GNN Power Load Forecasting: A Diagnostic Protocol to Disentangle Parameter Sharing from Neighbor Access

Why a Diagnostic Protocol Is Needed

Graph neural networks (GNNs) are often cited in power load forecasting as evidence that "graph structure brings gains." But a GNN does two things at once: it shares parameters across sequences and it reads neighbor sequences. Any improvement over a non-graph model may come from the former rather than the latter. Without disentangling the source of the gain, it is hard to judge whether maintaining graph structure is worth the effort.

To this end, researchers propose a model diagnostic protocol that compares a GNN against three reference models: a per-node independent network, a cross-node shared network without neighbors, and an isomorphic GNN with edges removed. In addition, degree-preserving rewiring is used to test whether neighbor identity truly matters. After tuning the baseline on French regional load and UK low-voltage feeder data, the protocol is further applied to scenarios with deliberately shortened node histories—for example, when only recent observations are available under non-stationary demand.

Design Logic of the Diagnostic Protocol

The Meaning of the Three Reference Models

The per-node network represents a fully personalized baseline; the shared network strips away neighbor information and retains only the inductive bias from parameter sharing; the edge-removed GNN keeps the architecture unchanged but cuts off neighborhood access. Through these three layers of comparison, one can pinpoint whether the gain comes from parameter sharing, neighbor reading, or their interaction.

Inductive bias refers to the prior constraints a model imposes on its hypothesis space during learning, making it favor certain solutions over others. In load forecasting, sharing parameters across sequences is itself an inductive bias: it assumes a commonality in the mapping relationships across different nodes, thereby providing a regularization effect when data is limited and reducing the risk of overfitting. A per-node independent network has almost no such cross-sequence constraint—each node is fitted separately, offering high flexibility but large variance. By stripping away neighbor information, the shared network isolates exactly the contribution of this pure inductive bias from parameter sharing. Understanding this concept helps clarify that a GNN's gain may not come from the graph structure itself, but from the shared-parameter mechanism inherent in its backbone.

The Role of Degree-Preserving Rewiring

If neighbor identity matters, random rewiring (keeping the degree distribution unchanged) should significantly degrade model performance. Conversely, if performance barely changes after rewiring, the model is merely exploiting the smoothing effect of neighborhood aggregation rather than specific adjacency relationships. This test provides direct evidence for whether the graph is worth maintaining.

Degree-preserving rewiring is a graph perturbation technique: while keeping each node's degree unchanged, edge endpoints are randomly swapped to generate a control graph with the same degree distribution as the original but randomized adjacency. Its core logic is controlling variables—if model performance drops significantly after rewiring, the model genuinely depends on specific neighbor identities; if performance barely changes, the model benefits only from the smoothing or denoising effect of neighborhood aggregation rather than true topological information. This method is widely used in graph learning evaluation to test whether graph structure is effectively utilized, and is a key tool for distinguishing "true graph gain" from "aggregation-smoothing illusion."

Key Finding: Parameter Sharing Is the Main Source of Gain

On feeder data, parameter sharing recovers most of the error gap between node-specific models and the GNN—about two-thirds relative to the regularized baseline. Adding edges to the same backbone yields a smaller gain, more than half of which disappears after rewiring.

On customer consumption sequences with shorter windows, the neighbor mean actually degrades per-node models, and the edge gain cannot be reliably distinguished from zero. On French regional data, when each node's own history is sufficiently informative, the ranking between per-node models and the GNN varies with tuning. Synthetic studies indicate that noisy local measurements are one of the few cases where neighbor information may be beneficial.

Across all three datasets, none showed that edges contributed the majority of the GNN's advantage over node-specific models. This means that forecasting gains should not be attributed directly to graph structure without per-node and shared reference comparisons.

The error gap in this context refers to the difference in prediction error between a node-specific model (per-node independent network) and the GNN. Researchers describe it as "parameter sharing recovers about two-thirds of the error gap": when the GNN is replaced by a network that only shares parameters without reading neighbors, its error is already close to the GNN's, indicating that most of the advantage is captured by the shared backbone before edges are removed. The remaining edge-derived gain is smaller, and most of it disappears after degree-preserving rewiring, further suggesting that this portion of the gain is insensitive to neighbor identity. This gap-decomposition approach is the core quantitative tool of the diagnostic protocol, turning "is the graph worth it" from a qualitative judgment into a comparable numerical conclusion.

Additional Observation on Online Aggregation

In an exploratory online aggregation, graph models and non-graph predictors showed complementarity, but the weight assigned to the GNN was disproportionate to its actual contribution. This suggests that ensemble strategies should allocate weights based on diagnosis rather than default assumptions.

Online aggregation/ensemble refers to dynamically combining the outputs of multiple predictors during sequence forecasting; common strategies include inverse-error weighting, exponential weighting, or meta-learning-based weight allocation. The exploratory observation in this article finds that graph models and non-graph predictors are complementary, but the system assigns more weight to the GNN than its actual contribution warrants, suggesting that default ensemble mechanisms may overestimate graph models. This implies that weight allocation in online aggregation should be based on the gain attribution provided by the diagnostic protocol, rather than simply assuming "graph models are stronger" or relying on passive feedback from historical errors, which could otherwise introduce suboptimal ensemble bias.

Practical Implications

Before deploying a GNN for load forecasting, at minimum the per-node and shared-parameter references should be run. Only when edges still yield a stable gain under the rewiring test is there sufficient reason to maintain graph structure. For scenarios with short history windows and noisy local measurements, neighbor information may be useful, but this must be verified case by case.

The value of this diagnostic protocol lies not in rejecting GNNs, but in turning "is the graph worth it" from an intuitive judgment into an actionable comparative experiment.

One-line Summary

GNN load forecasting gains come mainly from parameter sharing rather than neighbor reading, and must be disentangled and verified using a diagnostic protocol.

Paragraph Summary

The article proposes a GNN model diagnostic protocol to disentangle whether the gains of graph neural networks in power load forecasting come from cross-sequence parameter sharing or neighbor information reading. The protocol sets up three references—a per-node independent network, a shared network without neighbors, and an edge-removed GNN—supplemented by degree-preserving rewiring to test the importance of neighbor identity. Experiments on French regional load and UK low-voltage feeder data show that parameter sharing recovers about two-thirds of the error gap between node-specific models and the GNN, while the edge-derived gain is smaller and mostly disappears after rewiring; none of the three datasets showed edges contributing the main advantage of the GNN over node models. The article accordingly recommends running at least the per-node and shared-parameter references before deployment, and notes that GNN weight in online aggregation is disproportionate to its actual contribution, so ensembles should be based on diagnosis rather than default assumptions.