Vector Symbolic Algebras for the Abstraction and Reasoning Corpus

TL;DR

This paper introduces a novel neurosymbolic approach using Vector Symbolic Algebras to create a cognitively plausible solver for the ARC-AGI benchmark, demonstrating promising results and efficiency.

Contribution

It is the first to apply Vector Symbolic Algebras to ARC-AGI, integrating System 1 and System 2 reasoning for object-centric program synthesis.

Findings

Achieved 10.8% on ARC-AGI-1-Train and 3.0% on ARC-AGI-1-Eval.

Scored 94.5% on Sort-of-ARC and 83.1% on 1D-ARC, outperforming GPT-4 in efficiency.

Proposed a cognitively plausible neurosymbolic framework for fluid intelligence tasks.

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.