THGFM: Dual-Branch Temporal Heterogeneous Graph Fusion Model

# THGFM: Dual-Branch Temporal Heterogeneous Graph Fusion Model
Source: [https://arxiv.org/html/2607.27303](https://arxiv.org/html/2607.27303)
11institutetext:RWTH Aachen University, Aachen, Germany
11email:\{peng,jin,decker\}@dbis\.rwth\-aachen\.de22institutetext:Fraunhofer FIT, Sankt Augustin, Germany
22email:diego\.collarana\.vargas@fit\.fraunhofer\.de###### Abstract

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 proposeTHGFM, a web\-scale temporal heterogeneous graph fusion model that addresses both limitations within a unified dual\-path architecture\. THGFM couples aShared\-Space Temporal Attentionbranch for parameter\-efficient cross\-type transfer with aRelational Type\-Partitioned Temporal Attentionbranch for relation\-aware specialization, and integrates them throughDual\-Path Relational–Shared Fusion, instantiated withType\-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 introducesRotary 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%\+3\.25\\%six\-task mean gain, with peak relative gains of\+12\.37%\+12\.37\\%on OAG\-CS PV,\+4\.87%\+4\.87\\%on PF\-L2L\_\{2\}, and\+1\.18%\+1\.18\\%on PF\-L1L\_\{1\}, and\+4\.24%\+4\.24\\%,\+3\.73%\+3\.73\\%, and\+4\.61%\+4\.61\\%on OGBN\-MAG, HTAG\-ArXiv, and HTAG\-DBLP, respectively\.

## 1Introduction

A heterogeneous graph is a graph in which each node and edge is associated with a type, providing a natural representation for real\-world relational systems where diverse object types interact through multiple semantic relations\. Representative examples include academic graphs, e\-commerce graphs, scientific knowledge graphs, and enterprise information networks\[[6](https://arxiv.org/html/2607.27303#bib.bib24),[16](https://arxiv.org/html/2607.27303#bib.bib11),[29](https://arxiv.org/html/2607.27303#bib.bib10),[19](https://arxiv.org/html/2607.27303#bib.bib25)\]\. As illustrated in Fig\.[1](https://arxiv.org/html/2607.27303#S1.F1), an Open Academic Graph \(OAG\) instance comprises*author*,*paper*,*venue*, and*field\-of\-study*nodes linked by relations such as*written\-by*,*published\-in*,*belongs\-to*,*associated\-with*and*cites*\. These relation types encode different semantics, while node types exhibit markedly different feature distributions\. Moreover, OAG is inherently temporal: new papers and collaborations appear continuously, and the context of existing entities changes as surrounding publications and links evolve over time\. Modeling such temporal heterogeneous graphs, therefore, requires jointly capturing cross\-type structural heterogeneity and temporal dynamics\.

![Refer to caption](https://arxiv.org/html/2607.27303v1/pictures/Graph.png)Figure 1:OAG as a temporal heterogeneous graph with multiple node types and relation semantics that evolve over time\. Timestamp availability is relation\-dependent: publication\-related edges are time\-stamped by publication year, while*author\-affiliation*links in this example do not provide explicit timestamps and are therefore treated as edges with missing time \(ψ​\(e\)=⊥\\psi\(e\)=\\bot\)\. The figure is adapted from\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\]\.Recent heterogeneous graphtransformerssuch as HGT\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\], together with emerging graph foundation models\[[1](https://arxiv.org/html/2607.27303#bib.bib3)\], have significantly advanced graph representation learning\. Yet temporal heterogeneous graph learning remains much less developed than the broader dynamic graph learning researches\[[4](https://arxiv.org/html/2607.27303#bib.bib23)\], with only a limited number of methods designed specifically for temporal heterogeneous graphs, including HTGNN\[[3](https://arxiv.org/html/2607.27303#bib.bib20)\], CTRL\[[10](https://arxiv.org/html/2607.27303#bib.bib21)\], and THAN\[[11](https://arxiv.org/html/2607.27303#bib.bib22)\]\. Two challenges are particularly important for temporal heterogeneous graphs learning\. First, heterogeneous modeling involves two design choices that are not competing alternatives but*complementary*and jointly necessary: type\- and relation\-specific parameters, which preserve the fine\-grained per\-type and per\-relation semantics that make heterogeneous graphs informative\[[7](https://arxiv.org/html/2607.27303#bib.bib44),[9](https://arxiv.org/html/2607.27303#bib.bib1),[18](https://arxiv.org/html/2607.27303#bib.bib8),[23](https://arxiv.org/html/2607.27303#bib.bib9),[28](https://arxiv.org/html/2607.27303#bib.bib42)\], and shared cross\-type transformations, which enable parameter\-efficient cross\-type transfer and better generalization to rare node and relation types by amortizing statistics across the graph\[[30](https://arxiv.org/html/2607.27303#bib.bib46),[15](https://arxiv.org/html/2607.27303#bib.bib27),[21](https://arxiv.org/html/2607.27303#bib.bib43)\]\. Recent work on billion\-scale graph foundation models provides evidence that the shared and specialized views are complementary in principle: within a single heterogeneous attention block, combining type\-agnostic and type\-conditioned attention can express graph functions that neither component alone can realize\[[1](https://arxiv.org/html/2607.27303#bib.bib3)\]\. This argues against dropping either side of the design and motivates architectures that keep both signals and learn how to combine them, rather than treating them as an expressivity\-versus\-efficiency trade\-off\. Second, temporal information is still commonly handled outside the attention kernel itself\. HGT and later temporal heterogeneous graph models such as HTGNN, THAN, and CTRL already incorporate temporal signals, but they do so mainly through additive encodings, across\-time aggregation, or continuous\-time influence modeling\. More specifically, in HGT, Relative Temporal Encoding \(RTE\) influences attention only indirectly through the source representation\. For temporal heterogeneous graphs, however, relative time should affect not only what message is sent, but which neighbors deserve attention\.

On OAG, for example, two papers appearing at a conference may discuss closely related topics, yet their predictive relevance to a target paper in citation or collaboration contexts usually decays as their publication years become more distant\. Therefore, temporal separation should reshape which neighbors receive high attention, not only the encoding of the messages they send\.

Moreover, recent graph models have shown that adaptive fusion is useful when different information sources should contribute unequally across nodes\. In heterogeneous graphs, HGAMLP\[[12](https://arxiv.org/html/2607.27303#bib.bib29)\]introduces a node\-adaptive weight adjustment mechanism to fuse different knowledge sources, while AFMF\[[13](https://arxiv.org/html/2607.27303#bib.bib26)\]shows that globally shared fusion weights can become too rigid when neighborhood evidence varies across nodes\. This issue is especially central to our setting: a dual\-path temporal heterogeneous model is only effective if it can decide, for each target node, how much to rely on shared cross\-type transfer versus relation\-aware specialization\. In temporal heterogeneous graphs, both are necessary, but their relative importance varies across node types, neighborhood structures, and temporal contexts\. We therefore foreground dual\-branch fusion as a principal architectural decision rather than a post hoc aggregation step, and introduce*Type\-Conditioned Non\-Competitive Gated Sum Fusion*\(TC\-NGSF\), which learns two independent feature\-wise gates conditioned jointly on the paired branch representations and the target\-node type, and then combines the recalibrated branches through summation\. Unlike competitive fusion, TC\-NGSF does not force the two branches into a zero\-sum trade\-off, allowing THGFM to amplify or suppress shared and specialized evidence independently when both are informative\.

These observations motivate THGFM, a*Temporal Heterogeneous Graph Fusion Model*\(Figure[2](https://arxiv.org/html/2607.27303#S4.F2)\), a transformer\-based architecture that combines a*Shared\-Space Temporal Attention*\(SSTA\) branch, which improves parameter sharing and cross\-type transfer, with a*Relational Type\-Partitioned Temporal Attention*\(RTTA\) branch, which preserves type\- and relation\-aware semantics\. The two branches are integrated through*Dual\-Path Relational–Shared Fusion*\(DRSF\), where TC\-NGSF serves as the core adaptive fusion mechanism of the full THGFM model\. To model graph dynamics more directly, THGFM further introduces*Rotary Temporal Attention*\(RoTA\), which injects edge\-wise relative time into attention by rotating the query and key with opposite half\-phases determined by the relative time interval before score computation, which is inspired by the rotary\-positioning principle of RoFormer\[[20](https://arxiv.org/html/2607.27303#bib.bib32)\]\. Hence THGFM is particularly well suited to temporal heterogeneous graphs, where heterogeneity, dynamics, and distribution imbalance must be handled simultaneously\.

##### Contributions\.

1. 1\.We proposeTHGFM, a dual\-path temporal heterogeneous graph fusion model built on two complementary attention branches:*SSTA*sharesQ/K/VQ/K/Vprojections after type\-specific adapters to support parameter\-efficient cross\-type transfer, while*RTTA*preserves fine\-grained semantics through target\-type queries, source\-type keys/values, and relation\-grouped per\-relation transforms\.
2. 2\.We introduce two operators tailored to temporal heterogeneous fusion\.*RoTA*injects edge\-wise relative time directly into attention scoring by rotating queries and keys with opposite half\-phases of the time interval;*TC\-NGSF*combines the two branches through independent type\-conditioned feature\-wise gates and additive aggregation, avoiding zero\-sum competition between them\.
3. 3\.Although RTTA is inspired by HGT, it reduces the per\-layer edge cost from𝒪​\(\|E\|​\|𝒯\|2​\|ℛ\|\)\\mathcal\{O\}\(\|E\|\|\\mathcal\{T\}\|^\{2\}\|\\mathcal\{R\}\|\)to𝒪​\(\|E\|​\(\|𝒯\|\+\|ℛ\|\)\)\\mathcal\{O\}\(\|E\|\(\|\\mathcal\{T\}\|\{\+\}\|\\mathcal\{R\}\|\)\), while retaining comparable accuracy to HGT and even improving performance on some tasks\.
4. 4\.On OAG\-CS, OGBN\-MAG, HTAG\-ArXiv, and HTAG\-DBLP, THGFM consistently outperforms HGT, attaining a\+3\.25%\+3\.25\\%six\-task mean gain and up to\+12\.37%\+12\.37\\%peak; an ablation over branches, temporal switches, and six DRSF operators validates each design choice\.

The rest of the paper is organized as follows\. Section[2](https://arxiv.org/html/2607.27303#S2)reviews the most relevant literature\. Section[3](https://arxiv.org/html/2607.27303#S3)introduces the temporal heterogeneous graph setting and relative temporal encoding\. Section[4](https://arxiv.org/html/2607.27303#S4)presents the THGFM architecture and the proposed operators\. Section[5](https://arxiv.org/html/2607.27303#S5)describes the experimental setup and reports the empirical results\. Section[6](https://arxiv.org/html/2607.27303#S6)concludes the paper\.

## 2Related Work

We organize related work along three lines most relevant to THGFM: heterogeneous graph representation learning, temporal graph learning and temporal encoding, and adaptive fusion of complementary information sources\.

