A Locality Radius Framework for Understanding Relational Inductive Bias in Database Learning

Foreign key discovery and related schema-level prediction tasks are often modeled using graph neural networks (GNNs), implicitly assuming that relational inductive bias improves performance. However, it remains unclear when multi-hop structural reasoning is actually necessary. In this work, we introduce locality radius, a formal measure of the minimum structural neighborhood required to determine a prediction in relational schemas. We hypothesize that model performance depends critically on alignment between task locality radius and architectural aggregation depth. We conduct a controlled empirical study across foreign key prediction, join cost estimation, blast radius regression, cascade impact classification, and additional graph-derived schema tasks. Our evaluation includes multi-seed experiments, capacity-matched comparisons, statistical significance testing, scaling analysis, and synthetic radius-controlled benchmarks. Results reveal a consistent bias-radius alignment effect.

💡 Research Summary

The paper introduces a formal notion called “locality radius” (r*) to quantify the minimal structural context required for a correct prediction on relational database schemas. A schema is represented as a labeled graph whose nodes are tables and attributes and whose edges capture table‑attribute membership as well as candidate attribute‑attribute compatibility. For any candidate edge e (e.g., a potential foreign‑key relationship), the locality radius r* is defined as the smallest integer k such that the label y(e) becomes conditionally independent of the rest of the graph once the k‑hop induced subgraph N_k(e) is observed. In other words, r* measures how many hops of relational information a task truly needs: r* = 0 means pure attribute‑level signals suffice, r* = 1 requires immediate relational context, and r* ≥ 2 indicates that multi‑hop reasoning over foreign‑key chains or other long‑range dependencies is necessary.

Based on this definition the authors formulate the “Bias‑Locality Alignment” hypothesis: a model that aggregates information over k hops (a k‑local GNN) will underfit when k < r*, achieve optimal performance when k ≈ r*, and suffer from over‑smoothing and noise propagation when k ≫ r*. This hypothesis links the architectural inductive bias of graph neural networks directly to a task‑specific structural property.

To test the hypothesis, the authors conduct a rigorously controlled empirical study across five tasks:

1. Foreign‑key (FK) discovery,
2. Join‑cost estimation,
3. Blast‑radius regression,
4. Cascade‑impact classification,
5. Synthetic benchmarks where r* is explicitly set.

For each task they compare three families of models:

• 0‑hop local models (MLP, XGBoost, CatBoost) that use only endpoint attribute features,
• 1‑hop shallow models that add simple structural statistics (degree, neighbor type distribution),
• k‑layer GNNs (GCN‑style message passing) with k ranging from 1 to 5.

All experiments use identical data splits, negative‑sampling strategies, and hyper‑parameter search pipelines. The authors perform multi‑seed runs (≥10 seeds), match model capacities (parameter counts), and apply statistical significance testing (Wilcoxon signed‑rank, bootstrap confidence intervals). They also evaluate scalability by varying schema size from 1 K to 100 K nodes.

Key empirical findings:

• r = 0 tasks (FK discovery)* – Local models dramatically outperform GNNs (ΔF1 = 0.276, p = 0.0002) despite using fewer parameters. This confirms that attribute‑level lexical and type features are sufficient.
• r ≥ 2 tasks (blast‑radius, join‑cost, cascade impact)* – GNNs with depth matching the estimated radius achieve large gains (e.g., R² improves from 0.51 to 0.83 on blast‑radius, p < 0.001). Performance peaks when the number of GNN layers equals the measured r*.
• Over‑smoothing – When depth exceeds r* (e.g., 5‑layer GNN on r* = 2 tasks) performance declines, and node embeddings converge toward the principal eigenvector of the normalized adjacency, indicating loss of discriminative information.
• Correlation – Across all real tasks, the Spearman correlation between GNN advantage and locality radius is 0.69, evidencing a monotonic relationship.
• Synthetic benchmarks – By constructing graphs where the true labeling depends on exactly k‑hop patterns, the authors show that any model restricted to fewer than k hops cannot achieve Bayes‑optimal risk, confirming Proposition 1.

The theoretical contribution includes a formal proposition that the relational radius provides a lower bound on the necessary aggregation depth for any message‑passing architecture. The authors also discuss how r* does not capture non‑linear interactions within the k‑hop neighborhood, so even when k = r* a model still needs sufficient expressive power (e.g., depth‑wise non‑linearities, attention) to exploit the available context.

Practical implications:

1. Task‑driven depth selection – Before deploying a GNN, practitioners should estimate the locality radius (via statistical tests or domain knowledge) and set the number of message‑passing layers accordingly.
2. Hybrid architectures – For heterogeneous workloads where some predictions are local and others require multi‑hop reasoning, a mixture of local classifiers and shallow GNNs can avoid unnecessary over‑smoothing while still capturing long‑range dependencies.
3. Scalability – The study shows that a 3‑layer GNN scales to schemas with 100 K nodes without prohibitive memory or time costs, suggesting that modest depth is sufficient for most real‑world database tasks.

In conclusion, the paper provides a clear, quantifiable framework for understanding when relational inductive bias (embodied by GNNs) is beneficial in database learning. By introducing locality radius and empirically validating the bias‑locality alignment hypothesis, it bridges a gap between inductive bias theory and practical schema‑level machine learning, offering concrete guidelines for model selection and system design in data‑intensive environments.