DuetGraph: Dual-Pathway Global-Local KG Reasoning

• DuetGraph is a knowledge-graph reasoning framework that segregates local message passing and global attention to prevent score over-smoothing.
• It adaptively fuses dual pathways via a learnable gate and employs a two-stage coarse-to-fine optimization to enhance candidate discrimination.
• Empirical results show up to +8.7% Hits@1 improvement and 1.8× faster training, validating its state-of-the-art performance in KG completion.

DuetGraph is a knowledge-graph reasoning mechanism introduced for coarse-to-fine reasoning with dual-pathway global-local fusion. It is designed to address score over-smoothing in knowledge graph (KG) reasoning, a phenomenon in which correct and incorrect candidate entities receive nearly indistinguishable scores after deep, mixed stacking of local message passing and global attention layers. The method separates local and global computations into two distinct pathways, fuses them adaptively, and combines this architecture with a two-stage coarse-to-fine optimization that partitions entities into high- and low-score subsets. Reported results show state-of-the-art performance on inductive and transductive benchmarks, with up to an 8.7% improvement in reasoning quality and a 1.8$\times$ acceleration in training efficiency (Li et al., 15 Jul 2025).

1. Problem setting and motivation

Knowledge-graph reasoning methods must simultaneously exploit local neighborhood signals and global structural information. In the formulation associated with DuetGraph, local information is handled through multi-hop propagation or message passing, whereas global information is modeled through attention over long-range dependencies. Existing hybrid methods are described as often relying on stacking graph neural network layers and transformer-attention layers in a single sequence. According to the DuetGraph formulation, such deep, mixed stacking empirically leads to score over-smoothing, which blurs the distinction between correct and incorrect answers and impairs ranking reliability (Li et al., 15 Jul 2025).

The paper characterizes this effect by examining the normalized score gap between correct and incorrect candidates. If $S_{\mathrm{correct}}$ and $S_{\mathrm{incorrect}}$ are the final logits, the relevant quantity is

$$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$

For one-stage stacked models, including HousE, RED-GNN, and SAttLE, the distribution of this quantity is described as piling up near zero, indicating weak discrimination between correct and incorrect answers (Li et al., 15 Jul 2025).

DuetGraph addresses this failure mode through two linked ideas. First, it segregates local and global processing into parallel pathways rather than stacking them. Second, it applies a coarse-to-fine optimization that narrows the candidate space and sharpens the score gap between high- and low-score subsets. The stated objective is not merely architectural modularity, but the preservation of representational discrimination during reasoning (Li et al., 15 Jul 2025).

2. Dual-pathway global-local fusion

At each reasoning step, DuetGraph produces two sets of entity representations: one from a local pathway based on message passing and one from a global pathway based on attention over all entities. These are then fused through a learnable gate $\alpha$, after which an MLP maps the fused representations to scores over candidate tail entities (Li et al., 15 Jul 2025).

Local pathway

The knowledge graph is represented as $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$, and a query has the form $(h,r,?)$. The local pathway is described using a small GNN, exemplified by a 2-layer GCN. Let

$A \in \mathbb{R}^{|\mathcal V|\times|\mathcal V|}$

be the symmetrically normalized adjacency matrix including self-loops, and let $$\mathbf{X}^{(0)}\in\mathbb{R}^{|\mathcal V|\times d}$$ denote the initial entity embeddings, with the head entity embedding possibly appended with a relation embedding. A standard $\ell$-layer GCN update is

$S_{\mathrm{correct}}$0

where $S_{\mathrm{correct}}$1 and $S_{\mathrm{correct}}$2 is a nonlinearity. The local pathway output is

$S_{\mathrm{correct}}$3

with $S_{\mathrm{correct}}$4 the number of message-passing layers (Li et al., 15 Jul 2025).

Global pathway

In parallel, DuetGraph applies a lightweight transformer or self-attention module to all entity embeddings $S_{\mathrm{correct}}$5. For a single-headed attention layer,

$S_{\mathrm{correct}}$6

and the attention scores and outputs are

$S_{\mathrm{correct}}$7

The account notes that the model may use $S_{\mathrm{correct}}$8 such layers and/or multi-head attention, but emphasizes that the global attention layers do not consume GNN-updated features, and the GNN pathway does not consume attention-updated features. This separation is central to the model’s stated mechanism for preventing mutual interference (Li et al., 15 Jul 2025).

