A small method for schema linking in Text-to-SQL: recovering the tables a question needs — including the bridge tables a join requires but that a retriever scores poorly on surface similarity.

The same lightweight IDF retriever is used for every strategy — no LLM, no embedding model, no API — so the comparison is reproducible from the repo alone. Metric: recall@k = fraction of questions whose entire gold table set is in the top-k.

Multi-table questions (378 of 1,034 — where join structure, and the graph, actually matter):

Beyond the aggregate, edge-path recovers a join-bridge table in 23 cases the plain retriever drops out of the top-3. A real example from the car_1 DB:

"Find the model of the car whose weight is below the average weight." needs car_names and cars_data. A plain retriever ranks cars_data only #4 (outside top-3); edge-path propagates score along the foreign-key path and lifts it to #3, recovering the full join.

python experiments/spider_experiment.py --spider-dir <spider> --examples 3

(The gains are modest — Spider's schemas are small and dense. The method targets large, sparse schemas; see Open Questions.)

When a database has many tables, a retriever surfaces the obviously-relevant ones but misses bridge tables — needed by a join, scored low on their own. The idea: let a high-scoring table lend some of its score to the low-scoring tables it connects to through foreign keys — a "semantic halo" flowing along short paths in the FK graph.

Score is propagated along paths of length ≤ 3 with a polynomial 1/|p|^2 length decay and a boost-only rule (structure can only raise a score, never lower it), so it never demotes a table whose score was already clearly higher. I tried standard Personalized PageRank first; on sparse FK graphs its 1-hop expansion floods the candidate set and washes out the signal, which led to this local, path-based alternative.

src/semhalo/edge_path.py           the edge-path optimiser (relationship source is injectable)
experiments/spider_experiment.py   the reproducible Spider evaluation above
demo/demo.py                       a zero-dependency synthetic illustration of the mechanism

Run python demo/demo.py for a tiny, no-data illustration (a synthetic sparse-FK schema where a low-scored bridge table is lifted into the top ranks).

An early write-up with worked-out properties (order-preservation, scale-invariance, a path-kernel form) exists; the interesting work is still ahead:

1. Provable propagation bounds. The properties above are about the fusion rule, not the propagation itself — can it be recast as a query-guided propagation with convergence / approximation guarantees?
2. Scale. An efficient push-based backend for large, weight-skewed sparse graphs would let this run on much larger schemas.
3. Evaluate properly. Spider's schemas are small and dense; the method targets large, sparse ones, and needs a study on larger-schema benchmarks and on end-to-end SQL accuracy, not just retrieval recall.

Feedback and pointers welcome.

© 2026 Zihan Dai. This repository documents original, ongoing research on edge-path re-ranking for schema linking, first published here on 6 July 2026, and now continued as a supervised research project at the University of Melbourne. All rights reserved — this is not open-source software. If you wish to build on this work, please get in touch: [email protected]