# Learning Higher-Order Programs without Meta-Interpretive Learning

arXiv: https://arxiv.org/abs/2112.14603 · HTML: https://mlsanity.com/paper/2112.14603/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [Logical reduction of metarules](https://mlsanity.com/paper/1907.10952/) (2019)
- [Exploiting Answer Set Programming with External Sources for Meta-Interpretive Learning](https://mlsanity.com/paper/1805.00068/) (2018)
- [Learning higher-order logic programs](https://mlsanity.com/paper/1907.10953/) (2019)
- [Predicate Invention by Learning From Failures](https://mlsanity.com/paper/2104.14426/) (2021)
- [Forgetting to learn logic programs](https://mlsanity.com/paper/1911.06643/) (2019)

## Built on by (most cited first, 14 of 14)

- [Learning MDL logic programs from noisy data](https://mlsanity.com/paper/2308.09393/) (2023)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Anti-unification and Generalization: A Survey](https://mlsanity.com/paper/2302.00277/) (2023)
- [Generalisation Through Negation and Predicate Invention](https://mlsanity.com/paper/2301.07629/) (2023)
- [Learning programs with magic values](https://mlsanity.com/paper/2208.03238/) (2022)
- [Relational program synthesis with numerical reasoning](https://mlsanity.com/paper/2210.00764/) (2022)
- [Rule Learning by Modularity](https://mlsanity.com/paper/2212.12335/) (2022)
- [Learning logic programs by discovering higher-order abstractions](https://mlsanity.com/paper/2308.08334/) (2023)
- [Differentiable Inductive Logic Programming in High-Dimensional Space](https://mlsanity.com/paper/2208.06652/) (2022)
- [Efficient rule induction by ignoring pointless rules](https://mlsanity.com/paper/2502.01232/) (2025)
- [Honey, I shrunk the hypothesis space (through logical preprocessing)](https://mlsanity.com/paper/2506.06739/) (2025)
- [Symmetry breaking for inductive logic programming](https://mlsanity.com/paper/2508.06263/) (2025)
- [Ultra Strong Machine Learning: LLM-Generated Explanations Do Not Yet Suffice for Teaching Humans Active Learning Strategy](https://mlsanity.com/paper/2509.00961/) (2025)
- [Satisfiability Modulo Theory Meets Inductive Logic Programming](https://mlsanity.com/paper/2512.12918/) (2025)

## Abstract (arXiv)

Learning complex programs through inductive logic programming (ILP) remains a formidable challenge. Existing higher-order enabled ILP systems show improved accuracy and learning performance, though remain hampered by the limitations of the underlying learning mechanism. Experimental results show that our extension of the versatile Learning From Failures paradigm by higher-order definitions significantly improves learning performance without the burdensome human guidance required by existing systems. Our theoretical framework captures a class of higher-order definitions preserving soundness of existing subsumption-based pruning methods.