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An Evaluation of Approaches to Train Embeddings for Logical Inference (Student Abstract)
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Improves triplet-loss training of an atom embedding model for guided backward-chaining over Datalog knowledge bases, using outlier-atom generation, rule-based mutations for positive/negative atoms, and hard-sample refinement, and reports fewer nodes explored than standard and previous unification reasoners.
Problem
Backward-chaining reasoners over knowledge bases explore huge search spaces without manual optimization; learned embeddings for logical atoms need better training to guide search efficiently.
Approach
Replace random triplet generation with rule-based mutations of anchor atoms to produce positive and negative atoms, oversample outlier atoms with repeated variables/constants, and refine the model on the highest-loss triplets to train an atom embedding model that guides backward chaining.
Key results
- On 250-statement KBs, the new embeddings reasoner explored 90.4 nodes on average versus 224.0 for previous unification and 17,204.0 for the standard reasoner.
- On 375-statement KBs, the new embeddings reasoner explored 33,280.0 nodes versus 207,489.7 for previous unification and 167,297.8 for standard.
- The authors report a 5x to 188x reduction in nodes explored relative to the standard reasoner and a 2x to 6x reduction relative to the previous unification approach.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use New Embeddings instead of the Standard reasoner | Backward-chaining reasoner · Synthetic KBs (250 statements) | nodes explored: 17,204.0 -> 90.4 | Helped |
| Use New Embeddings instead of Previous Unification | Backward-chaining reasoner · Synthetic KBs (250 statements) | nodes explored: 224.0 -> 90.4 | Helped |
| Use New Embeddings instead of the Standard reasoner | Backward-chaining reasoner · Synthetic KBs (375 statements) | nodes explored: 167,297.8 -> 33,280.0 | Helped |
| Use New Embeddings instead of Previous Unification | Backward-chaining reasoner · Synthetic KBs (375 statements) | nodes explored: 207,489.7 -> 33,280.0 | Helped |
Surprising findings
- The previous unification approach explored more nodes than the standard reasoner on 375-statement KBs (207,489.7 vs 167,297.8).
Limitations
- Evaluation limited to small synthetic knowledge bases of 250 and 375 statements.
- Restricted to Datalog (function-free Horn logic).
- Only 100 test queries per KB and 5 KBs per size; results are preliminary.
Experimental setup
Datasets: synthetic knowledge bases (5 per size, 250 and 375 statements)
Benchmarks: synthetic knowledge bases of 250 and 375 statements
Metrics: mean nodes explored
Baselines: Standard backward-chaining reasoner Previous Unification approach
Builds on: triplet loss unification-guided backward chaining (Arnold and Heflin 2022)
Closest papers by meaning
- Faithful Embeddings for Knowledge Base Queries (NeurIPS 2020 · similarity 0.89)
- Improving Soft Unification with Knowledge Graph Embedding Methods (ICML 2025 · similarity 0.86)
- Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors (ICLR 2024 · similarity 0.86)
- From Noise to Diversity: Random Embedding Injection in LLM Reasoning (NeurIPS 2026 · similarity 0.86)
- Logically Consistent Language Models via Neuro-Symbolic Integration (ICLR 2025 · similarity 0.86)
- On the Hardness of Probabilistic Neurosymbolic Learning (ICML 2024 · similarity 0.85)
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