### 2\.1Heterogeneous Graph Representation Learning

Work on heterogeneous graph learning has gradually moved from schema\-guided designs to learned relation\-aware models\. Early methods such as HAN\[[23](https://arxiv.org/html/2607.27303#bib.bib9)\]and MAGNN\[[5](https://arxiv.org/html/2607.27303#bib.bib14)\]rely on meta\-paths to capture heterogeneous semantics\. These models are effective when good semantic paths are known in advance, but their behavior still depends heavily on handcrafted structure\. Later methods such as RGCN\[[18](https://arxiv.org/html/2607.27303#bib.bib8)\]and Simple\-HGN\[[15](https://arxiv.org/html/2607.27303#bib.bib27)\]reduce this dependence by learning relation\-aware transformations or heterogeneous attention directly from data\. More recent scalable baseline, including SeHGNN\[[25](https://arxiv.org/html/2607.27303#bib.bib28)\], further shows that efficiency and large\-graph training are now central concerns in practical heterogeneous learning\.

This progression highlights the primary motivation for THGFM: an effective model for heterogeneous graphs should preserve relation\-specific semantics without relying on handcrafted meta\-paths, while avoiding fully type\-isolated modeling, which does not scale efficiently to large graphs\. Thus, heterogeneous learning requires both specialization and controlled sharing\. THGFM is designed to achieve this balance\.

### 2\.2Temporal Graph Learning and Temporal Encoding

Temporal graph learning asks how evolving interactions should change representation learning beyond static structure alone\. Representative approaches include continuous\-time attention models such as TGAT\[[24](https://arxiv.org/html/2607.27303#bib.bib15)\]and memory\-based event models such as TGN\[[17](https://arxiv.org/html/2607.27303#bib.bib17)\]\. These methods establish that temporal information is often essential, but they are mainly designed for homogeneous graphs or settings with limited type complexity\.

For heterogeneous temporal graphs, HGT\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\]is the most relevant starting point because it combines heterogeneous attention with Relative Temporal Encoding \(RTE\)\. Later work such as HTGNN\[[3](https://arxiv.org/html/2607.27303#bib.bib20)\]and CTRL\[[10](https://arxiv.org/html/2607.27303#bib.bib21)\]extend temporal modeling through across\-time aggregation or event\-driven continuous\-time mechanisms\. However, the dominant pattern is still to inject time through source features, temporal histories, or auxiliary dynamics modules\. In other words, time affects attention indirectly\. For temporal heterogeneous graphs, this is not enough: temporal distance should influence not only what information a neighbor carries, but also how strongly that neighbor is matched by the attention kernel itself\. This is the gap targeted by our temporal design\.

### 2\.3Fusion of Complementary Information Sources

Adaptive fusion has become increasingly important when multiple information sources provide complementary but uneven evidence across nodes\. In heterogeneous graph learning, HGAMLP\[[12](https://arxiv.org/html/2607.27303#bib.bib29)\]uses node\-adaptive weighting to combine different knowledge sources, while AFMF\[[13](https://arxiv.org/html/2607.27303#bib.bib26)\]shows that globally shared fusion weights can be overly rigid under diverse neighborhood patterns\. These studies establish the value of data\-dependent fusion, but they are not designed for the dual\-path temporal heterogeneous setting considered here\.

In our setting, fusion must reconcile two distinct inductive biases: shared\-space cross\-type transfer and relation\-aware specialization\. This requirement is more structured than standard feature\-view fusion, because the two branches should be allowed to be simultaneously strong or simultaneously weak depending on node type, neighborhood structure, and temporal context\. THGFM addresses this regime with branch\-level type\-conditioned non\-competitive gating, which avoids forcing the two branches into a zero\-sum trade\-off\.

## 3Preliminaries

### 3\.1Temporal Heterogeneous Graph Setting

We extend the definition of temporal heterogeneous graphs from HGT\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\]to include edge timestamps\. A temporal heterogeneous graph is a directed typed graphG⋆=\(V⋆,E⋆,τ,ϕ,ψ\)G^\{\\star\}=\(V^\{\\star\},E^\{\\star\},\\tau,\\phi,\\psi\), whereτ:V⋆→𝒜\\tau:V^\{\\star\}\\to\\mathcal\{A\}maps nodes to node types,ϕ:E⋆→ℛ\\phi:E^\{\\star\}\\to\\mathcal\{R\}maps edges to relation types, andψ:E⋆→ℤ∪\{⊥\}\\psi:E^\{\\star\}\\to\\mathbb\{Z\}\\cup\\\{\\bot\\\}provides an optional timestamp per edge \(e\.g\. Author\-Affiliation links do not provide explicit timestamps\)\. For an edgee=\(u,v\)e=\(u,v\)with relationr=ϕ​\(e\)r=\\phi\(e\), its meta relation is⟨τ​\(u\),r,τ​\(v\)⟩\\langle\\tau\(u\),r,\\tau\(v\)\\rangle; if reverse edges are explicitly included, we denote the inverse relation byr−1r^\{\-1\}\. Edge timestamps are used whenever they are semantically well defined \(e\.g\., publication\-year on Paper\-Field or Paper\-Venue edges\)\. Relations without a timestamp are assigned⊥\\bot\. For training, each iteration operates on a locally sampled subgraphG=\(V,E\)G=\(V,E\)using HGSampling as in HGT\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\]\. Each sampled nodev∈Vv\\in V, when treated as a target node, is assigned an induced context timetv∈ℤt\_\{v\}\\in\\mathbb\{Z\}\. When expanding along an incoming edgee=\(j,i\)e=\(j,i\)from targetii, the source\-node time is assigned as

tj←\{ψ​\(e\),ψ​\(e\)≠⊥,ti,ψ​\(e\)=⊥\.t\_\{j\}\\leftarrow\\begin\{cases\}\\psi\(e\),&\\psi\(e\)\\neq\\bot,\\\\ t\_\{i\},&\\psi\(e\)=\\bot\.\\end\{cases\}\(1\)Following the HGSampling procedure of HGT, the assignment in Eq\. \([1](https://arxiv.org/html/2607.27303#S3.E1)\) preserves temporal consistency along each sampled path: timestamped edges propagate their own event time, while non\-timestamped edges inherit the current target context time\. A side effect is that the same global node may receive different induced times across sampled batches\. We keep this assignment rule aligned with HGT to ensure a fair baseline comparison under matched sampling semantics, so observed improvements primarily reflect the model architecture rather than a changed temporal propagation protocol\.

After tensorization, we relabel sampled nodes to local indices\{0,…,\|V\|−1\}\\\{0,\\ldots,\|V\|\-1\\\}\. LetN=\|V\|N=\|V\|andM=\|E\|M=\|E\|\. We construct𝐗∈ℝN×din\\mathbf\{X\}\\in\\mathbb\{R\}^\{N\\times d\_\{\\mathrm\{in\}\}\}\(node features\),𝝉∈𝒜N\\boldsymbol\{\\tau\}\\in\\mathcal\{A\}^\{N\}\(node\-type IDs\), and an edge index𝐀∈\{0,…,N−1\}2×M\\mathbf\{A\}\\in\\\{0,\\ldots,N\-1\\\}^\{2\\times M\}, whoseee\-th column stores a directed edge\(je,ie\)\(j\_\{e\},i\_\{e\}\)\. In the same edge order, we store relation IDsϕ∈ℛM\\boldsymbol\{\\phi\}\\in\\mathcal\{R\}^\{M\}and define edge\-wise relative time from induced node times:

Δ​tj​i=ti−tj\+c,\\Delta t\_\{ji\}=t\_\{i\}\-t\_\{j\}\+c,\(2\)wherec∈ℤc\\in\\mathbb\{Z\}is a fixed offset chosen so that values are non\-negative\. Equivalently, for edge slotee,Δ​te=tie−tje\+c\\Delta t\_\{e\}=t\_\{i\_\{e\}\}\-t\_\{j\_\{e\}\}\+c, yielding𝚫​𝒕∈ℤ≥0M\\boldsymbol\{\\Delta t\}\\in\\mathbb\{Z\}\_\{\\geq 0\}^\{M\}\. Hence𝚫​𝒕\\boldsymbol\{\\Delta t\}is an edge\-aligned input used in message passing, computed on\-the\-fly from batch\-local induced node times rather than stored as a static global field\. The tuple\(𝐗,𝝉,𝐀,ϕ,𝚫​𝒕\)\(\\mathbf\{X\},\\boldsymbol\{\\tau\},\\mathbf\{A\},\\boldsymbol\{\\phi\},\\boldsymbol\{\\Delta t\}\)is the input of THGFM\.

### 3\.2Relative Temporal Encoding

Following HGT, we use the relative interval defined in Eq\. \([2](https://arxiv.org/html/2607.27303#S3.E2)\)\. Given source representationhjh\_\{j\}, Relative Temporal Encoding \(RTE\) injects time through additive sinusoidal features:

h~j→i=hj\+𝐖t​PE⁡\(Δ​tj​i\),\\tilde\{h\}\_\{j\\to i\}=h\_\{j\}\+\\mathbf\{W\}\_\{t\}\\operatorname\{PE\}\\\!\\left\(\\Delta t\_\{ji\}\\right\),\(3\)wherePE⁡\(⋅\)\\operatorname\{PE\}\(\\cdot\)is sinusoidal positional encoding and𝐖t\\mathbf\{W\}\_\{t\}is a learnable projection\. This source\-side temporal augmentation is used during edge\-wise message construction\.

### 3\.3Rotary Temporal Attention

Besides additive temporal encoding, THGFM further uses Rotary Temporal Attention \(RoTA\) so that relative time also affects the matching stage of attention\. For each headmm, letqi\(m\)q\_\{i\}^\{\(m\)\}andkj→i\(m\)k\_\{j\\to i\}^\{\(m\)\}denote the query and key on edge\(j,r,i\)\(j,r,i\)\. We apply an edge\-dependent rotary transformRot⁡\(⋅,θj​i\)\\operatorname\{Rot\}\(\\cdot,\\theta\_\{ji\}\), whereθj​i∝Δ​tj​i\\theta\_\{ji\}\\propto\\Delta t\_\{ji\}, and compute attention from the rotated vectors\. The symmetric rotation is

q¯i\(m\)\\displaystyle\\bar\{q\}\_\{i\}^\{\(m\)\}=Rot⁡\(qi\(m\),\+θj​i/2\),\\displaystyle=\\operatorname\{Rot\}\\\!\\left\(q\_\{i\}^\{\(m\)\},\+\\theta\_\{ji\}/2\\right\),\(4\)k¯j→i\(m\)\\displaystyle\\bar\{k\}\_\{j\\to i\}^\{\(m\)\}=Rot⁡\(kj→i\(m\),−θj​i/2\)\.\\displaystyle=\\operatorname\{Rot\}\\\!\\left\(k\_\{j\\to i\}^\{\(m\)\},\-\\theta\_\{ji\}/2\\right\)\.Attention is then scored by the dot product⟨q¯i\(m\),k¯j→i\(m\)⟩\\langle\\bar\{q\}\_\{i\}^\{\(m\)\},\\bar\{k\}\_\{j\\to i\}^\{\(m\)\}\\rangle\. In this way, temporal intervals act directly on attention score computation\.

