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Towards Learning Abductive Reasoning using VSA Distributed Representations

Giacomo Camposampiero, Michael Hersche, Aleksandar Terzić, Roger Wattenhofer, Abu Sebastian, Abbas Rahimi

TL;DR

This work addresses learning abductive reasoning for RPM-like tasks by introducing ARLC, a context-aware extension of Learn-VRF that unifies rule execution and selection with a shared, context-driven rule template. ARLC reduces parameter count while increasing expressiveness, enabling programmable knowledge to be added on top of learned rules and improving downstream performance on I-RAVEN, including both in-distribution and out-of-distribution scenarios. Empirical results show state-of-the-art accuracy with robust transfer to unseen constellations and resilience to post-programming training, indicating improved generalization and stability. The proposed context-aware formulation and generalized rule template offer a scalable path to data-efficient, interpretable neuro-symbolic reasoning beyond RPM, with potential applicability to broader abstract reasoning benchmarks.

Abstract

We introduce the Abductive Rule Learner with Context-awareness (ARLC), a model that solves abstract reasoning tasks based on Learn-VRF. ARLC features a novel and more broadly applicable training objective for abductive reasoning, resulting in better interpretability and higher accuracy when solving Raven's progressive matrices (RPM). ARLC allows both programming domain knowledge and learning the rules underlying a data distribution. We evaluate ARLC on the I-RAVEN dataset, showcasing state-of-the-art accuracy across both in-distribution and out-of-distribution (unseen attribute-rule pairs) tests. ARLC surpasses neuro-symbolic and connectionist baselines, including large language models, despite having orders of magnitude fewer parameters. We show ARLC's robustness to post-programming training by incrementally learning from examples on top of programmed knowledge, which only improves its performance and does not result in catastrophic forgetting of the programmed solution. We validate ARLC's seamless transfer learning from a 2x2 RPM constellation to unseen constellations. Our code is available at https://github.com/IBM/abductive-rule-learner-with-context-awareness.

Towards Learning Abductive Reasoning using VSA Distributed Representations

TL;DR

This work addresses learning abductive reasoning for RPM-like tasks by introducing ARLC, a context-aware extension of Learn-VRF that unifies rule execution and selection with a shared, context-driven rule template. ARLC reduces parameter count while increasing expressiveness, enabling programmable knowledge to be added on top of learned rules and improving downstream performance on I-RAVEN, including both in-distribution and out-of-distribution scenarios. Empirical results show state-of-the-art accuracy with robust transfer to unseen constellations and resilience to post-programming training, indicating improved generalization and stability. The proposed context-aware formulation and generalized rule template offer a scalable path to data-efficient, interpretable neuro-symbolic reasoning beyond RPM, with potential applicability to broader abstract reasoning benchmarks.

Abstract

We introduce the Abductive Rule Learner with Context-awareness (ARLC), a model that solves abstract reasoning tasks based on Learn-VRF. ARLC features a novel and more broadly applicable training objective for abductive reasoning, resulting in better interpretability and higher accuracy when solving Raven's progressive matrices (RPM). ARLC allows both programming domain knowledge and learning the rules underlying a data distribution. We evaluate ARLC on the I-RAVEN dataset, showcasing state-of-the-art accuracy across both in-distribution and out-of-distribution (unseen attribute-rule pairs) tests. ARLC surpasses neuro-symbolic and connectionist baselines, including large language models, despite having orders of magnitude fewer parameters. We show ARLC's robustness to post-programming training by incrementally learning from examples on top of programmed knowledge, which only improves its performance and does not result in catastrophic forgetting of the programmed solution. We validate ARLC's seamless transfer learning from a 2x2 RPM constellation to unseen constellations. Our code is available at https://github.com/IBM/abductive-rule-learner-with-context-awareness.
Paper Structure (11 sections, 9 equations, 2 figures, 1 table)

This paper contains 11 sections, 9 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Vector Symbolic Architectures
  4. Raven's Progressive Matrices
  5. Learning to Reason with Distributed Representations
  6. From Visual Attributes to VSA.
  7. Learning RPM Rules as an Assignment Problem.
  8. Executing and Selecting the Learned Rules.
  9. Methods
  10. Learning Context-Augmented RPM Rules
  11. Improving Rule Selection through Template Generalization

Figures (2)

  • Figure 1: Proposed ARLC architecture. a) Overview of the end-to-end inference pipeline. b) Detailed rule computation block, exploded from (a), which highlights the difference between the two steps of the rule computation: rule selection and rule execution. We also illustrate the proposed context-augmentation abstraction (that translates VSA vectors into different sets $X_{R_i}$ and $O_{R_i}$ depending on the row ${R_i}$), and the parameter sharing between rules ($r_1, \dots, r_R$) across the selection and execution steps (rule blocks with the same color share the same parameters $\mathbf{w}$, $\mathbf{u}$, $\mathbf{v}$).
  • Figure 2: Visualization of current samples ($X=\{x_1,x_2\}$, in yellow) and context ($O=\{o_1,\dots,o_5\}$, in green) panels when predicting the third panel for different rows, namely the first row (left), second row (center) and third row (right). Black objects represent panels that are not used for the computation, while the question mark represents the unknown test panel, which is unavailable during inference.

Theorems & Definitions (2)

  • definition thmcounterdefinition: VSA
  • definition thmcounterdefinition: Rule Set Optimality