# High Quality Embeddings for Horn Logic Reasoning

arXiv: https://arxiv.org/abs/2605.20467 · HTML: https://mlsanity.com/paper/2605.20467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 6 of 6)

- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Smart Mining for Deep Metric Learning](https://mlsanity.com/paper/1704.01285/) (2017)
- [ENIGMA: Efficient Learning-based Inference Guiding Machine](https://mlsanity.com/paper/1701.06532/) (2017)
- [Neurosymbolic AI -- Why, What, and How](https://mlsanity.com/paper/2305.00813/) (2023)
- [Can we learn better with hard samples?](https://mlsanity.com/paper/2304.03486/) (2023)

## Abstract (arXiv)

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.