# Abstracting Concept-Changing Rules for Solving Raven's Progressive Matrix Problems

arXiv: https://arxiv.org/abs/2307.07734 · HTML: https://mlsanity.com/paper/2307.07734/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 81 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [Stratified Rule-Aware Network for Abstract Visual Reasoning](https://mlsanity.com/paper/2002.06838/) (2020)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Self-supervised learning through the eyes of a child](https://mlsanity.com/paper/2007.16189/) (2020)
- [Learning Perceptual Inference by Contrasting](https://mlsanity.com/paper/1912.00086/) (2019)
- [The Scattering Compositional Learner: Discovering Objects, Attributes, Relationships in Analogical Reasoning](https://mlsanity.com/paper/2007.04212/) (2020)
- [Scale-Localized Abstract Reasoning](https://mlsanity.com/paper/2009.09405/) (2020)
- [Abstract Spatial-Temporal Reasoning via Probabilistic Abduction and Execution](https://mlsanity.com/paper/2103.14230/) (2021)
- [Abstract Diagrammatic Reasoning with Multiplex Graph Networks](https://mlsanity.com/paper/2006.11197/) (2020)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [Abstract Reasoning with Distracting Features](https://mlsanity.com/paper/1912.00569/) (2019)
- [Improving Generalization for Abstract Reasoning Tasks Using Disentangled Feature Representations](https://mlsanity.com/paper/1811.04784/) (2018)
- [Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning](https://mlsanity.com/paper/2111.12990/) (2021)
- [Effective Abstract Reasoning with Dual-Contrast Network](https://mlsanity.com/paper/2205.13720/) (2022)
- [Solving Raven's Progressive Matrices with Multi-Layer Relation Networks](https://mlsanity.com/paper/2003.11608/) (2020)
- [Attention on Abstract Visual Reasoning](https://mlsanity.com/paper/1911.05990/) (2019)
- [Generating Correct Answers for Progressive Matrices Intelligence Tests](https://mlsanity.com/paper/2011.00496/) (2020)
- [Raven's Progressive Matrices Completion with Latent Gaussian Process Priors](https://mlsanity.com/paper/2103.12045/) (2021)

## Built on by (most cited first, 6 of 6)

- [Triple-CFN: Separating Concepts and Features Enhances Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2403.03190/) (2024)
- [Funny-Valen-Tine: Planning Solution Distribution Enhances Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2407.02688/) (2024)
- [Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture](https://mlsanity.com/paper/2501.11896/) (2025)
- [D4C: Improving Negative Example Quality to Enhance Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2403.03452/) (2024)
- [Johnny: Structuring Representation Space to Enhance Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2506.01970/) (2025)
- [DIO: Refining Mutual Information and Causal Chain to Enhance Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2508.15387/) (2025)

## Abstract (arXiv)

The abstract visual reasoning ability in human intelligence benefits discovering underlying rules in the novel environment. Raven's Progressive Matrix (RPM) is a classic test to realize such ability in machine intelligence by selecting from candidates. Recent studies suggest that solving RPM in an answer-generation way boosts a more in-depth understanding of rules. However, existing generative solvers cannot discover the global concept-changing rules without auxiliary supervision (e.g., rule annotations and distractors in candidate sets). To this end, we propose a deep latent variable model for Concept-changing Rule ABstraction (CRAB) by learning interpretable concepts and parsing concept-changing rules in the latent space. With the iterative learning process, CRAB can automatically abstract global rules shared on the dataset on each concept and form the learnable prior knowledge of global rules. CRAB outperforms the baselines trained without auxiliary supervision in the arbitrary-position answer generation task and achieves comparable and even higher accuracy than the compared models trained with auxiliary supervision. Finally, we conduct experiments to illustrate the interpretability of CRAB in concept learning, answer selection, and global rule abstraction.