Vector Symbolic Algebras for the Abstraction and Reasoning Corpus

2025-11-11

AI Summary

Current AI systems struggle with human-like abstract reasoning on ARC-AGI—a benchmark designed to assess fluid intelligence. Method: We propose the first neural-symbolic approach for ARC-AGI grounded in Vector Symbolic Algebra (VSA), unifying System 1 intuition and System 2 reasoning to enable interpretable, object-centric, few-shot program synthesis. Our method leverages VSA for abstraction representation and structured reasoning, yielding a solver more aligned with cognitive principles. Contribution/Results: On ARC-AGI-1-Train and Eval sets, our method achieves 10.8% and 3.0% accuracy, respectively. It attains 94.5% accuracy on Sort-of-ARC and 83.1% on 1D-ARC—surpassing GPT-4 with drastically lower computational overhead. This work establishes a novel paradigm for efficient, interpretable abstract reasoning in artificial general intelligence.

Technology Category

• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Computer Vision: Visual Reasoning & Symbolic Representations
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) is a generative, few-shot fluid intelligence benchmark. Although humans effortlessly solve ARC-AGI, it remains extremely difficult for even the most advanced artificial intelligence systems. Inspired by methods for modelling human intelligence spanning neuroscience to psychology, we propose a cognitively plausible ARC-AGI solver. Our solver integrates System 1 intuitions with System 2 reasoning in an efficient and interpretable process using neurosymbolic methods based on Vector Symbolic Algebras (VSAs). Our solver works by object-centric program synthesis, leveraging VSAs to represent abstract objects, guide solution search, and enable sample-efficient neural learning. Preliminary results indicate success, with our solver scoring 10.8% on ARC-AGI-1-Train and 3.0% on ARC-AGI-1-Eval. Additionally, our solver performs well on simpler benchmarks, scoring 94.5% on Sort-of-ARC and 83.1% on 1D-ARC -- the latter outperforming GPT-4 at a tiny fraction of the computational cost. Importantly, our approach is unique; we believe we are the first to apply VSAs to ARC-AGI and have developed the most cognitively plausible ARC-AGI solver yet. Our code is available at: https://github.com/ijoffe/ARC-VSA-2025.

Problem

• Solving the challenging ARC-AGI benchmark for artificial general intelligence
• Developing cognitively plausible reasoning using Vector Symbolic Algebras
• Integrating System 1 intuitions with System 2 reasoning efficiently

Innovation

• Uses Vector Symbolic Algebras for neurosymbolic reasoning
• Integrates System 1 intuition with System 2 reasoning
• Performs object-centric program synthesis for ARC-AGI