Omission-Aware Message-Passing in Graph Models

• Omission-aware message-passing is a family of techniques that explicitly treats missing data as informative structural features in graph-based inference.
• It distinguishes between intra-source and inter-source omission relations to optimize prediction accuracy and decision-making in partially observed settings.
• Applications span misinformation detection, data completion, and knowledge graph inference, showing measurable improvements over traditional methods.

Omission-aware message-passing is a family of techniques for relational modeling and inference in settings characterized by incomplete, missing, or omitted observations. These techniques fuse the principles of message-passing over graphs with explicit modeling of omissions and omissions' consequences, providing a rigorous mechanism for tasks where hidden structure or omitted relations fundamentally affect prediction, generalization, or decision-making. Omission-aware message-passing underpins architectures and inference strategies for data completion under partial observation, misinformation detection with latent omission intent, principled social network reconstruction, and knowledge-graph completion in open-world scenarios.

1. Defining Omission-Oriented Relation Modeling

Omission-oriented relation modeling treats the absence or omission of information not as noise to be ignored but as an informative structural feature of the data. Rather than standard message-passing, which aggregates information locally or over relational graphs without distinction between known and omitted observations, omission-aware approaches construct explicit representations of what is missing—either at the edge, node, or relation level—and integrate these representations into the message-passing pipeline.

In OmiGraph, omission-oriented relation modeling distinguishes two classes of edges: (a) intra-source relations, measuring contextual dependencies within a data source (reflecting coherence or internal contradiction), and (b) inter-source omission-intent relations, defined between a target and its contextual environment, capturing why particular pieces of information are omitted (Wang et al., 1 Dec 2025). In the OR-Net framework for data completion, omission-aware relational message-passing is implemented as distinct inner-relationship and cross-relationship modules, encoding both available context and connections to missing or unobserved variables (Feng et al., 2021). In statistical network cognition and estimation, omission-oriented inference is formalized in the explicit quantification and balancing of omission (false-negative) rates against commission (false-positive) rates, guiding optimal aggregation (Yenigun et al., 2016). In knowledge-graph inference, the multi-label classification in SHALLoM treats all missing relations for observed entity pairs as legitimate prediction targets, aligning the modeling with the open-world assumption (Demir et al., 2021).

2. Omission-Aware Graph Construction and Edge Attribution

Omission-aware methods use customized graph-based formulations, in which nodes represent context points, variables, segments, or entities, and edge attributes are instantiated to explicitly encode presence, absence, or hypothesized omission relations. In OmiGraph, the attributed graph $\mathcal{G}=(\mathcal{V}, \mathcal{E})$ encodes both internal segment dependencies (intra-source) and omission-intent edges connecting each target segment to complementary segments in the contextual environment.

For each intra-source pair, an edge vector is computed as

$$\mathbf{e}_{\mathrm{intra}}^{ij} = \mathrm{MLP} \left( \mathbf{h}_i \,\|\, \mathbf{h}_j \,\|\, |\mathbf{h}_i - \mathbf{h}_j| \right)$$

where $\mathbf{h}_i$ and $\mathbf{h}_j$ are segment embeddings, $\|\,$ denotes concatenation, and $|\cdot|$ is element-wise absolute difference.

For each inter-source omission-intent edge, an LLM generates a free-text explanation of hypothesized omission, which is embedded by a pre-trained LLM: $$\mathbf{e}_{\mathrm{inter}}^{ij} = \mathrm{PLM}\bigl(\mathcal{M}(s_\text{tgt}^i,\,s_\text{ctx}^j)\bigr)$$ These edge attributions inform subsequent message-passing and are type-encoded via learnable edge-type embeddings (Wang et al., 1 Dec 2025).

In OR-Net, position-aware graphs are constructed over context and target sets, with learned geometric edge embeddings $r_{ij}$ computed from spatial or structural coordinates, capturing topology among observed and unobserved points. The omission of direct links (missing data) is systematically modeled by cross-relationship module construction (Feng et al., 2021).

3. Message-Passing Mechanisms and Integration

Message-passing in omission-aware settings generalizes conventional GNN or latent-variable message-passing to propagate information not only about present context but about absences, uncertainties, and omission semantics.

OmiGraph Omission-Aware Message-Passing

Message propagation is modulated by attention weights over edge-enhanced node representations: $$\alpha_{ij} = \mathrm{softmax} \left( \left(\mathbf{h}_i^{(l-1)} + \widehat{\mathbf{e}_{t}^{ij}} \right) \cdot \left(\mathbf{h}_j^{(l-1)} + \widehat{\mathbf{e}_{t}^{ij}} \right) \right)$$ where edge vectors are type-enriched as

$$\widehat{\mathbf{e}_{t}^{ij}} = \mathrm{MLP} \left( \mathbf{h}_t \,\|\, \mathbf{e}_{t}^{ij} \right),\quad t\in\{\mathrm{intra},\mathrm{inter}\}$$

This specialized message-passing pipeline allows the GNN to distinguish standard context aggregation from the propagation of “what was left unsaid.” Global aggregation is achieved via a “super-root” node, fusing messages to prevent over-smoothing and ensure global narrative information is integrated at each segment (Wang et al., 1 Dec 2025).

OR-Net Inner/Cross-Relationship Message-Passing

In OR-Net, the Inner-Relationship Module aggregates context relations: $$h_i' = \sigma \left( \sum_{j\in N(i)} \alpha_{ij} m_{ij} \right)$$ while the Cross-Relationship Module propagates messages from observed contexts to missing targets, handling the explicit structure of omissions in the context–target bipartition (Feng et al., 2021).

