# Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture

arXiv: https://arxiv.org/abs/2501.11896 · HTML: https://mlsanity.com/paper/2501.11896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (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)
- [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)
- [Learning Perceptual Inference by Contrasting](https://mlsanity.com/paper/1912.00086/) (2019)
- [Learning to Make Analogies by Contrasting Abstract Relational Structure](https://mlsanity.com/paper/1902.00120/) (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)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Abstract Diagrammatic Reasoning with Multiplex Graph Networks](https://mlsanity.com/paper/2006.11197/) (2020)
- [Abstract Reasoning with Distracting Features](https://mlsanity.com/paper/1912.00569/) (2019)
- [Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning](https://mlsanity.com/paper/2111.12990/) (2021)
- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [On Neural Architecture Inductive Biases for Relational Tasks](https://mlsanity.com/paper/2206.05056/) (2022)
- [Multi-Label Contrastive Learning for Abstract Visual Reasoning](https://mlsanity.com/paper/2012.01944/) (2020)
- [Effective Abstract Reasoning with Dual-Contrast Network](https://mlsanity.com/paper/2205.13720/) (2022)
- [Learning to reason over visual objects](https://mlsanity.com/paper/2303.02260/) (2023)
- [Solving Raven's Progressive Matrices with Multi-Layer Relation Networks](https://mlsanity.com/paper/2003.11608/) (2020)
- [Abstractors and relational cross-attention: An inductive bias for explicit relational reasoning in Transformers](https://mlsanity.com/paper/2304.00195/) (2023)
- [Abstract Visual Reasoning: An Algebraic Approach for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2303.11730/) (2023)
- [Probabilistic Abduction for Visual Abstract Reasoning via Learning Rules in Vector-symbolic Architectures](https://mlsanity.com/paper/2401.16024/) (2024)
- [Towards Learning Abductive Reasoning using VSA Distributed Representations](https://mlsanity.com/paper/2406.19121/) (2024)
- [Multi-Viewpoint and Multi-Evaluation with Felicitous Inductive Bias Boost Machine Abstract Reasoning Ability](https://mlsanity.com/paper/2210.14914/) (2022)

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

- [Can Large Reasoning Models do Analogical Reasoning under Perceptual Uncertainty?](https://mlsanity.com/paper/2503.11207/) (2025)

## Abstract (arXiv)

In abstract visual reasoning, monolithic deep learning models suffer from limited interpretability and generalization, while existing neuro-symbolic approaches fall short in capturing the diversity and systematicity of attributes and relation representations. To address these challenges, we propose a Systematic Abductive Reasoning model with diverse relation representations (Rel-SAR) in Vector-symbolic Architecture (VSA) to solve Raven's Progressive Matrices (RPM). To derive attribute representations with symbolic reasoning potential, we introduce not only various types of atomic vectors that represent numeric, periodic and logical semantics, but also the structured high-dimentional representation (SHDR) for the overall Grid component. For systematic reasoning, we propose novel numerical and logical relation functions and perform rule abduction and execution in a unified framework that integrates these relation representations. Experimental results demonstrate that Rel-SAR achieves significant improvement on RPM tasks and exhibits robust out-of-distribution generalization. Rel-SAR leverages the synergy between HD attribute representations and symbolic reasoning to achieve systematic abductive reasoning with both interpretable and computable semantics.