## 4The Temporal Heterogeneous Graph Fusion Model

Building on the preliminaries, THGFM is a dual\-branch temporal heterogeneous graph fusion model\. It combines an SSTA branch for shared\-space cross\-type transfer and an RTTA branch for relation\-aware specialization, integrates them via DRSF, and injects edge\-wise temporal bias through RoTA\. Figure[2](https://arxiv.org/html/2607.27303#S4.F2)gives an overview of this architecture\.

![Refer to caption](https://arxiv.org/html/2607.27303v1/pictures/THGFM_Architecture_v2.png)Figure 2:Overall architecture of THGFM\. Each layer executes two temporal heterogeneous attention branches—SSTA \(Shared\-Space Temporal Attention\) and RTTA \(Relational Type\- Partitioned Temporal Attention\)—both modulated by Rotary Temporal Attention \(RoTA\), and fuses their outputs through Dual\-Path Relational–Shared Fusion \(DRSF\) before passing to the next layer via a gated residual connection\.### 4\.1Overall THGFM Architecture

As defined in Section[3\.1](https://arxiv.org/html/2607.27303#S3.SS1), THGFM receives the node features, node types, edge indices, relation IDs, and relative times of a sampled temporal heterogeneous subgraph\. The model first maps the raw heterogeneous features to a shared hidden space via type\-specific input adapters\. For nodevv, the initial representation is

𝐡v\(0\)=Dropout⁡\(tanh⁡\(𝐖τ​\(v\)in​𝐱v\)\),\\mathbf\{h\}^\{\(0\)\}\_\{v\}=\\operatorname\{Dropout\}\\\!\\left\(\\tanh\\\!\\left\(\\mathbf\{W\}^\{\\mathrm\{in\}\}\_\{\\tau\(v\)\}\\mathbf\{x\}\_\{v\}\\right\)\\right\),\(5\)where𝐖τ​\(v\)in∈ℝd×din\\mathbf\{W\}^\{\\mathrm\{in\}\}\_\{\\tau\(v\)\}\\in\\mathbb\{R\}^\{d\\times d\_\{\\mathrm\{in\}\}\}is a learnable type\-specific input projection\.

Representations are then updated byLLstacked THGFM layers:

𝐡v\(ℓ\)=THGFM\(ℓ\)⁡\(\{𝐡u\(ℓ−1\)\}u∈V,𝝉,𝐀,ϕ,𝚫​𝒕\),ℓ=1,…,L\.\\mathbf\{h\}^\{\(\\ell\)\}\_\{v\}=\\operatorname\{THGFM\}^\{\(\\ell\)\}\\\!\\left\(\\\{\\mathbf\{h\}^\{\(\\ell\-1\)\}\_\{u\}\\\}\_\{u\\in V\},\\boldsymbol\{\\tau\},\\mathbf\{A\},\\boldsymbol\{\\phi\},\\boldsymbol\{\\Delta t\}\\right\),\\qquad\\ell=1,\\dots,L\.\(6\)At each layer, attention\-based heterogeneous message passing uses hidden states together with node types, relation types, graph structure, and relative time\. Thus, one layer aggregates one\-hop neighborhoods, and the stack in Eq\. \([6](https://arxiv.org/html/2607.27303#S4.E6)\) yields an effectiveLL\-hop receptive field on the sampled subgraph\. When DRSF is enabled, SSTA and RTTA are both computed and fused*within*the same layer before the residual update, i\.e\., THGFM adopts layer\-wise fusion rather than late fusion over the final branch outputs\.

Each THGFM layer has two stages: \(i\)message construction and attention normalizationover incoming edges \(including intra\-layer SSTA–RTTA fusion when DRSF is used\), which produces a pre\-residual representation𝐳i\(ℓ\)∈ℝd\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}\\in\\mathbb\{R\}^\{d\}for each target nodeii; and \(ii\)gated residual mixing with type\-specific normalization\. Let𝐡i\(ℓ−1\)\\mathbf\{h\}\_\{i\}^\{\(\\ell\-1\)\}denote the layer input for nodeii\. The update rule is

ατ​\(i\)\\displaystyle\\alpha\_\{\\tau\(i\)\}=σ​\(gτ​\(i\)\),\\displaystyle=\\sigma\\\!\\left\(g\_\{\\tau\(i\)\}\\right\),\(7\)𝐫i\(ℓ\)\\displaystyle\\mathbf\{r\}\_\{i\}^\{\(\\ell\)\}=ατ​\(i\)​𝐳i\(ℓ\)\+\(1−ατ​\(i\)\)​𝐡i\(ℓ−1\),\\displaystyle=\\alpha\_\{\\tau\(i\)\}\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}\+\\bigl\(1\-\\alpha\_\{\\tau\(i\)\}\\bigr\)\\mathbf\{h\}\_\{i\}^\{\(\\ell\-1\)\},𝐡i\(ℓ\)\\displaystyle\\mathbf\{h\}\_\{i\}^\{\(\\ell\)\}=LayerNormτ​\(i\)⁡\(𝐫i\(ℓ\)\)\.\\displaystyle=\\operatorname\{LayerNorm\}\_\{\\tau\(i\)\}\\\!\\left\(\\mathbf\{r\}\_\{i\}^\{\(\\ell\)\}\\right\)\.The update in Eq\. \([7](https://arxiv.org/html/2607.27303#S4.E7)\) is shared across single\-branch \(SSTA\-only or RTTA\-only\) and DRSF settings: only𝐳i\(ℓ\)\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}changes with the message block, while residual and normalization remain identical\. Heregτ​\(i\)g\_\{\\tau\(i\)\}is a learnable scalar gate per target type,σ\\sigmais the logistic function, andατ​\(i\)∈\(0,1\)\\alpha\_\{\\tau\(i\)\}\\in\(0,1\)controls interpolation between𝐳i\(ℓ\)\\mathbf\{z\}\_\{i\}^\{\(\\ell\)\}and𝐡i\(ℓ−1\)\\mathbf\{h\}\_\{i\}^\{\(\\ell\-1\)\}\.

### 4\.2Dual\-Path Relational–Shared Fusion \(DRSF\)

DRSF combines two branches with complementary inductive roles:*SSTA*for shared\-space cross\-type transfer and*RTTA*for relation\-aware heterogeneous interactions\. The two branches are fused within each THGFM layer before the target\-side residual update, and the fused representation serves as the layer output\. Figures[3](https://arxiv.org/html/2607.27303#S4.F3)and[4](https://arxiv.org/html/2607.27303#S4.F4)illustrate the two branches and the fusion module, respectively\.

![Refer to caption](https://arxiv.org/html/2607.27303v1/pictures/SSTA_v2.png)

\(a\) SSTA\. Type\-specific input projections first map source/target features into a shared latent space, followed by sharedQ/K/VQ/K/Vprojections\. RoTA rotatesq,kq,kwith edge\-wise relative time before score computation, and attention is globally normalized across all incoming neighbors\.

![Refer to caption](https://arxiv.org/html/2607.27303v1/pictures/RTTA_v2.png)

\(b\) RTTA\. Target\-type\-specific queries and source\-type\-specific keys/values are further modulated by relation\-specific transforms \(Ar,MrA\_\{r\},M\_\{r\}\)\. After RoTA, attention is normalized within each source\-type partition\.

Figure 3:Two THGFM attention branches used by DRSF\. SSTA provides parameter\-efficient cross\-type transfer in a shared space, while RTTA preserves type\- and relation\-aware specialization; both apply RoTA before attention scoring\.#### 4\.2\.1Shared\-Space Branch: SSTA

SSTA first maps source and target representations into a shared latent space via type\-specific projections:

zj→i=Wτ​\(j\)type​h~j→i,zi=Wτ​\(i\)type​hi\.z\_\{j\\to i\}=W^\{\\text\{type\}\}\_\{\\tau\(j\)\}\\tilde\{h\}\_\{j\\to i\},\\qquad z\_\{i\}=W^\{\\text\{type\}\}\_\{\\tau\(i\)\}h\_\{i\}\.\(8\)It then applies sharedQ/K/VQ/K/Vprojections to obtain the per\-head query, key, and value vectorsqi\(m\)q\_\{i\}^\{\(m\)\},kj→i\(m\)k\_\{j\\to i\}^\{\(m\)\}, andvj→i\(m\)v\_\{j\\to i\}^\{\(m\)\}, respectively\. After RoTA phase\-rotatesqi\(m\)q\_\{i\}^\{\(m\)\}andkj→i\(m\)k\_\{j\\to i\}^\{\(m\)\}with edge\-wise relative time, attention is normalized*globally*over all neighbors regardless of type:

αj​i\(m\)=softmaxj∈𝒩​\(i\)⁡\(⟨q¯i\(m\),k¯j→i\(m\)⟩dk\),\\alpha\_\{ji\}^\{\(m\)\}=\\operatorname\{softmax\}\_\{j\\in\\mathcal\{N\}\(i\)\}\\\!\\left\(\\tfrac\{\\langle\\bar\{q\}\_\{i\}^\{\(m\)\},\\bar\{k\}\_\{j\\to i\}^\{\(m\)\}\\rangle\}\{\\sqrt\{d\_\{k\}\}\}\\right\),\(9\)so neighbors of different source types compete in a single attention domain\.

