals. We define distance-misaligned training as a mismatch between where label-relevant information lies and where the model allocates communication over graph distance. On this benchmark, we find three points. First, the preferred graph-distance bias changes systematically with task locality. Second, an oracle adaptive controller, given offline access to the task-side distance target, nearly matches the best fixed bias across regimes and strongly improves over a neutral baseline on mixed and local tasks. Third, a task-agnostic zero-gap controller is weaker, indicating that adaptation alone is not enough and that the control target matters. These results suggest that distance-resolved diagnosis is useful for understanding Graph Transformer failures and for designing graph-aware control.
Scalable and Adaptive Parallel Training of Graph Transformer on Large Graphs
Graph foundation models have demonstrated remarkable adaptability across diverse downstream tasks through large-scale pretraining on graphs. However, existing implementations of the backbone model, graph transformers, are typically limited to single-GPU systems, leading to long training times or out-of-memory issues on large graphs. Moreover, parallelizing graph transformer training over the full graph is challenging, as efficiency depends heavily on both the graph structure and system characteristics, such as bandwidth and memory capacity. In this work, we introduce a distributed training framework for graph transformers, which automatically selects and optimizes parallelization strategies based on the graph structure and hardware configuration. With our implementation of distributed sparse operations, we accelerate sparse graph attention by up to 3.8x and reduce memory consumption by 78% compared to state-of-the-art frameworks. On large graph benchmarks, our proposed framework achieves up to 6x speedup with system scaling up to 8 GPUs. These results demonstrate that the proposed framework improves the scalability of graph transformers, bringing them closer to serving as practical graph foundation models.
Context-aware Skin Cancer Epithelial Cell Classification with Scalable Graph Transformers
Whole-slide images (WSIs) from cancer patients contain rich information that can be used for medical diagnosis or to follow treatment progress. To automate their analysis, numerous deep learning methods based on convolutional neural networks and Vision Transformers have been developed and have achieved strong performance in segmentation and classification tasks. However, due to the large size and complex cellular organization of WSIs, these models rely on patch-based representations, losing vital tissue-level context. We propose using scalable Graph Transformers on a full-WSI cell graph for classification. We evaluate this methodology on a challenging task: the classification of healthy versus tumor epithelial cells in cutaneous squamous cell carcinoma (cSCC), where both cell types exhibit very similar morphologies and are therefore difficult to differentiate for image-based approaches. We first compared image-based and graph-based methods on a single WSI. Graph Transformer models SGFormer and DIFFormer achieved balanced accuracies of ( standard error) and in 3-fold cross-validation, respectively, whereas the best image-based method reached . By evaluating several node feature configurations, we found that the most informative representation combined morphological and texture features as well as the cell classes of non-epithelial cells, highlighting the importance of the surrounding cellular context. We then extended our work to train on several WSIs from several patients. To address the computational constraints of image-based models, we extracted four pixel patches from each image and converted them into graphs. In this setting, DIFFormer achieved a balanced accuracy of (3-fold cross-validation), while the state-of-the-art image-based model CellViT256 reached .