Adaptive fusion

After the two pathways produce $S_{\mathrm{correct}}$9 and $S_{\mathrm{incorrect}}$0, DuetGraph fuses them using a learnable scalar $S_{\mathrm{incorrect}}$1:

$S_{\mathrm{incorrect}}$2

The fused representation matrix $S_{\mathrm{incorrect}}$3 is then passed through an MLP shared across entities to produce logits $S_{\mathrm{incorrect}}$4 for candidate tails. In the DuetGraph description, this fusion is adaptive rather than hard-coded, allowing the model to weight local and global evidence jointly while still preserving the independence of their upstream computations (Li et al., 15 Jul 2025).

3. Theoretical account of over-smoothing mitigation

DuetGraph includes a theoretical justification for the claim that segregated dual-pathway fusion mitigates over-smoothing. The one-stage stacked model is associated with a linearized operator

$S_{\mathrm{incorrect}}$5

whereas the dual-pathway fusion operator is

$S_{\mathrm{incorrect}}$6

Lemma 1 states that after $S_{\mathrm{incorrect}}$7 layers, the score gap between any two entities $S_{\mathrm{incorrect}}$8 and $S_{\mathrm{incorrect}}$9 is bounded by

$$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$0

where $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$1 is the MLP’s Lipschitz constant. The paper further states in Theorem 1 that $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$2 under a mild condition on $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$3, implying that the dual-pathway operator slows the exponential decay of score gaps as depth grows (Li et al., 15 Jul 2025).

Within the paper’s framing, the relevance of this bound is that over-smoothing is manifested as vanishing score separation between entities. By preserving a larger effective operator norm in the dual-pathway setting, DuetGraph is argued to retain more discriminative scores at larger depth. This does not eliminate the dependence on depth, but it changes the rate at which score gaps deteriorate (Li et al., 15 Jul 2025).

The paper also gives a complexity comparison. If the local pathway uses $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$4 GNN layers, each with cost $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$5, and the global pathway uses $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$6 attention layers, each with cost $$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$7, then running the two pathways in parallel yields

$$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$8

By contrast, a stacked one-pathway design has cost

$$\frac{\lvert S_{\mathrm{correct}} - S_{\mathrm{incorrect}}\rvert}{\mathrm{std}(S)}.$$9

The paper identifies this distinction as one reason for the reported 1.8$\alpha$0 speedup in wall-clock training time (Li et al., 15 Jul 2025).

4. Coarse-to-fine reasoning optimization

Beyond the dual-pathway architecture, DuetGraph introduces a two-stage reasoning procedure. A single one-shot model is described as having limited discrimination because it scores all entities jointly and selects the top one. DuetGraph instead separates reasoning into a coarse-grained stage followed by a fine-grained stage (Li et al., 15 Jul 2025).

In Stage 1, an external coarse model—triplet-based, GNN-based, or hybrid—produces a full score table for a query $\alpha$1:

$\alpha$2

The entities are sorted by descending score and split at rank $\alpha$3 into

$\alpha$4

In Stage 2, DuetGraph re-scores the two subsets separately using the full dual-pathway fusion model. Let

$\alpha$5

The method then computes the gap

$\alpha$6

If $\alpha$7, where $\alpha$8 is a small threshold, the output is $\alpha$9; otherwise it is $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$0. The paper explicitly notes that this mechanism can rescue a correct answer that was ranked just outside the top-$\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$1 in the coarse stage but scores significantly higher after fine-grained re-evaluation (Li et al., 15 Jul 2025).

The theoretical effect of this split is given in Theorem 2. Under mild assumptions on score distributions, the expected gap between the maxima of the two subsets is lower-bounded by a constant fraction of the global score standard deviation $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$2:

$\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$3

for typical $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$4. The paper contrasts this with baseline one-stage methods that show gaps below $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$5, arguing that the split-and-compare procedure further improves discrimination and alleviates over-smoothing (Li et al., 15 Jul 2025).

A common misconception would be to treat the coarse stage as an internal pretraining phase or an iterative refinement loop. The described inference regime does not do this: no inner gradient updates occur during inference, and both coarse and fine models are fixed (Li et al., 15 Jul 2025).

5. Training regime and inference procedure

During training, the dual-pathway model is optimized with a negative-sampling log-sigmoid loss. For each true triple $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$6 and a set of negative tail entities $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$7, the loss is

$\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$8

where $\mathcal G=(\mathcal V,\mathcal E,\mathcal R)$9. Negative tail entities are sampled uniformly from $(h,r,?)$0 (Li et al., 15 Jul 2025).

