# Variable Assignment Invariant Neural Networks for Learning Logic Programs

arXiv: https://arxiv.org/abs/2408.10709 · HTML: https://mlsanity.com/paper/2408.10709/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks](https://mlsanity.com/paper/1810.00825/) (2018)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Making sense of sensory input](https://mlsanity.com/paper/1910.02227/) (2019)
- [Transformer Reasoning Network for Image-Text Matching and Retrieval](https://mlsanity.com/paper/2004.09144/) (2020)
- [Learning First-Order Rules with Differentiable Logic Program Semantics](https://mlsanity.com/paper/2204.13570/) (2022)

## Built on by (most cited first, 4 of 4)

- [Differentiable Rule Induction from Raw Sequence Inputs](https://mlsanity.com/paper/2602.13583/) (2026)
- [A Foundation Model for Zero-Shot Logical Rule Induction](https://mlsanity.com/paper/2605.04916/) (2026)
- [Disentangling Neural Disjunctive Normal Form Models](https://mlsanity.com/paper/2507.10546/) (2025)
- [Pretrain on Small Synthetic Data, Scale Large for Free: Symmetry-Aware Foundation Model for Logic Rule Induction](https://mlsanity.com/paper/2608.00383/) (2026)

## Abstract (arXiv)

Learning from interpretation transition (LFIT) is a framework for learning rules from observed state transitions. LFIT has been implemented in purely symbolic algorithms, but they are unable to deal with noise or generalize to unobserved transitions. Rule extraction based neural network methods suffer from overfitting, while more general implementation that categorize rules suffer from combinatorial explosion. In this paper, we introduce a technique to leverage variable permutation invariance inherent in symbolic domains. Our technique ensures that the permutation and the naming of the variables would not affect the results. We demonstrate the effectiveness and the scalability of this method with various experiments. Our code is publicly available at https://github.com/phuayj/delta-lfit-2