Omission-Aware Aggregation in Statistical Networks

In omission-oriented network reconstruction, message-passing is not over a learned neural network but consists of thresholded aggregation of observations, balancing omission and commission error rates. The process systematically aggregates respondent perceptions, adjusting the threshold $k$ to optimize omission/commission trade-off via a weighted ROC criterion (Yenigun et al., 2016).

4. Loss Functions, Training Objectives, and Optimization

Omission-aware message-passing architectures rely on objectives that tie relational inference to end-task supervision but do not directly supervise omissions. In OmiGraph, all graph, message, and relation parameters are optimized using a standard binary cross-entropy on the final task (e.g., misinformation class), with no separate objective on omission-intent or intra-source relations: $$\mathcal{L}_\mathrm{cls} = -\,\bigl[y\log(\hat y)\;+\;(1-y)\log(1-\hat y)\bigr]$$ The edge and message representations relevant for omissions are refined via backpropagation through the global discriminative loss (Wang et al., 1 Dec 2025).

In OR-Net, the training objective is a conditional variational ELBO, supplemented with an information bottleneck: $L = L_D + \lambda L_{IB}$ where $L_D$ is the usual expected log-likelihood minus KL divergence term, and $L_{IB}$ penalizes information in latent $z$ that is specific to the targets but not the context, discouraging overfitting to “noisy” unobserved data (Feng et al., 2021). This suggests a general principle: the loss function encourages latent and relational representations to reflect both empirical contexts and patterns in what is omitted.

In omission-aware threshold-based aggregation, the optimal threshold is chosen via minimization of a (possibly weighted) ROC distance, balancing omission and commission errors for robust relational inference (Yenigun et al., 2016).

5. Applications and Empirical Outcomes

Omission-aware message-passing has demonstrable benefits in a range of inference and prediction domains:

• Misinformation Detection: OmiGraph achieves mean improvements of +5.4% F1 and +5.3% accuracy on two large-scale misinformation detection benchmarks, outperforming BERT, MSynFD, and external-evidence verifiers. Ablation confirms both omission-intent and intra-source relation modeling are critical; removing either reduces F1 scores by up to 8 points (Wang et al., 1 Dec 2025).
• Data Completion Under Partial Observation: OR-Net, using explicit inner- and cross-relationship modules, yields RMSE 0.08$\pm$0.01 (vs. 0.15$\pm$0.02 for Attentive NP) on 1D function regression and MSE 0.049$\pm$0.005 (vs. 0.056$\pm$0.010 for ANP and 0.073$\pm$0.013 for CNP) on MNIST image completion. On CelebA with 10% pixel observation, omission-aware modeling reduces MSE from 0.032 (ANP) to 0.021 (Feng et al., 2021).
• Knowledge Graph Completion: SHALLoM applies omission-oriented multi-label relation prediction, avoiding negative sampling and supporting the open-world assumption. On WN18RR, SHALLoM achieves up to +8 percentage point improvement in Hits@5 and trains in less than 8 minutes (Demir et al., 2021).
• Social Network Estimation: Weighted ROC-based omission-aware aggregation methods robustly recover network structure, with similarity index $S_{14}$ converging to 1 as sample size grows. The approach offers principled tuning between omission vs. commission costs (Yenigun et al., 2016).

6. Theoretical and Practical Considerations

Omission-aware frameworks demonstrate that neglected or omitted relational evidence can be modeled systematically to enhance both discriminative and generative performance. The fundamental premise underlying these techniques is that omission-related structure (missing links, segments, predicates, respondent errors) reflects information, not mere absence. In practical terms:

• The exact graph construction and edge attribution scheme must reflect the specific omission mechanism of the domain (e.g., narrative omission vs. partial data vs. social perception).
• The design of edge and relation representations must enable both high-order semantic modeling (via LLMs or learned embeddings) and efficient message-passing.
• Weighted loss or aggregation functions, whether variational, cross-entropy, or ROC-based, can calibrate the system's sensitivity to omissions according to real-world cost structure.

A plausible implication is that as neural and statistical relational inference systems are increasingly deployed in settings with high degrees of missingness, omission-aware message-passing architectures will provide a foundation for robust and explainable inference.

7. Connections to Related Methods and Limitations

Omission-aware message-passing extends canonical GNN methodologies by encoding the semantic and structural significance of absences, rather than imputing or ignoring them. This distinguishes it from standard node-classification GNNs, standard latent variable imputation, and unstructured negative-sampling-based approaches. For instance, SHALLoM’s omission-oriented formulation eliminates negative sampling and respects the open-world setting, but remains limited to observed entity pairs and may miss multi-hop patterns (Demir et al., 2021). OmiGraph’s reliance on LLM-generated omission-intent explanations introduces a dependency on LLM accuracy and interpretability (Wang et al., 1 Dec 2025). In social networks, the thresholded aggregation paradigm is sensitive to estimates of network sparsity and may require block decomposition for large-scale settings (Yenigun et al., 2016).

In summary, omission-aware message-passing unifies a diverse set of relational inference tasks by treating absence as structure, encoding both observed and unobserved relations, and coupling these representations to domain-appropriate aggregation and optimization schemes. This provides a systematic approach to robust inference in complex, partially observed, or adversarial information environments.