# Raven's Progressive Matrices Completion with Latent Gaussian Process Priors

arXiv: https://arxiv.org/abs/2103.12045 · HTML: https://mlsanity.com/paper/2103.12045/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [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)
- [Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEs](https://mlsanity.com/paper/1901.07017/) (2019)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [Learning Disentangled Joint Continuous and Discrete Representations](https://mlsanity.com/paper/1804.00104/) (2018)
- [Learning Perceptual Inference by Contrasting](https://mlsanity.com/paper/1912.00086/) (2019)
- [Improving Generalization for Abstract Reasoning Tasks Using Disentangled Feature Representations](https://mlsanity.com/paper/1811.04784/) (2018)
- [V-PROM: A Benchmark for Visual Reasoning Using Visual Progressive Matrices](https://mlsanity.com/paper/1907.12271/) (2019)
- [Differentiable Compositional Kernel Learning for Gaussian Processes](https://mlsanity.com/paper/1806.04326/) (2018)
- [Learning Discrete and Continuous Factors of Data via Alternating Disentanglement](https://mlsanity.com/paper/1905.09432/) (2019)
- [Explicit Disentanglement of Appearance and Perspective in Generative Models](https://mlsanity.com/paper/1906.11881/) (2019)
- [Modeling Gestalt Visual Reasoning on the Raven's Progressive Matrices Intelligence Test Using Generative Image Inpainting Techniques](https://mlsanity.com/paper/1911.07736/) (2019)

## Built on by (most cited first, 9 of 9)

- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [A Review of Emerging Research Directions in Abstract Visual Reasoning](https://mlsanity.com/paper/2202.10284/) (2022)
- [Abstract Visual Reasoning: An Algebraic Approach for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2303.11730/) (2023)
- [Abstracting Concept-Changing Rules for Solving Raven's Progressive Matrix Problems](https://mlsanity.com/paper/2307.07734/) (2023)
- [A Cognitively-Inspired Neural Architecture for Visual Abstract Reasoning Using Contrastive Perceptual and Conceptual Processing](https://mlsanity.com/paper/2309.10532/) (2023)
- [Compositional Law Parsing with Latent Random Functions](https://mlsanity.com/paper/2209.09115/) (2022)
- [Time-Conditioned Generative Modeling of Object-Centric Representations for Video Decomposition and Prediction](https://mlsanity.com/paper/2301.08951/) (2023)
- [Towards Generative Abstract Reasoning: Completing Raven's Progressive Matrix via Rule Abstraction and Selection](https://mlsanity.com/paper/2401.09966/) (2024)
- [Deep Non-Monotonic Reasoning for Visual Abstract Reasoning Tasks](https://mlsanity.com/paper/2302.07137/) (2023)

## Abstract (arXiv)

Abstract reasoning ability is fundamental to human intelligence. It enables humans to uncover relations among abstract concepts and further deduce implicit rules from the relations. As a well-known abstract visual reasoning task, Raven's Progressive Matrices (RPM) are widely used in human IQ tests. Although extensive research has been conducted on RPM solvers with machine intelligence, few studies have considered further advancing the standard answer-selection (classification) problem to a more challenging answer-painting (generating) problem, which can verify whether the model has indeed understood the implicit rules. In this paper we aim to solve the latter one by proposing a deep latent variable model, in which multiple Gaussian processes are employed as priors of latent variables to separately learn underlying abstract concepts from RPMs; thus the proposed model is interpretable in terms of concept-specific latent variables. The latent Gaussian process also provides an effective way of extrapolation for answer painting based on the learned concept-changing rules. We evaluate the proposed model on RPM-like datasets with multiple continuously-changing visual concepts. Experimental results demonstrate that our model requires only few training samples to paint high-quality answers, generate novel RPM panels, and achieve interpretability through concept-specific latent variables.