#### 4\.2\.2RTTA Branch

RTTA instead uses target\-type\-specific queries, source\-type\-specific keys/values, and relation\-specific transforms:

qi\(m\)\\displaystyle q\_\{i\}^\{\(m\)\}=Wτ​\(i\)Q,\(m\)​hi,\\displaystyle=W\_\{\\tau\(i\)\}^\{Q,\(m\)\}h\_\{i\},\(10\)k^j→i\(m\)\\displaystyle\\hat\{k\}\_\{j\\to i\}^\{\(m\)\}=Ar\(m\)​Wτ​\(j\)K,\(m\)​h~j→i,\\displaystyle=A\_\{r\}^\{\(m\)\}W\_\{\\tau\(j\)\}^\{K,\(m\)\}\\tilde\{h\}\_\{j\\to i\},v^j→i\(m\)\\displaystyle\\hat\{v\}\_\{j\\to i\}^\{\(m\)\}=Mr\(m\)​Wτ​\(j\)V,\(m\)​h~j→i\.\\displaystyle=M\_\{r\}^\{\(m\)\}W\_\{\\tau\(j\)\}^\{V,\(m\)\}\\tilde\{h\}\_\{j\\to i\}\.RoTA is applied toqi\(m\)q\_\{i\}^\{\(m\)\}andk^j→i\(m\)\\hat\{k\}\_\{j\\to i\}^\{\(m\)\}as in SSTA\. Unlike the global normalization in Eq\. \([9](https://arxiv.org/html/2607.27303#S4.E9)\), RTTA normalizes attention*within each source\-type partition*:

αj​i\(m\)=softmaxk∈𝒩τ​\(j\)​\(i\)⁡\(⟨q¯i\(m\),k¯j→i\(m\)⟩dk\)\.\\alpha\_\{ji\}^\{\(m\)\}=\\operatorname\{softmax\}\_\{k\\in\\mathcal\{N\}\_\{\\tau\(j\)\}\(i\)\}\\\!\\left\(\\tfrac\{\\langle\\bar\{q\}\_\{i\}^\{\(m\)\},\\bar\{k\}\_\{j\\to i\}^\{\(m\)\}\\rangle\}\{\\sqrt\{d\_\{k\}\}\}\\right\)\.\(11\)
![Refer to caption](https://arxiv.org/html/2607.27303v1/pictures/DRSF_Fusion.png)Figure 4:DRSF\. Branch outputszisstaz\_\{i\}^\{\\text\{ssta\}\}andzirttaz\_\{i\}^\{\\text\{rtta\}\}are activated with GELU and fed into one of six fusion operators\. Gated fusion operators \(NGLF, NGSF, TC\-NGLF, TC\-NGSF\) compute non\-competitive sigmoid gates from concatenated branch features—optionally conditioned on a target\-type embeddingeτ​\(i\)e\_\{\\tau\(i\)\}—to recalibrate each branch before linear projection or summation\.
#### 4\.2\.3Fusion in DRSF

Within a THGFM layer, DRSF executes the SSTA and RTTA branches in parallel and fuses their outputs before the type\-wise residual update \(Figure[4](https://arxiv.org/html/2607.27303#S4.F4)\)\. RoTA is applied in both branches before attention\-score computation\. Letzirtta,zissta∈ℝdz\_\{i\}^\{\\text\{rtta\}\},z\_\{i\}^\{\\text\{ssta\}\}\\in\\mathbb\{R\}^\{d\}denote the pre\-fusion aggregated outputs for target nodeii, matching the split of the message\-passing aggregate before fusion\. We apply GELU to obtainuirtta=GELU⁡\(zirtta\)u\_\{i\}^\{\\text\{rtta\}\}=\\operatorname\{GELU\}\(z\_\{i\}^\{\\text\{rtta\}\}\)anduissta=GELU⁡\(zissta\)u\_\{i\}^\{\\text\{ssta\}\}=\\operatorname\{GELU\}\(z\_\{i\}^\{\\text\{ssta\}\}\), and then compare six DRSF operators: SF, LF, NGLF, NGSF, TC\-NGLF, and TC\-NGSF\.

##### Ungated fusion \(LF and SF\)\.

The two ungated operators are

fiLF\\displaystyle f\_\{i\}^\{\\text\{LF\}\}=Dropout⁡\(Wfuse​\[uirtta;uissta\]\),\\displaystyle=\\operatorname\{Dropout\}\\\!\\left\(W^\{\\text\{fuse\}\}\[u\_\{i\}^\{\\text\{rtta\}\};u\_\{i\}^\{\\text\{ssta\}\}\]\\right\),\(12\)fiSF\\displaystyle f\_\{i\}^\{\\text\{SF\}\}=Dropout⁡\(uirtta\+uissta\)\.\\displaystyle=\\operatorname\{Dropout\}\\\!\\left\(u\_\{i\}^\{\\text\{rtta\}\}\+u\_\{i\}^\{\\text\{ssta\}\}\\right\)\.

##### Non\-competitive gating\.

Four gated fusion operators \(NGLF, NGSF, TC\-NGLF, TC\-NGSF\) compute two feature\-wise sigmoid gates without cross\-branch competition\. Their gate inputs, gates, and recalibrated features are jointly defined as

γi\\displaystyle\\gamma\_\{i\}=\{\[uirtta;uissta\],NGLF/NGSF,\[uirtta;uissta;eτ​\(i\)\],TC\-NGLF/TC\-NGSF,\\displaystyle=\(13\)\[girtta;gissta\]\\displaystyle\[g\_\{i\}^\{\\text\{rtta\}\};g\_\{i\}^\{\\text\{ssta\}\}\]=sigmoid⁡\(W2​GELU⁡\(W1​γi\+b1\)\+b2\),\\displaystyle=\\operatorname\{sigmoid\}\\\!\\left\(W\_\{2\}\\,\\operatorname\{GELU\}\\\!\\left\(W\_\{1\}\\gamma\_\{i\}\+b\_\{1\}\\right\)\+b\_\{2\}\\right\),t~irtta\\displaystyle\\tilde\{t\}\_\{i\}^\{\\text\{rtta\}\}=girtta⊙uirtta,t~issta=gissta⊙uissta\.\\displaystyle=g\_\{i\}^\{\\text\{rtta\}\}\\odot u\_\{i\}^\{\\text\{rtta\}\},\\qquad\\tilde\{t\}\_\{i\}^\{\\text\{ssta\}\}=g\_\{i\}^\{\\text\{ssta\}\}\\odot u\_\{i\}^\{\\text\{ssta\}\}\.Here,γi∈ℝ2​d\\gamma\_\{i\}\\in\\mathbb\{R\}^\{2d\}for NGLF/NGSF andγi∈ℝ2​d\+dτ\\gamma\_\{i\}\\in\\mathbb\{R\}^\{2d\+d\_\{\\tau\}\}for their type\-conditioned variants;eτ​\(i\)∈ℝdτe\_\{\\tau\(i\)\}\\in\\mathbb\{R\}^\{d\_\{\\tau\}\}is a learnable target\-type embedding, andgirtta,gissta∈ℝdg\_\{i\}^\{\\text\{rtta\}\},g\_\{i\}^\{\\text\{ssta\}\}\\in\\mathbb\{R\}^\{d\}\. The parametersW1,W2,b1,b2W\_\{1\},W\_\{2\},b\_\{1\},b\_\{2\}use the corresponding input dimension\.

##### Gated fusion \(NGLF and NGSF\)\.

Using the recalibrated features in Eq\. \([13](https://arxiv.org/html/2607.27303#S4.E13)\), NGLF applies a linear projection, whereas NGSF uses summation:

fiNGLF\\displaystyle f\_\{i\}^\{\\text\{NGLF\}\}=Dropout⁡\(Wfuse​\[t~irtta;t~issta\]\),\\displaystyle=\\operatorname\{Dropout\}\\\!\\left\(W^\{\\text\{fuse\}\}\\left\[\\tilde\{t\}\_\{i\}^\{\\text\{rtta\}\};\\tilde\{t\}\_\{i\}^\{\\text\{ssta\}\}\\right\]\\right\),\(14\)fiNGSF\\displaystyle f\_\{i\}^\{\\text\{NGSF\}\}=Dropout⁡\(t~irtta\+t~issta\)\.\\displaystyle=\\operatorname\{Dropout\}\\\!\\left\(\\tilde\{t\}\_\{i\}^\{\\text\{rtta\}\}\+\\tilde\{t\}\_\{i\}^\{\\text\{ssta\}\}\\right\)\.

##### Type\-conditioned variants \(TC\-NGLF and TC\-NGSF\)\.

These variants use the second gate input in Eq\. \([13](https://arxiv.org/html/2607.27303#S4.E13)\)\. TC\-NGLF and TC\-NGSF otherwise follow the first and second lines of Eq\. \([14](https://arxiv.org/html/2607.27303#S4.E14)\), respectively; their outputs are denoted byfiTC\-NGLFf\_\{i\}^\{\\text\{TC\-NGLF\}\}andfiTC\-NGSFf\_\{i\}^\{\\text\{TC\-NGSF\}\}\.

All six DRSF fusion operators \(SF, LF, NGLF, NGSF, TC\-NGLF, and TC\-NGSF\) share the same type\-wise residual update described in Section[4\.1](https://arxiv.org/html/2607.27303#S4.SS1)\.

## 5Evaluation

### 5\.1Web\-Scale Datasets\.

We conduct experiments on temporal heterogeneous academic benchmarks built from both large\-scale academic graph sources and curated HTAG\[[14](https://arxiv.org/html/2607.27303#bib.bib39)\]releases\. OAG\-CS is derived from the Computer Science subgraph of the Open Academic Graph and Microsoft Academic Graph raw datasets\[[22](https://arxiv.org/html/2607.27303#bib.bib37),[29](https://arxiv.org/html/2607.27303#bib.bib10)\]\. HTAG\-ArXiv and HTAG\-DBLP are drawn from the HTAG datasets\[[14](https://arxiv.org/html/2607.27303#bib.bib39)\]\. These benchmarks are modeled as temporal heterogeneous graphs with typed nodes, typed directed edges, and edge times\. Table[1](https://arxiv.org/html/2607.27303#S5.T1)summarizes the scale and relation composition of these benchmarks\.

Table 1:Statistics of benchmarks\.\(a\) Entity\-scale statistics\.

Dataset\#Nodes\#Edges\#Papers\#Authors\#Fields\#Venues\#AffiliationOAG\-CS11,732,027107,263,8115,597,6055,985,759119,53727,43316,931OGBN\-MAG1,940,09227,196,251736,3891,134,64959,9653498,740HTAG\-ArXiv231,1512,075,69281,634127,59021,887––HTAG\-DBLP1,989,01929,830,033964,350958,96165,699––

\(b\) Relation counts by Meta\-path \(typed edges\)\.

Dataset\#P–A\#P–F\#P–V\#A–I\#P–POAG\-CS15,571,61447,462,5595,597,6067,190,48031,441,552OGBN\-MAG7,145,6607,505,078736,3891,043,99810,765,126HTAG\-ArXiv300,233755,835––1,019,624HTAG\-DBLP3,070,34310,080,164––16,679,526

### 5\.2Experimental Setup

##### Tasks\.

We evaluate THGFM on four temporal academic benchmarks\. On OAG\-CS, we consider paper–field prediction at two granularities \(L1L\_\{1\},L2L\_\{2\}\) and paper–venue prediction\[[29](https://arxiv.org/html/2607.27303#bib.bib10),[9](https://arxiv.org/html/2607.27303#bib.bib1)\]\. On OGBN\-MAG\[[8](https://arxiv.org/html/2607.27303#bib.bib38)\], we perform paper–venue classification over 349 venues\. HTAG\-ArXiv and HTAG\-DBLP\[[14](https://arxiv.org/html/2607.27303#bib.bib39)\]are multi\-class node\-classification tasks with dataset\-specific label semantics \(40 arXiv CS subject areas and 9 DBLP topic labels, respectively\)\. Temporal splits follow those benchmark protocols\.

##### Dataset Preprocessing\.

We use our temporal heterogeneous preprocessing pipeline across OAG\-CS, OGBN\-MAG, HTAG\-DBLP, and HTAG\-ArXiv, with a consistent schema and split\-aware supervision\. We build typed graphs over paper, author, field, and plus venues and affiliation when available\. Relations include paper–paper, paper–field, paper–venue, and author–paper edges\. Paper features follow benchmark\-native sources \(OAG XLNet\[[27](https://arxiv.org/html/2607.27303#bib.bib34)\], OGB word2vec\[[2](https://arxiv.org/html/2607.27303#bib.bib41)\], HTAG released dense embeddings\), while non\-paper features are propagated from paper neighborhoods\.

