# Probabilistic Abduction for Visual Abstract Reasoning via Learning Rules in Vector-symbolic Architectures

arXiv: https://arxiv.org/abs/2401.16024 · HTML: https://mlsanity.com/paper/2401.16024/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Emergent Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2212.09196/) (2022)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [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)
- [Evaluating the Impact of Model Scale for Compositional Generalization in Semantic Parsing](https://mlsanity.com/paper/2205.12253/) (2022)
- [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)
- [Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems](https://mlsanity.com/paper/2205.01128/) (2022)
- [Abstract Spatial-Temporal Reasoning via Probabilistic Abduction and Execution](https://mlsanity.com/paper/2103.14230/) (2021)
- [Visual Concept-Metaconcept Learning](https://mlsanity.com/paper/2002.01464/) (2020)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving](https://mlsanity.com/paper/1910.06611/) (2019)
- [Learning to Reason with Third-Order Tensor Products](https://mlsanity.com/paper/1811.12143/) (2018)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [Techniques for Symbol Grounding with SATNet](https://mlsanity.com/paper/2106.11072/) (2021)
- [In-Context Analogical Reasoning with Pre-Trained Language Models](https://mlsanity.com/paper/2305.17626/) (2023)
- [FALCON: Fast Visual Concept Learning by Integrating Images, Linguistic descriptions, and Conceptual Relations](https://mlsanity.com/paper/2203.16639/) (2022)
- [Knowledge-based Analogical Reasoning in Neuro-symbolic Latent Spaces](https://mlsanity.com/paper/2209.08750/) (2022)

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

- [Limits of Transformer Language Models on Learning to Compose Algorithms](https://mlsanity.com/paper/2402.05785/) (2024)
- [Towards Learning Abductive Reasoning using VSA Distributed Representations](https://mlsanity.com/paper/2406.19121/) (2024)
- [Towards Learning to Reason: Comparing LLMs with Neuro-Symbolic on Arithmetic Relations in Abstract Reasoning](https://mlsanity.com/paper/2412.05586/) (2024)
- [Generalized Holographic Reduced Representations](https://mlsanity.com/paper/2405.09689/) (2024)
- [A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectives](https://mlsanity.com/paper/2503.18213/) (2025)
- [H3DFact: Heterogeneous 3D Integrated CIM for Factorization with Holographic Perceptual Representations](https://mlsanity.com/paper/2404.04173/) (2024)
- [Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture](https://mlsanity.com/paper/2501.11896/) (2025)
- [NSFlow: An End-to-End FPGA Framework with Scalable Dataflow Architecture for Neuro-Symbolic AI](https://mlsanity.com/paper/2504.19323/) (2025)
- [Gram-Space: Structure-Preserving Codebook Compression for Memory-Efficient Neuro-Symbolic AI](https://mlsanity.com/paper/2608.01528/) (2026)

## Abstract (arXiv)

Abstract reasoning is a cornerstone of human intelligence, and replicating it with artificial intelligence (AI) presents an ongoing challenge. This study focuses on efficiently solving Raven's progressive matrices (RPM), a visual test for assessing abstract reasoning abilities, by using distributed computation and operators provided by vector-symbolic architectures (VSA). Instead of hard-coding the rule formulations associated with RPMs, our approach can learn the VSA rule formulations (hence the name Learn-VRF) with just one pass through the training data. Yet, our approach, with compact parameters, remains transparent and interpretable. Learn-VRF yields accurate predictions on I-RAVEN's in-distribution data, and exhibits strong out-of-distribution capabilities concerning unseen attribute-rule pairs, significantly outperforming pure connectionist baselines including large language models. Our code is available at https://github.com/IBM/learn-vector-symbolic-architectures-rule-formulations.