Graph-Aware Reranking and Semantic Proximity

The final stage of the Wikantik search pipeline (Phase 3) is a Graph-Aware Reranker (GraphRerankStep). While Phase 1 and 2 focus on textual and vector similarity, Phase 3 utilizes the topology of the Knowledge Graph to surface related content that might lack direct keyword or vector overlap.

1. The Proximity Heuristic

The reranker operates on a simple but powerful intuition: "If a page mentions entities that are closely connected in the Knowledge Graph to the user's intent, that page is likely highly relevant."

A. Graph Traversal (Multi-Source BFS)

The process begins by resolving query terms into a set of seed entity IDs ( $Q$ ). The system then performs a multi-source Breadth-First Search (BFS) through the kg_edges adjacency map up to a maximum radius ( $H_{max}$ , typically 2).

Distance Calculation: Every reachable entity $e$ is assigned a distance $d(Q, e)$ equal to the shortest undirected hop count from any seed entity.

B. Scoring Function

The proximity score $S_{prox}$ for a candidate page is determined by the maximum proximity of its mentioned entities:

S_{prox}(p) = \max_{m \in \text{Mentions}(p)} \left( \frac{1}{1 + d(Q, m)} \right)

Why Max?: Using the maximum (rather than the mean or sum) ensures that a single high-quality match is enough to boost a page, preventing relevant content from being diluted by "noisy" co-mentions of unrelated entities.

2. Implementation: The GraphRerankStep

The implementation is designed for high-performance and Graceful Degradation.

Candidate Anchoring: The input to the step is the fused list from Phase 2 (RRF). No pages are added or removed; the candidate set is fixed.
Bulk Loading: The PageMentionsLoader fetches all entity mentions for the entire candidate set (e.g., top 100 pages) in a single SQL round-trip using the ANY(?) operator.
Base Rank Scaling: To ensure the boost is proportional to the initial relevance, each page is assigned a base score derived from its fused rank: $B(p) = 1.0 - (\text{rank} / N)$ .
The Boost Calculation:
$\text{FinalScore}(p) = B(p) + (\text{boost\_weight} \times S_{prox}(p))$
Stable Reordering: The list is re-sorted by the final score. Because the sort is stable, pages with equal proximity scores retain their relative RRF ordering.

3. Fail-Safe Mechanics

The reranker is a "non-critical" enhancement. The GraphRerankStep is wrapped in a fail-closed logic:

Disabled: If the graph feature is off, returns input list verbatim.
Index Not Ready: If the kg_edges table is being rebuilt or exceeds memory caps, returns input list.
Zero Matches: If no query entities are resolved or no candidates mention the graph neighborhood, the proximity score is $0.0$ for all, and the RRF order is preserved bit-identically.

See Also:

Wikantik Search and Retrieval — The 4-phase overview.
Spectral Graph Theory — The theory of graph shape.
Knowledge Graph Extraction — Generating the co-mention edges.