All datasets are converted to a shared intermediate representation from which subprocesses materialize only batch\-local subgraphs at training time\. Compared with pyHGT preprocessing\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\], this pipeline enforces stricter temporal consistency and numerically stable structural features, improving memory efficiency and reducing dataset\-specific engineering variance\.

Table 2:\(a\)HGT vs\. our preprocessing \(OAG\-CS only\)\.\(b\)Peak RAM, offline graph prep\. time, and per\-epoch wall time for the same HGT setting, training recipe and with 4 data\-sampling subprocesses\.*Same HGT setting*fixes every implementation settings \(see "Implementation Details\." in section[5\.2](https://arxiv.org/html/2607.27303#S5.SS2)\), and varies only the data preprocessing pipeline\.\(a\) Evaluation results \(OAG\-CS\)\.

Preproc\. pipelinePF\-L1L\_\{1\}PF\-L2L\_\{2\}PVNDCGMRRNDCGMRRNDCGMRRpyHGT0\.718±0\.0140\.718\\pm 0\.0140\.823±0\.0190\.823\\pm 0\.0190\.403±0\.0410\.403\\pm 0\.0410\.439±0\.0780\.439\\pm 0\.0780\.473±0\.054\\text\{\{0\.473\}\}\\pm 0\.0540\.288±0\.0880\.288\\pm 0\.088Our \(Same HGT setting\)0\.8510±0\.013\\text\{\{0\.8510\}\}\\pm 0\.0130\.8328±0\.003\\text\{\{0\.8328\}\}\\pm 0\.0030\.4375±0\.009\\text\{\{0\.4375\}\}\\pm 0\.0090\.5118±0\.002\\text\{\{0\.5118\}\}\\pm 0\.0020\.4658±0\.0100\.4658\\pm 0\.0100\.2932±0\.014\\text\{\{0\.2932\}\}\\pm 0\.014

\(b\) Resource / latency \(OAG\-CS, Subproc\.=4=4\)\.

Preproc\. pipelineRAM \(GB\)Data prep \(s/ep\.\)Wall \(s/ep\.\)pyHGT26\.8626\.8614\.814\.8219\.4219\.4Our \(Same HGT setting\)4\.154\.154\.94\.9101\.9101\.9

Table[2](https://arxiv.org/html/2607.27303#S5.T2)shows that preprocessing alone can substantially affect HGT\. Our pipeline improves PF\-L1L\_\{1\}/PF\-L2L\_\{2\}NDCG/MRR while remaining competitive on PV \(panel\(a\)\), and it also cuts peak RAM from26\.8626\.86to4\.154\.15GB, shortens offline graph preparation from14\.814\.8to4\.94\.9s \(∼67%\\sim\\\!67\\%reduction relative to pyHGT\), and lowers wall\-clock time per training epoch from219\.4219\.4to101\.9101\.9s when using four data\-sampling subprocesses \(∼54%\\sim\\\!54\\%reduction; panel\(b\)\)\. We therefore use our preprocessing pipeline for all subsequent experiments\.

##### Baseline Models\.

We compare THGFM with ieHGCN\[[26](https://arxiv.org/html/2607.27303#bib.bib40)\], SeHGNN\[[25](https://arxiv.org/html/2607.27303#bib.bib28)\], HGT\[[9](https://arxiv.org/html/2607.27303#bib.bib1)\], and CTRL\[[10](https://arxiv.org/html/2607.27303#bib.bib21)\]\. ieHGCN and SeHGNN are strong heterogeneous baselines with efficient semantic aggregation, HGT is the primary heterogeneous\-transformer baseline under the same preprocessing and training protocol, and CTRL provides a SOTA temporal heterogeneous baseline that models continuous\-time relational influence\. Baselines use hyperparameters and protocols matched to THGFM\. Within THGFM, we further report SSTA\-only and RTTA\-only branch ablations, and all branch\-fusion operators\.

##### Implementation Details\.

We do not conduct an extensive hyperparameter search, as our goal is to evaluate the effectiveness of the proposed architecture rather than to obtain performance gains through model\-specific hyperparameter tuning\. To avoid introducing additional tuning confounds, we use a fixed HGT\-compatible hyperparameter configuration for all comparable models whenever applicable, covering the hidden dimension, number of layers and attention heads, optimizer, learning rate, dropout, sampling depth and width, and training budget\. All models are optimized with AdamW using a learning rate of10−310^\{\-3\}, a dropout rate of0\.20\.2, and gradient clipping at0\.250\.25\. Training proceeds for200200epochs\. In each epoch, we uniformly sample without replacement3232minibatches of256256papers from the training split and traverse these minibatches twice\. For each paper, we construct an ego subgraph with a sampling depth of66and a width of128128\. We use a hidden dimension of256256,L=3L=3layers for all models, and88attention heads for all multi\-head attention backbones\. To ensure reproducibility, we fix the global random seed to4343for Python, NumPy, and PyTorch and enable deterministic CUDA execution, including deterministic cuDNN kernels\. All experiments are conducted on a single NVIDIA H100 GPU with8080GB of memory\.

### 5\.3Experimental Results & Ablation Study

Throughout all ablations, the feature model, training pipeline, and sampling strategy are held fixed so that differences isolate the graph operator\. Table[3](https://arxiv.org/html/2607.27303#S5.T3)reports the full results compared with baselines on OAG\-CS, OGBN\-MAG, and HTAG under three branch temporal configurations\. Reported±\\pmvalues are standard deviations over nine runs, with three runs for each seed in\{41,42,43\}\\\{41,42,43\\\}\.

Notation\.RTE denotes additive temporal bias on node feature encoding, and RoTA rotates query/key features before attention scoring\. We compare threebranch temporal configurationsshared across all benchmarks\.r001\_s001enables RTE with RoTA off \(RTE\-Only\);r110\_s110enables RoTA with RTE off \(RoTA\-Only\);r111\_s111enables both RoTA and RTE\.

Table 3:Full detailed result grids under three branch temporal configurations on OAG\-CS, OGBN\-MAG, and HTAG\.\(a\) OAG\-CS: baselines and DRSF fusion operators\.

