# Differentiable Inductive Logic Programming in High-Dimensional Space

arXiv: https://arxiv.org/abs/2208.06652 · HTML: https://mlsanity.com/paper/2208.06652/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 13 Aug 2022.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Differentiable Reasoning on Large Knowledge Bases and Natural Language](https://mlsanity.com/paper/1912.10824/) (2019)
- [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021)
- [FF-NSL: Feed-Forward Neural-Symbolic Learner](https://mlsanity.com/paper/2106.13103/) (2021)
- [Learning Higher-Order Programs without Meta-Interpretive Learning](https://mlsanity.com/paper/2112.14603/) (2021)
- [Stacked Structure Learning for Lifted Relational Neural Networks](https://mlsanity.com/paper/1710.02221/) (2017)

## Abstract (arXiv)

Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In contrast, gradient descent provides an efficient way to find solutions within such high-dimensional spaces. Neuro-symbolic ILP approaches have not fully exploited this so far. We propose extending the δILP approach to inductive synthesis with large-scale predicate invention, thus allowing us to exploit the efficacy of high-dimensional gradient descent. We show that large-scale predicate invention benefits differentiable inductive synthesis through gradient descent and allows one to learn solutions for tasks beyond the capabilities of existing neuro-symbolic ILP systems. Furthermore, we achieve these results without specifying the precise structure of the solution within the language bias.