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Query2Box Multi-Hop Traversal

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About This MicroSim

Query2Box represents a query's answer set as an axis-aligned hyperrectangle (box) in embedding space. Entities inside the box are candidate answers. Projection operators shift and resize the box along each relation step; intersection operators narrow it to the region satisfying all conditions.

This MicroSim shows a 2D KG embedding space. A query panel on the left lets you compose \(1p\) (single-hop), \(2p\) (two-hop chain), and \(2i\) (two-chain intersection) queries. As you step through the query, boxes animate in the embedding space and entities inside the final box are highlighted as answers.

Learning objective (Bloom's Analyze (Level 4)): Watch Query2Box project and intersect axis-aligned boxes to resolve \(1p\), \(2p\), and \(2i\) queries over a toy knowledge graph. Each projection shifts and widens the box; intersection narrows to the overlap.

How to Use

  1. Choose a query type — \(1p\), \(2p\), or \(2i\) from the dropdown.
  2. Select a relation — choose the relation for each hop (e.g., "bornIn", "locatedIn").
  3. Step through — click "Next" to apply each projection or intersection operation.
  4. Read the answer — entities inside the final box are the candidate answers.
  5. Switch anchors — change the anchor entity (\(r_1\) or \(r_2\)) to see how the boxes shift.

Iframe Embed Code

You can embed this MicroSim in any web page with the following HTML:

<iframe src="https://AnvithPothula.github.io/graph-neural-networks-textbook/sims/ch13-kg-query-traversal/main.html"
        height="522"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Undergraduate / Graduate (College Level)

Duration

20–30 minutes

Prerequisites

Knowledge graph triples and completion (Chapter 12). Set intersection. Embedding space basics.

Activities

  1. Compose a \(2p\) query: (Einstein) → bornIn → ? → locatedIn → ?. Step through and identify which entities fall in the final box.
  2. Construct a \(2i\) query. Before applying intersection, observe how large the two individual query boxes are. After intersection, how much did the answer set shrink?
  3. Explain why boxes are a better representation than points for multi-hop queries with uncertain or multiple answers.

Assessment Question

Derive the projection operator p(q, r) for Query2Box: given a box q = (center, offset), write the update rule for applying relation r. Why must the offset grow monotonically during projection?

References

  1. Ren et al. (2020). Query2box: Reasoning over Knowledge Graphs in Vector Space Using Box Embeddings. ICLR.
  2. Hamilton et al. (2018). Embedding Methods for Link Prediction. Knowledge Graph Handbook.

Part of Chapter 13: Reasoning over Knowledge Graphs. Return to the chapter page or browse all MicroSims.