ModelsParams\(M\)PF\-L1L\_\{1\}NDCGPF\-L1L\_\{1\}MRRPF\-L1L\_\{1\}Rel\. Gainvs\. HGT \(%\)PF\-L2L\_\{2\}NDCGPF\-L2L\_\{2\}MRRPF\-L2L\_\{2\}Rel\. Gainvs\. HGT \(%\)PVNDCGPVMRRPVRel\. Gainvs\. HGT \(%\)CTRL15\.400\.8522±0\.015\\text\{\\lx@text@underline\{0\.8522\}\}\\pm 0\.0150\.8410±0\.007\\text\{\\lx@text@underline\{0\.8410\}\}\\pm 0\.007\+0\.56\+0\.560\.4041±0\.0030\.4041\\pm 0\.0030\.4462±0\.0060\.4462\\pm 0\.006−10\.23\-10\.230\.4850±0\.0030\.4850\\pm 0\.0030\.3157±0\.009\\text\{\\lx@text@underline\{0\.3157\}\}\\pm 0\.009\+5\.90\+5\.90ieHGCN9\.300\.8266±0\.0050\.8266\\pm 0\.0050\.8097±0\.0030\.8097\\pm 0\.003−2\.82\-2\.820\.3748±0\.0030\.3748\\pm 0\.0030\.3973±0\.0060\.3973\\pm 0\.006−18\.35\-18\.350\.4878±0\.005\\text\{\\lx@text@underline\{0\.4878\}\}\\pm 0\.0050\.3122±0\.0030\.3122\\pm 0\.003\+5\.60\+5\.60SeHGNN3\.800\.8319±0\.0060\.8319\\pm 0\.0060\.8221±0\.0120\.8221\\pm 0\.012−1\.76\-1\.760\.3771±0\.0020\.3771\\pm 0\.0020\.4035±0\.0050\.4035\\pm 0\.005−17\.48\-17\.480\.4421±0\.0120\.4421\\pm 0\.0120\.2658±0\.0020\.2658\\pm 0\.002−7\.22\-7\.22HGT8\.200\.8510±0\.0130\.8510\\pm 0\.0130\.8328±0\.0030\.8328\\pm 0\.0030\.000\.000\.4375±0\.009\\text\{\\lx@text@underline\{0\.4375\}\}\\pm 0\.0090\.5118±0\.002\\text\{\\lx@text@underline\{0\.5118\}\}\\pm 0\.0020\.000\.000\.4658±0\.0100\.4658\\pm 0\.0100\.2932±0\.0140\.2932\\pm 0\.0140\.000\.00Configurationr001\_s001SSTA4\.450\.8511±0\.0090\.8511\\pm 0\.0090\.8359±0\.0110\.8359\\pm 0\.011\+0\.19\+0\.190\.4504±0\.0001\\text\{\\lx@text@underline\{0\.4504\}\}\\pm 0\.00010\.5393±0\.0001\\text\{\\lx@text@underline\{0\.5393\}\}\\pm 0\.0001\+4\.16\+4\.160\.4963±0\.0130\.4963\\pm 0\.0130\.3185±0\.0090\.3185\\pm 0\.009\+7\.59\+7\.59RTTA7\.010\.8528±0\.0070\.8528\\pm 0\.0070\.8305±0\.0070\.8305\\pm 0\.007−0\.03\-0\.030\.4189±0\.0070\.4189\\pm 0\.0070\.4806±0\.0080\.4806\\pm 0\.008−5\.17\-5\.170\.4864±0\.0010\.4864\\pm 0\.0010\.3119±0\.0050\.3119\\pm 0\.005\+5\.40\+5\.40SF8\.590\.8542±0\.0010\.8542\\pm 0\.0010\.8353±0\.0030\.8353\\pm 0\.003\+0\.34\+0\.340\.4284±0\.00010\.4284\\pm 0\.00010\.4979±0\.00050\.4979\\pm 0\.0005−2\.40\-2\.400\.4990±0\.0130\.4990\\pm 0\.0130\.3260±0\.0050\.3260\\pm 0\.005\+9\.16\+9\.16LF8\.990\.8565±0\.0140\.8565\\pm 0\.0140\.8389±0\.0080\.8389\\pm 0\.008\+0\.69\+0\.690\.4240±0\.00070\.4240\\pm 0\.00070\.4910±0\.00130\.4910\\pm 0\.0013−3\.57\-3\.570\.4983±0\.0120\.4983\\pm 0\.0120\.3237±0\.0080\.3237\\pm 0\.008\+8\.69\+8\.69NGSF9\.380\.8598±0\.006\\text\{\\lx@text@underline\{0\.8598\}\}\\pm 0\.0060\.8435±0\.012\\text\{\\lx@text@underline\{0\.8435\}\}\\pm 0\.012\+1\.16\+1\.160\.4427±0\.00040\.4427\\pm 0\.00040\.5256±0\.00040\.5256\\pm 0\.0004\+1\.94\+1\.940\.4993±0\.015\\text\{\\lx@text@underline\{0\.4993\}\}\\pm 0\.0150\.3279±0\.009\\text\{\\lx@text@underline\{0\.3279\}\}\\pm 0\.009\+9\.51\+9\.51NGLF9\.780\.8580±0\.0140\.8580\\pm 0\.0140\.8402±0\.0090\.8402\\pm 0\.009\+0\.86\+0\.860\.4411±0\.00060\.4411\\pm 0\.00060\.5217±0\.00060\.5217\\pm 0\.0006\+1\.38\+1\.380\.4847±0\.0060\.4847\\pm 0\.0060\.3104±0\.0040\.3104\\pm 0\.004\+4\.96\+4\.96TC\-NGSF9\.430\.8569±0\.0060\.8569\\pm 0\.0060\.8385±0\.0110\.8385\\pm 0\.011\+0\.69\+0\.690\.4400±0\.00020\.4400\\pm 0\.00020\.5204±0\.00070\.5204\\pm 0\.0007\+1\.13\+1\.130\.4963±0\.0140\.4963\\pm 0\.0140\.3242±0\.0040\.3242\\pm 0\.004\+8\.56\+8\.56TC\-NGLF9\.830\.8586±0\.0110\.8586\\pm 0\.0110\.8423±0\.0090\.8423\\pm 0\.009\+1\.02\+1\.020\.4502±0\.00030\.4502\\pm 0\.00030\.5387±0\.00050\.5387\\pm 0\.0005\+4\.08\+4\.080\.4903±0\.0050\.4903\\pm 0\.0050\.3157±0\.0130\.3157\\pm 0\.013\+6\.47\+6\.47Configurationr110\_s110SSTA4\.450\.8515±0\.0040\.8515\\pm 0\.0040\.8362±0\.0080\.8362\\pm 0\.008\+0\.23\+0\.230\.4510±0\.0150\.4510\\pm 0\.0150\.5401±0\.0080\.5401\\pm 0\.008\+4\.31\+4\.310\.4810±0\.0120\.4810\\pm 0\.0120\.3046±0\.0120\.3046\\pm 0\.012\+3\.58\+3\.58RTTA7\.010\.8537±0\.0110\.8537\\pm 0\.0110\.8382±0\.0070\.8382\\pm 0\.007\+0\.48\+0\.480\.4238±0\.0150\.4238\\pm 0\.0150\.4881±0\.0100\.4881\\pm 0\.010−3\.88\-3\.880\.4865±0\.0120\.4865\\pm 0\.0120\.3120±0\.0040\.3120\\pm 0\.004\+5\.43\+5\.43SF8\.590\.8530±0\.0140\.8530\\pm 0\.0140\.8296±0\.0140\.8296\\pm 0\.014−0\.07\-0\.070\.4299±0\.00010\.4299\\pm 0\.00010\.5012±0\.00030\.5012\\pm 0\.0003−1\.90\-1\.900\.5102±0\.001\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.5102\}\}\}\}\\pm 0\.0010\.3378±0\.001\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.3378\}\}\}\}\\pm 0\.001\+12\.37\+12\.37LF8\.990\.8565±0\.0060\.8565\\pm 0\.0060\.8389±0\.0140\.8389\\pm 0\.014\+0\.69\+0\.690\.4072±0\.00030\.4072\\pm 0\.00030\.4548±0\.00150\.4548\\pm 0\.0015−9\.03\-9\.030\.4983±0\.0100\.4983\\pm 0\.0100\.3237±0\.0120\.3237\\pm 0\.012\+8\.69\+8\.69NGSF9\.380\.8603±0\.008\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.8603\}\}\}\}\\pm 0\.0080\.8426±0\.0090\.8426\\pm 0\.009\+1\.13\+1\.130\.4512±0\.0004\\text\{\\lx@text@underline\{0\.4512\}\}\\pm 0\.00040\.5410±0\.0015\\text\{\\lx@text@underline\{0\.5410\}\}\\pm 0\.0015\+4\.42\+4\.420\.4954±0\.0050\.4954\\pm 0\.0050\.3225±0\.0030\.3225\\pm 0\.003\+8\.17\+8\.17NGLF9\.780\.8577±0\.0120\.8577\\pm 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0\.0003\+2\.06\+2\.060\.4858±0\.0100\.4858\\pm 0\.0100\.3139±0\.0120\.3139\\pm 0\.012\+5\.68\+5\.68NGLF9\.780\.8526±0\.0090\.8526\\pm 0\.0090\.8302±0\.0010\.8302\\pm 0\.001−0\.06\-0\.060\.4528±0\.0003\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.4528\}\}\}\}\\pm 0\.00030\.5437±0\.0006\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.5437\}\}\}\}\\pm 0\.0006\+4\.87\+4\.870\.4879±0\.0050\.4879\\pm 0\.0050\.3139±0\.0040\.3139\\pm 0\.004\+5\.90\+5\.90TC\-NGSF9\.430\.8600±0\.001\\text\{\\lx@text@underline\{0\.8600\}\}\\pm 0\.0010\.8437±0\.001\\text\{\\lx@text@underline\{0\.8437\}\}\\pm 0\.001\+1\.18\+1\.180\.4394±0\.0140\.4394\\pm 0\.0140\.5177±0\.0130\.5177\\pm 0\.013\+0\.79\+0\.790\.4967±0\.0040\.4967\\pm 0\.0040\.3252±0\.0020\.3252\\pm 0\.002\+8\.77\+8\.77TC\-NGLF9\.830\.8569±0\.0090\.8569\\pm 0\.0090\.8409±0\.0100\.8409\\pm 0\.010\+0\.83\+0\.830\.4397±0\.0020\.4397\\pm 0\.0020\.5190±0\.0080\.5190\\pm 0\.008\+0\.95\+0\.950\.4936±0\.0030\.4936\\pm 0\.0030\.3214±0\.0100\.3214\\pm 0\.010\+7\.79\+7\.79

\(b\) OGBN\-MAG and HTAG: baselines and DRSF fusion operators\.

