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

Michael Hersche, Francesco di Stefano, Thomas Hofmann, Abu Sebastian, Abbas Rahimi

TL;DR

This paper addresses abstract visual reasoning via RPM by introducing Learn-VRF, a vector-symbolic architecture (VSA) based method that learns rule formulations in a convex-optimization framework. It translates perceptual PMFs into high-dimensional VSA vectors, learns $R$ rule formulations in the rule space, and estimates the missing panel through confidence-weighted combinations or sampling of rules, all with a compact parameter budget. The approach demonstrates competitive in-distribution accuracy on I-RAVEN and clear out-of-distribution generalization to unseen attribute-rule pairs, surpassing large language models and several neural baselines while maintaining interpretability of learned rules. The results suggest that probabilistic abduction in VSA space can deliver robust abstract reasoning with efficient, transparent representations, offering practical benefits for neuro-symbolic reasoning tasks and RPM-like evaluations.

Abstract

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.

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

TL;DR

This paper addresses abstract visual reasoning via RPM by introducing Learn-VRF, a vector-symbolic architecture (VSA) based method that learns rule formulations in a convex-optimization framework. It translates perceptual PMFs into high-dimensional VSA vectors, learns rule formulations in the rule space, and estimates the missing panel through confidence-weighted combinations or sampling of rules, all with a compact parameter budget. The approach demonstrates competitive in-distribution accuracy on I-RAVEN and clear out-of-distribution generalization to unseen attribute-rule pairs, surpassing large language models and several neural baselines while maintaining interpretability of learned rules. The results suggest that probabilistic abduction in VSA space can deliver robust abstract reasoning with efficient, transparent representations, offering practical benefits for neuro-symbolic reasoning tasks and RPM-like evaluations.

Abstract

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.
Paper Structure (20 sections, 13 equations, 3 figures, 7 tables)

This paper contains 20 sections, 13 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Vector-symbolic Architectures (VSA)
  4. I-RAVEN Dataset
  5. Methods
  6. Translating PMFs to VSA
  7. Learning VSA Rule Formulations (Learn-VRF)
  8. Confidence value computation
  9. Final estimation using sampling or weighted combination
  10. Training loss
  11. Experimental Results
  12. I-RAVEN: in-distribution
  13. I-RAVEN: out-of-distribution
  14. Interpretation of learned rule formulations
  15. Conclusion
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Learn-VRF for solving Raven's progressive matrices.
  • Figure A1: MLP baseline which uses one MLP per each attribute.
  • Figure A2: Prompt for GPT-3 experiment with three in-context examples in entangled setting. The single object in the center constellation is encoded into (type, size color). The OOD test focuses on the arithmetic rule on the attribute size. In-context examples show examples of arithmetic rule on attribute color. In this prompt, the empty panel in the text example is filled with the first candidate panel, which is not the correct one.