The optimizer is Adam. The reported hyper-parameter search includes learning rate in $(h,r,?)$1 and weight decay in $(h,r,?)$2. Typical embedding dimensions are $(h,r,?)$3, message-passing depth $(h,r,?)$4, attention depth $(h,r,?)$5, and negative sample size in $(h,r,?)$6 (Li et al., 15 Jul 2025).

Inference combines coarse ranking and restricted fine scoring. DuetGraph is called only on the high-score and low-score subsets rather than on the entire entity set. The sorting cost is reported as $(h,r,?)$7 and described as negligible relative to $(h,r,?)$8 (Li et al., 15 Jul 2025). A plausible implication is that the efficiency gain is tied not only to parallel local-global computation but also to the decision to invoke the full fine-stage model only on candidate subsets.

The method therefore occupies an intermediate position between standard full-catalog scoring and narrowly pruned retrieval-based methods. It remains a KG completion approach that scores entity candidates, but its fine-grained reasoning stage is conditioned on an upstream partition of the candidate space rather than a single global pass (Li et al., 15 Jul 2025).

6. Empirical results, ablations, and significance

The empirical evaluation spans inductive and transductive settings. The inductive experiments use disjoint-entity splits of FB15k-237, WN18RR, and NELL-995, with four divisions each. The transductive experiments use standard FB15k-237, WN18RR, NELL-995, and YAGO3-10. Evaluation metrics are Mean Reciprocal Rank (MRR), Hits@1, and Hits@10 under the filtered setting (Li et al., 15 Jul 2025).

The baseline set includes triplet-based methods (TransE, DistMult, RotatE, HousE), GNN-based methods (CompGCN, NBFNet, RED-GNN, A*Net, AdaProp, ULTRA), transformer-based methods (HittER, SAttLE, KGT5, N-Former), hybrid methods (KnowFormer), and others (MetaSD, RNNLogic, TuckER-IVR) (Li et al., 15 Jul 2025).

On the 12 inductive splits, DuetGraph is reported to outrank all baselines, with improvements of up to +8.7% in Hits@1 and +8.6% in MRR over the strongest prior, KnowFormer. On the four transductive datasets, the reported gains include +0.026 MRR and +1.8% Hits@1 on FB15k-237 relative to KnowFormer, +0.015 MRR and +1.4% Hits@1 on WN18RR, and similar gains on NELL-995 and YAGO3-10. The paper also reports overall gains of up to +37.2% relative MRR improvement versus the earliest baselines and +52.8% Hits@1 (Li et al., 15 Jul 2025).

Training-efficiency results are presented on FB15k-237 and YAGO3-10. DuetGraph is reported to reach top Hits@1 in roughly half the wall-clock time of the next-best method, KnowFormer, which the paper interprets as empirical validation of the parallel-pathway speedup (Li et al., 15 Jul 2025).

The ablation studies on the four transductive datasets isolate the contributions of individual components. Removing the local pathway causes a -1.0% Hits@1 drop; removing the global pathway causes -1.2%; removing coarse-to-fine reasoning causes -2.5%; removing dual-pathway fusion in favor of a one-stage stacked design causes -9.8%; and removing the threshold $(h,r,?)$9 while always selecting from the high subset causes -4.4% (Li et al., 15 Jul 2025). These results indicate that neither pathway alone accounts for the reported performance, and that the coarse-to-fine inference rule is not a peripheral addition.

An additional ablation swaps the coarse model among HousE, RED-GNN, and KnowFormer, with the fine stage of DuetGraph still improving each by +1.7 to 2.6 points of Hits@1 (Li et al., 15 Jul 2025). This suggests that the fine-stage mechanism is not tied to a single coarse-model family. The paper’s broader claim is that the theoretical ablations—Theorems 1–3 and Lemmas 1–3—align with the empirical ablations in attributing gains to both dual-pathway gating and coarse-to-fine splitting.

In significance, DuetGraph is best understood as a KG reasoning framework organized around two anti-over-smoothing principles: segregated global-local computation and candidate-space partition with thresholded comparison. The reported evidence positions these principles as jointly responsible for improved discriminability, faster training, and stronger KG completion accuracy across both inductive and transductive regimes (Li et al., 15 Jul 2025).