ModelsParams\(M\)OGBN\-MAG\(PV\)Test Acc\.OGBN\-MAG\(PV\)Val\. Acc\.OGBN\-MAGRel\. Gainvs\. HGT \(%\)HTAG\-ArXivTest Acc\.HTAG\-ArXivVal\. Acc\.HTAG\-ArXivRel\. Gainvs\. HGT \(%\)HTAG\-DBLPTest Acc\.HTAG\-DBLPVal\. Acc\.HTAG\-DBLPRel\. Gainvs\. HGT \(%\)CTRL15\.400\.4017±0\.007\\text\{\\lx@text@underline\{0\.4017\}\}\\pm 0\.0070\.4019±0\.0080\.4019\\pm 0\.008−0\.82\-0\.820\.8443±0\.010\\text\{\\lx@text@underline\{0\.8443\}\}\\pm 0\.0100\.8415±0\.003\\text\{\\lx@text@underline\{0\.8415\}\}\\pm 0\.003\+2\.08\+2\.080\.7540±0\.014\\text\{\\lx@text@underline\{0\.7540\}\}\\pm 0\.0140\.7634±0\.0050\.7634\\pm 0\.005\+0\.53\+0\.53ieHGCN9\.300\.3703±0\.0080\.3703\\pm 0\.0080\.3879±0\.0140\.3879\\pm 0\.014−6\.51\-6\.510\.8232±0\.0120\.8232\\pm 0\.0120\.8115±0\.0130\.8115\\pm 0\.013−1\.02\-1\.020\.7305±0\.0090\.7305\\pm 0\.0090\.7651±0\.0140\.7651\\pm 0\.014−0\.92\-0\.92SeHGNN3\.800\.3694±0\.0090\.3694\\pm 0\.0090\.3684±0\.0120\.3684\\pm 0\.012−8\.94\-8\.940\.8281±0\.0130\.8281\\pm 0\.0130\.8289±0\.0120\.8289\\pm 0\.012\+0\.34\+0\.340\.7383±0\.0110\.7383\\pm 0\.0110\.7656±0\.020\\text\{\\lx@text@underline\{0\.7656\}\}\\pm 0\.020−0\.37\-0\.37HGT8\.200\.3906±0\.0120\.3906\\pm 0\.0120\.4208±0\.020\\text\{\\lx@text@underline\{0\.4208\}\}\\pm 0\.020\+0\.00\+0\.000\.8352±0\.0140\.8352\\pm 0\.0140\.8164±0\.0050\.8164\\pm 0\.005\+0\.00\+0\.000\.7508±0\.0290\.7508\\pm 0\.0290\.7586±0\.0150\.7586\\pm 0\.015\+0\.00\+0\.00Configurationr001\_s001SSTA4\.450\.4006±0\.0190\.4006\\pm 0\.0190\.4175±0\.0140\.4175\\pm 0\.014\+0\.89\+0\.890\.8277±0\.0110\.8277\\pm 0\.0110\.8246±0\.0140\.8246\\pm 0\.014\+0\.05\+0\.050\.7645±0\.0130\.7645\\pm 0\.0130\.7728±0\.0090\.7728\\pm 0\.009\+1\.85\+1\.85RTTA7\.010\.4001±0\.0130\.4001\\pm 0\.0130\.4176±0\.0260\.4176\\pm 0\.026\+0\.84\+0\.840\.8539±0\.0090\.8539\\pm 0\.0090\.8430±0\.0140\.8430\\pm 0\.014\+2\.75\+2\.750\.7848±0\.0120\.7848\\pm 0\.0120\.7754±0\.0120\.7754\\pm 0\.012\+3\.37\+3\.37SF8\.590\.3992±0\.0080\.3992\\pm 0\.0080\.4238±0\.0050\.4238\\pm 0\.005\+1\.46\+1\.460\.8570±0\.011\\text\{\\lx@text@underline\{0\.8570\}\}\\pm 0\.0110\.8430±0\.0170\.8430\\pm 0\.017\+2\.93\+2\.930\.7699±0\.0070\.7699\\pm 0\.0070\.7656±0\.0080\.7656\\pm 0\.008\+1\.73\+1\.73LF8\.990\.3952±0\.0080\.3952\\pm 0\.0080\.4105±0\.0100\.4105\\pm 0\.010−0\.64\-0\.640\.8418±0\.0140\.8418\\pm 0\.0140\.8434±0\.0120\.8434\\pm 0\.012\+2\.05\+2\.050\.7617±0\.0130\.7617\\pm 0\.0130\.7715±0\.0130\.7715\\pm 0\.013\+1\.58\+1\.58NGSF9\.380\.4036±0\.022\\text\{\\lx@text@underline\{0\.4036\}\}\\pm 0\.0220\.4249±0\.011\\text\{\\lx@text@underline\{0\.4249\}\}\\pm 0\.011\+2\.15\+2\.150\.8449±0\.0120\.8449\\pm 0\.0120\.8426±0\.0140\.8426\\pm 0\.014\+2\.19\+2\.190\.7797±0\.0120\.7797\\pm 0\.0120\.7695±0\.0070\.7695\\pm 0\.007\+2\.64\+2\.64NGLF9\.780\.3865±0\.0110\.3865\\pm 0\.0110\.4042±0\.0100\.4042\\pm 0\.010−2\.50\-2\.500\.8359±0\.0140\.8359\\pm 0\.0140\.8406±0\.0170\.8406\\pm 0\.017\+1\.52\+1\.520\.7570±0\.0130\.7570\\pm 0\.0130\.7637±0\.0130\.7637\\pm 0\.013\+0\.75\+0\.75TC\-NGSF9\.430\.3982±0\.0130\.3982\\pm 0\.0130\.4232±0\.0090\.4232\\pm 0\.009\+1\.26\+1\.260\.8316±0\.0110\.8316\\pm 0\.0110\.8379±0\.0070\.8379\\pm 0\.007\+1\.10\+1\.100\.7863±0\.015\\text\{\\lx@text@underline\{0\.7863\}\}\\pm 0\.0150\.7820±0\.007\\text\{\\lx@text@underline\{0\.7820\}\}\\pm 0\.007\+3\.91\+3\.91TC\-NGLF9\.830\.3808±0\.0150\.3808\\pm 0\.0150\.4047±0\.0100\.4047\\pm 0\.010−3\.17\-3\.170\.8441±0\.0090\.8441\\pm 0\.0090\.8438±0\.010\\text\{\\lx@text@underline\{0\.8438\}\}\\pm 0\.010\+2\.21\+2\.210\.7660±0\.0100\.7660\\pm 0\.0100\.7652±0\.0120\.7652\\pm 0\.012\+1\.45\+1\.45Configurationr110\_s110SSTA4\.450\.3878±0\.0150\.3878\\pm 0\.0150\.4049±0\.0180\.4049\\pm 0\.018−2\.25\-2\.250\.7766±0\.0120\.7766\\pm 0\.0120\.7773±0\.0150\.7773\\pm 0\.015−5\.90\-5\.900\.7398±0\.0120\.7398\\pm 0\.0120\.7527±0\.0150\.7527\\pm 0\.015−1\.12\-1\.12RTTA7\.010\.4002±0\.0130\.4002\\pm 0\.0130\.4188±0\.0240\.4188\\pm 0\.024\+0\.99\+0\.990\.8301±0\.0170\.8301\\pm 0\.0170\.8324±0\.0150\.8324\\pm 0\.015\+0\.67\+0\.670\.7840±0\.0090\.7840\\pm 0\.0090\.7758±0\.0120\.7758\\pm 0\.012\+3\.34\+3\.34SF8\.590\.3998±0\.0050\.3998\\pm 0\.0050\.4248±0\.0150\.4248\\pm 0\.015\+1\.65\+1\.650\.8570±0\.009\\text\{\\lx@text@underline\{0\.8570\}\}\\pm 0\.0090\.8441±0\.0170\.8441\\pm 0\.017\+3\.00\+3\.000\.7848±0\.0170\.7848\\pm 0\.0170\.7707±0\.0070\.7707\\pm 0\.007\+3\.06\+3\.06LF8\.990\.3847±0\.0140\.3847\\pm 0\.0140\.4078±0\.0080\.4078\\pm 0\.008−2\.30\-2\.300\.8418±0\.0130\.8418\\pm 0\.0130\.8406±0\.0170\.8406\\pm 0\.017\+1\.88\+1\.880\.7672±0\.0160\.7672\\pm 0\.0160\.7711±0\.0070\.7711\\pm 0\.007\+1\.92\+1\.92NGSF9\.380\.4127±0\.015\\text\{\\lx@text@underline\{0\.4127\}\}\\pm 0\.0150\.4327±0\.015\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.4327\}\}\}\}\\pm 0\.015\+4\.24\+4\.240\.8430±0\.0150\.8430\\pm 0\.0150\.8258±0\.0140\.8258\\pm 0\.014\+1\.04\+1\.040\.7871±0\.0080\.7871\\pm 0\.0080\.7754±0\.0070\.7754\\pm 0\.007\+3\.52\+3\.52NGLF9\.780\.3804±0\.0150\.3804\\pm 0\.0150\.4056±0\.0160\.4056\\pm 0\.016−3\.11\-3\.110\.8469±0\.0220\.8469\\pm 0\.0220\.8352±0\.0080\.8352\\pm 0\.008\+1\.85\+1\.850\.7807±0\.0010\.7807\\pm 0\.0010\.7984±0\.035\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.7984\}\}\}\}\\pm 0\.035\+4\.61\+4\.61TC\-NGSF9\.430\.4065±0\.0120\.4065\\pm 0\.0120\.4257±0\.0160\.4257\\pm 0\.016\+2\.62\+2\.620\.8406±0\.0130\.8406\\pm 0\.0130\.8430±0\.0110\.8430\\pm 0\.011\+1\.95\+1\.950\.7875±0\.013\\text\{\\lx@text@underline\{0\.7875\}\}\\pm 0\.0130\.7754±0\.0070\.7754\\pm 0\.007\+3\.55\+3\.55TC\-NGLF9\.830\.3838±0\.0200\.3838\\pm 0\.0200\.4079±0\.0220\.4079\\pm 0\.022−2\.40\-2\.400\.8398±0\.0070\.8398\\pm 0\.0070\.8473±0\.015\\text\{\\lx@text@underline\{0\.8473\}\}\\pm 0\.015\+2\.17\+2\.170\.7852±0\.0130\.7852\\pm 0\.0130\.7789±0\.0060\.7789\\pm 0\.006\+3\.63\+3\.63Configurationr111\_s111SSTA4\.450\.4017±0\.0180\.4017\\pm 0\.0180\.4166±0\.0170\.4166\\pm 0\.017\+0\.92\+0\.920\.7660±0\.0130\.7660\\pm 0\.0130\.7723±0\.0160\.7723\\pm 0\.016−6\.84\-6\.840\.7473±0\.0080\.7473\\pm 0\.0080\.7621±0\.0090\.7621\\pm 0\.009\+0\.00\+0\.00RTTA7\.010\.3999±0\.0130\.3999\\pm 0\.0130\.4163±0\.0130\.4163\\pm 0\.013\+0\.66\+0\.660\.8391±0\.0090\.8391\\pm 0\.0090\.8367±0\.0150\.8367\\pm 0\.015\+1\.48\+1\.480\.7766±0\.0120\.7766\\pm 0\.0120\.7766±0\.0070\.7766\\pm 0\.007\+2\.90\+2\.90SF8\.590\.4012±0\.0180\.4012\\pm 0\.0180\.4246±0\.0220\.4246\\pm 0\.022\+1\.81\+1\.810\.8544±0\.0020\.8544\\pm 0\.0020\.8586±0\.026\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.8586\}\}\}\}\\pm 0\.026\+3\.73\+3\.730\.7742±0\.0130\.7742\\pm 0\.0130\.7594±0\.0130\.7594\\pm 0\.013\+1\.61\+1\.61LF8\.990\.3958±0\.0140\.3958\\pm 0\.0140\.4156±0\.0160\.4156\\pm 0\.016\+0\.05\+0\.050\.8297±0\.0130\.8297\\pm 0\.0130\.8293±0\.0130\.8293\\pm 0\.013\+0\.46\+0\.460\.7730±0\.0130\.7730\\pm 0\.0130\.7578±0\.0100\.7578\\pm 0\.010\+1\.43\+1\.43NGSF9\.380\.4046±0\.0170\.4046\\pm 0\.0170\.4265±0\.018\\text\{\\lx@text@underline\{0\.4265\}\}\\pm 0\.018\+2\.47\+2\.470\.8387±0\.0100\.8387\\pm 0\.0100\.8344±0\.0130\.8344\\pm 0\.013\+1\.31\+1\.310\.7895±0\.010\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.7895\}\}\}\}\\pm 0\.0100\.7727±0\.0130\.7727\\pm 0\.013\+3\.51\+3\.51NGLF9\.780\.3785±0\.0120\.3785\\pm 0\.0120\.3955±0\.0090\.3955\\pm 0\.009−4\.56\-4\.560\.8270±0\.0060\.8270\\pm 0\.0060\.8313±0\.0110\.8313\\pm 0\.011\+0\.42\+0\.420\.7836±0\.0080\.7836\\pm 0\.0080\.7777±0\.0130\.7777\\pm 0\.013\+3\.44\+3\.44TC\-NGSF9\.430\.4150±0\.005\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.4150\}\}\}\}\\pm 0\.0050\.4253±0\.0160\.4253\\pm 0\.016\+3\.66\+3\.660\.8531±0\.0070\.8531\\pm 0\.0070\.8414±0\.0150\.8414\\pm 0\.015\+2\.60\+2\.600\.7879±0\.0110\.7879\\pm 0\.0110\.7809±0\.0080\.7809\\pm 0\.008\+3\.94\+3\.94TC\-NGLF9\.830\.3715±0\.0170\.3715\\pm 0\.0170\.3981±0\.0160\.3981\\pm 0\.016−5\.14\-5\.140\.8598±0\.019\\text\{\{\\color\[rgb\]\{1,0,0\}\{\\lx@text@underline\{0\.8598\}\}\}\}\\pm 0\.0190\.8422±0\.0090\.8422\\pm 0\.009\+3\.05\+3\.050\.7754±0\.0120\.7754\\pm 0\.0120\.7816±0\.015\\text\{\\lx@text@underline\{0\.7816\}\}\\pm 0\.015\+3\.15\+3\.15

To summarize models on cross\-dataset behavior, we aggregate OAG\-CS \(PF\-L1L\_\{1\}, PF\-L2L\_\{2\}, PV\), OGBN\-MAG \(PV\), HTAG\-ArXiv, and HTAG\-DBLP into a*six\-task mean gain*against HGT: for each task, we take the*Relative Gain \(%\) vs\. HGT*reported in Table[3](https://arxiv.org/html/2607.27303#S5.T3)and average the six tasks with equal weight\. The same table also lists all result cells under each branch temporal configuration; Table[4](https://arxiv.org/html/2607.27303#S5.T4)gives a compact structural summary\.

Table 4:Cross\-dataset fusion summarized by six\-task mean gain vs\. HGT\.\(a\) Top three fusion operators for each fixed branch temporal configuration\.

Config\.Rank 1Rank 2Rank 3Overall Mean Gainvs\. HGT \(%\)Fusion Op\.P\.\(M\)Mean\(%\)Fusion Op\.P\.\(M\)Mean\(%\)Fusion Op\.P\.\(M\)Mean\(%\)r001\_s001NGSF9\.38\+3\.27\+3\.27TC\-NGSF9\.43\+2\.78\+2\.78SSTA4\.45\+2\.46\+2\.46\+2\.83\+2\.83r110\_s110NGSF9\.38\+3\.75\+3\.75TC\-NGSF9\.43\+3\.48\+3\.48SF8\.59\+3\.02\+3\.02\+3\.42r111\_s111TC\-NGSF9\.43\+3\.49\+3\.49NGSF9\.38\+2\.68\+2\.68SF8\.59\+2\.59\+2\.59\+2\.92\+2\.92

\(b\) Per\-task gains for fusion pools and for each task’s best single \(operator, configuration\)\.

