# A Foundation Model for Zero-Shot Logical Rule Induction

arXiv: https://arxiv.org/abs/2605.04916 · HTML: https://mlsanity.com/paper/2605.04916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Fast Interpretable Greedy-Tree Sums](https://mlsanity.com/paper/2201.11931/) (2022)
- [FOLD-R++: A Scalable Toolset for Automated Inductive Learning of Default Theories from Mixed Data](https://mlsanity.com/paper/2110.07843/) (2021)
- [Variable Assignment Invariant Neural Networks for Learning Logic Programs](https://mlsanity.com/paper/2408.10709/) (2024)
- [Abductive Logical Rule Induction by Bridging Inductive Logic Programming and Multimodal Large Language Models](https://mlsanity.com/paper/2509.21874/) (2025)
- [GLIDR: Graph-Like Inductive Logic Programming with Differentiable Reasoning](https://mlsanity.com/paper/2508.06716/) (2025)

## Built on by (most cited first, 1 of 1)

- [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)

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.