# Visual Perceptual to Conceptual First-Order Rule Learning Networks

arXiv: https://arxiv.org/abs/2604.07897 · HTML: https://mlsanity.com/paper/2604.07897/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Faithful Reasoning Using Large Language Models](https://mlsanity.com/paper/2208.14271/) (2022)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [Deep k-Means: Jointly clustering with k-Means and learning representations](https://mlsanity.com/paper/1806.10069/) (2018)
- [LogiCoT: Logical Chain-of-Thought Instruction-Tuning](https://mlsanity.com/paper/2305.12147/) (2023)
- [Techniques for Symbol Grounding with SATNet](https://mlsanity.com/paper/2106.11072/) (2021)
- [MIRAGE: Evaluating and Explaining Inductive Reasoning Process in Language Models](https://mlsanity.com/paper/2410.09542/) (2024)
- [Kandinsky Patterns](https://mlsanity.com/paper/1906.00657/) (2019)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [Exploiting Answer Set Programming with External Sources for Meta-Interpretive Learning](https://mlsanity.com/paper/1805.00068/) (2018)
- [Neuro-Symbolic Learning of Answer Set Programs from Raw Data](https://mlsanity.com/paper/2205.12735/) (2022)
- [The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning](https://mlsanity.com/paper/2402.01889/) (2024)
- [Neuro-symbolic Rule Learning in Real-world Classification Tasks](https://mlsanity.com/paper/2303.16674/) (2023)
- [Inductive Learning of Logical Theories with LLMs: An Expressivity-Graded Analysis](https://mlsanity.com/paper/2408.16779/) (2024)
- [Learning First-Order Rules with Differentiable Logic Program Semantics](https://mlsanity.com/paper/2204.13570/) (2022)
- [Learning big logical rules by joining small rules](https://mlsanity.com/paper/2401.16215/) (2024)
- [Neural DNF-MT: A Neuro-symbolic Approach for Learning Interpretable and Editable Policies](https://mlsanity.com/paper/2501.03888/) (2025)
- [Predicate Renaming via Large Language Models](https://mlsanity.com/paper/2510.25517/) (2025)
- [Differentiable Rule Induction from Raw Sequence Inputs](https://mlsanity.com/paper/2602.13583/) (2026)

## Abstract (arXiv)

Learning rules plays a crucial role in deep learning, particularly in explainable artificial intelligence and enhancing the reasoning capabilities of large language models. While existing rule learning methods are primarily designed for symbolic data, learning rules from image data without supporting image labels and automatically inventing predicates remains a challenge. In this paper, we tackle these inductive rule learning problems from images with a framework called γILP, which provides a fully differentiable pipeline from image constant substitution to rule structure induction. Extensive experiments demonstrate that γILP achieves strong performance not only on classical symbolic relational datasets but also on relational image data and pure image datasets, such as Kandinsky patterns.