Vector Symbolic Algebras for the Abstraction and Reasoning Corpus

TL;DR

This work presents a neurosymbolic ARC-AGI solver based on Vector Symbolic Algebras (VSAs) to encode abstract objects and programmatic transformations. It combines object-centric representations (colour, centre, shape) with a domain-specific DSL and a three-stage solving pipeline (demonstration abduction, rule induction, answer deduction) to achieve sample-efficient learning and interpretable reasoning. While initial results on ARC-AGI remain modest, the solver shows strong performance on related, simpler benchmarks and demonstrates the potential of VSAs to bridge symbolic and connectionist approaches for abstract reasoning tasks. The study argues for cognitive plausibility and proposes a scalable framework for integrating inductive biases with explicit rule-based search, offering a pathway toward more general and efficient ARC-like reasoning systems.

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.

Figures (8)

• Figure 1: ARC-AGI task 0962bcdd. Here, the implicit pattern is to transform each multi-coloured object into a larger object.
• Figure 2: ARC-AGI task 54d9e175. Here, the implicit pattern is to colour each black region partitioned by the grey pixels according to the colour of the lone pixel at its centre (blue to pink, red to orange, green to cyan, and yellow to purple).
• Figure 3: ARC-AGI task a61ba2ce. Here, the implicit pattern is to rearrange the four blocks into a hollow square on a small grid.
• Figure 4: ARC-AGI task a61f2674. Here, the implicit pattern is to recolour the shortest stripe red and the tallest stripe blue.
• Figure 5: Visualization of the object representations for the input grid in the first demonstration of ARC-AGI task a61ba2ce (see Fig. \ref{['fig:task_a61ba2ce']}). The colour subfigure (left) shows the similarity of the object's colour representation to each of the ten possible colour vectors. The centre subfigure (middle) shows the similarity of the object's centre representation to the SSP encoding each location in the grid. The shape subfigure (right) shows the similarity of the object's shape representation to the SSP encoding each possible location in two-dimensional space. These representations use $N \! = \! 1024$-dimensional vectors.