# Learning Invariants through Soft Unification

arXiv: https://arxiv.org/abs/1909.07328 · HTML: https://mlsanity.com/paper/1909.07328/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Learning Symbolic Rules for Reasoning in Quasi-Natural Language](https://mlsanity.com/paper/2111.12038/) (2021)
- [Through the Looking Glass, and what Horn Clause Programs Found There](https://mlsanity.com/paper/2407.20413/) (2024)

## Abstract (arXiv)

Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using variables "someone" and "somewhere" instead of mentioning specific people or places. Humans learn what variables are and how to use them at a young age. This paper explores whether machines can also learn and use variables solely from examples without requiring human pre-engineering. We propose Unification Networks, an end-to-end differentiable neural network approach capable of lifting examples into invariants and using those invariants to solve a given task. The core characteristic of our architecture is soft unification between examples that enables the network to generalise parts of the input into variables, thereby learning invariants. We evaluate our approach on five datasets to demonstrate that learning invariants captures patterns in the data and can improve performance over baselines.