Learning to solve arithmetic problems with a virtual abacus

TL;DR

This paper presents a deep reinforcement learning framework enabling agents to learn arithmetic operations using a virtual abacus, achieving high accuracy and analyzing error patterns to understand limitations.

Contribution

It introduces a novel RL-based approach for learning arithmetic with a virtual abacus, demonstrating effective multi-digit addition and subtraction capabilities.

Findings

Error rate below 1% on test problems

Agents generalize to longer operands than trained on

Analysis of common error patterns

Abstract

Acquiring mathematical skills is considered a key challenge for modern Artificial Intelligence systems. Inspired by the way humans discover numerical knowledge, here we introduce a deep reinforcement learning framework that allows to simulate how cognitive agents could gradually learn to solve arithmetic problems by interacting with a virtual abacus. The proposed model successfully learn to perform multi-digit additions and subtractions, achieving an error rate below 1% even when operands are much longer than those observed during training. We also compare the performance of learning agents receiving a different amount of explicit supervision, and we analyze the most common error patterns to better understand the limitations and biases resulting from our design choices.