\(Pool of\) fusion operatorsOAG\-CSPF\-L1L\_\{1\}OAG\-CSPF\-L2L\_\{2\}OAG\-CSPVOGBN\-MAGHTAG\-ArXivHTAG\-DBLPMean Gainvs\. HGT \(%\)SF\+0\.34\+0\.34−2\.32\-2\.32\+10\.60\+10\.60\+1\.64\+1\.64\+3\.22\+3\.22\+2\.13\+2\.13\+2\.60\+2\.60LF\+0\.73\+0\.73−5\.50\-5\.50\+8\.87\+8\.87−0\.96\-0\.96\+1\.46\+1\.46\+1\.64\+1\.64\+1\.04\+1\.04NGSF\+1\.12\+1\.12\+2\.81\+2\.81\+7\.79\+7\.79\+2\.95\+2\.95\+1\.51\+1\.51\+3\.22\+3\.22\+3\.23\+3\.23NGLF\+0\.60\+0\.60\+2\.47\+2\.47\+5\.38\+5\.38−3\.39\-3\.39\+1\.26\+1\.26\+2\.93\+2\.93\+1\.54\+1\.54TC\-NGSF\+1\.02\+1\.02\+1\.23\+1\.23\+9\.04\+9\.04\+2\.51\+2\.51\+1\.88\+1\.88\+3\.80\+3\.80\+3\.25TC\-NGLF\+0\.87\+0\.87\+1\.17\+1\.17\+7\.51\+7\.51−3\.57\-3\.57\+2\.48\+2\.48\+2\.74\+2\.74\+1\.87\+1\.87Plain \(SF, LF\)\+0\.53\+0\.53−3\.91\-3\.91\+9\.74\+9\.74\+0\.34\+0\.34\+2\.34\+2\.34\+1\.89\+1\.89\+1\.82\+1\.82NG∗\(NGSF, NGLF\)\+0\.86\+0\.86\+2\.64\+2\.64\+6\.58\+6\.58−0\.22\-0\.22\+1\.39\+1\.39\+3\.08\+3\.08\+2\.39\+2\.39TC\-NG∗\(TC\-NGSF, TC\-NGLF\)\+0\.95\+0\.95\+1\.20\+1\.20\+8\.27\+8\.27−0\.53\-0\.53\+2\.18\+2\.18\+3\.27\+3\.27\+2\.56Sum\-style \(SF, NGSF, TC\-NGSF\)\+0\.82\+0\.82\+0\.57\+0\.57\+9\.14\+9\.14\+2\.37\+2\.37\+2\.21\+2\.21\+3\.05\+3\.05\+3\.03Linear\-style \(LF, NGLF, TC\-NGLF\)\+0\.73\+0\.73−0\.62\-0\.62\+7\.25\+7\.25−2\.64\-2\.64\+1\.73\+1\.73\+2\.44\+2\.44\+1\.48\+1\.48Best single\(operator, configuration\)TC\-NGSF@r111\_s111\+1\.18\+1\.18NGLF@r111\_s111\+4\.87\+4\.87SF@r110\_s110\+12\.37\+12\.37NGSF@r110\_s110\+4\.24\+4\.24SF@r111\_s111\+3\.73\+3\.73NGLF@r110\_s110\+4\.61\+4\.61\+5\.17\+5\.17

Table[4](https://arxiv.org/html/2607.27303#S5.T4)\(a\)fixes each branch temporal configuration and ranks the top three fusion operators by six\-task mean gain\. NGSF ranks first under RTE\-only and under RoTA\-only, while TC\-NGSF ranks first when both are enabled \(r111\_s111\)\. Averaging the top\-three entries in each row,RoTA\-onlyattains the highest mean \(\+3\.42%\+3\.42\\%\), clearly above RTE\-only \(\+2\.83%\+2\.83\\%\), so RoTA contributes more than RTE in this aggregate view\. Enabling RoTA and RTE together lowers the mean to\+2\.92%\+2\.92\\%, i\.e\., a drop from the RoTA\-only peak, but this joint setting still outperforms RTE\-only \(\+2\.92%\+2\.92\\%vs\.\+2\.83%\+2\.83\\%\)\.

Table[4](https://arxiv.org/html/2607.27303#S5.T4)\(b\)average fusion operators inside each pool, then averages over the three configurations\. Under this aggregation, six\-task pool\-mean gains increase monotonically from Plain \(\+1\.82%\+1\.82\\%\) to NG∗\(\+2\.39%\+2\.39\\%\) toTC\-NG∗\(\+2\.56%\+2\.56\\%\), shows theTC\-NG∗pool improves reliably over NG∗and over ungated sum/linear fusion\. Separately,sum\-stylepooling \(SF, NGSF, TC\-NGSF\) at\+3\.03%\+3\.03\\%beats linear\-style pooling \(LF, NGLF, TC\-NGLF\) at\+1\.48%\+1\.48\\%, shows sum\-style fusion outperform linear\-style fusion on the cross\-task average in this grid\.

### 5\.4Discussion

Table 5:Per\-layer compute complexity\.NNandMMare the number of nodes and edges in a sampled batch subgraph,ddis the hidden dimension,dτd\_\{\\tau\}the type\-embedding dimension, and\|𝒯\|\|\\mathcal\{T\}\|,\|ℛ\|\|\\mathcal\{R\}\|are the numbers of node types and relation types\.Module / operatorCompute complexity \(per layer\)\(Baseline\) HGT𝒪​\(N​d2\+M​d\+M​\|𝒯\|2​\|ℛ\|\)\\mathcal\{O\}\(Nd^\{2\}\+Md\+M\|\\mathcal\{T\}\|^\{2\}\|\\mathcal\{R\}\|\)*Single\-branch*SSTA𝒪​\(N​d2\+M​d\)\\mathcal\{O\}\(Nd^\{2\}\+Md\)RTTA𝒪​\(N​d2\+M​d\+M​\(\|𝒯\|\+\|ℛ\|\)\)\\mathcal\{O\}\\\!\\bigl\(Nd^\{2\}\+Md\+M\(\|\\mathcal\{T\}\|\+\|\\mathcal\{R\}\|\)\\bigr\)*THGFM*SFS​S​T​A\+R​T​T​A\+𝒪​\(N​d\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd\)LFS​S​T​A\+R​T​T​A\+𝒪​\(N​d2\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd^\{2\}\)NGLFS​S​T​A\+R​T​T​A\+𝒪​\(N​d2\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd^\{2\}\)NGSFS​S​T​A\+R​T​T​A\+𝒪​\(N​d2\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd^\{2\}\)TC\-NGLFS​S​T​A\+R​T​T​A\+𝒪​\(N​d2\+N​d​dτ\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd^\{2\}\+Ndd\_\{\\tau\}\)TC\-NGSFS​S​T​A\+R​T​T​A\+𝒪​\(N​d2\+N​d​dτ\)SSTA\+RTTA\+\\mathcal\{O\}\(Nd^\{2\}\+Ndd\_\{\\tau\}\)

Table[2](https://arxiv.org/html/2607.27303#S5.T2)is intended to isolate the contribution of preprocessing\. It keeps the HGT architecture and training configuration fixed while varying only the preprocessing pipeline, thereby directly quantifying the gains attributable to preprocessing\. In contrast, the HGT results reported in Tables[3](https://arxiv.org/html/2607.27303#S5.T3)and[4](https://arxiv.org/html/2607.27303#S5.T4)already incorporate our preprocessing pipeline\. Consequently, the improvements of THGFM in these tables are measured against a stronger HGT baseline under identical preprocessing, feature construction, sampling, and training protocols, thus isolating the gains from the proposed model components and operators\. The complete experimental grids in Table[3](https://arxiv.org/html/2607.27303#S5.T3)further substantiate the contribution of RTTA\. Moreover, comparing the per\-layer computational hierarchy in Table[5](https://arxiv.org/html/2607.27303#S5.T5)with the six\-task mean gains in Table[4](https://arxiv.org/html/2607.27303#S5.T4)\(b\)reveals two distinct performance–efficiency trade\-off directions\.*\(i\) Gating direction:*moving Plain→\\toNG∗→\\toTC\-NG∗adds only adτd\_\{\\tau\}\-dimensional conditioning \(\+0\.05\+0\.05M parameters for TC\-NG∗over NG∗\) but lifts mean gain monotonically from\+1\.82%\+1\.82\\%to\+2\.39%\+2\.39\\%to\+2\.56%\+2\.56\\%; type\-conditioning is thus effectively free while reliably positive\.*\(ii\) Aggregation direction:*plain SF adds only𝒪​\(N​d\)\\mathcal\{O\}\(Nd\), while LF adds𝒪​\(N​d2\)\\mathcal\{O\}\(Nd^\{2\}\); after NG/TC gating, sum\-style and linear\-style variants have the same leading𝒪​\(N​d2\)\\mathcal\{O\}\(Nd^\{2\}\)fusion order\. Yet sum\-style yields\+3\.03%\+3\.03\\%vs\.\+1\.48%\+1\.48\\%for linear\-style, so allocating the fusion budget to gated summation is more effective than linear mixing in this regime\. The intersection of the two directions,TC\-NGSF, attains the best single\-operator mean gain \(\+3\.25%\+3\.25\\%\) at only9\.439\.43M parameters, which is cheaper than both TC\-NGLF \(9\.839\.83M\) and NGLF \(9\.789\.78M\)\. Finally, because the temporal switches have identical parameter and computational complexity, this comparison isolates the temporal operator itself:RoTA\-only\(r110\_s110\) gives the highest aggregate gain \(\+3\.42%\+3\.42\\%\), clearly aboveRTE\-only\(r001\_s001,\+2\.83%\+2\.83\\%\)\. Thus,TC\-NGSF under RoTA\-onlyemerges as the most suitable THGFM configuration: it lies at the knee of the accuracy–cost curve, and outperforms both plain and linear\-style fusion on the cross\-task average\.

## 6Conclusion

We proposed THGFM, a dual\-branch temporal heterogeneous graph fusion model that pairs a shared\-space branch \(SSTA\) with a relation\-partitioned branch \(RTTA\), fuses them through a type\-conditioned non\-competitive gated sum mechanism \(TC\-NGSF\), and injects relative time into attention via rotary encoding \(RoTA\)\. THGFM consistently outperforms HGT on OAG\-CS, OGBN\-MAG, HTAG\-ArXiv, and HTAG\-DBLP, reaching up to\+12\.37%\+12\.37\\%on OAG\-CS PV and a\+3\.25%\+3\.25\\%six\-task mean gain\. Three directions remain open: \(i\) developing globally consistent node\-time assignment schemes compatible with mini\-batch sampling, to address the induced\-time inconsistency discussed in Section[3](https://arxiv.org/html/2607.27303#S3); \(ii\) scaling THGFM into a temporal heterogeneous graph foundation model\[[1](https://arxiv.org/html/2607.27303#bib.bib3)\]pretrained across more other graphs; and \(iii\) applying THGFM to Relation Deep Learning\.

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