The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMs

TL;DR

This paper investigates why large language models struggle with multi-operand addition, revealing that their reliance on a simple lookahead heuristic limits their ability to handle complex carry-over logic in arithmetic.

Contribution

The study identifies the fundamental limitation of LLMs' one-digit lookahead heuristic in multi-operand addition and analyzes the impact of tokenization on arithmetic performance.

Findings

LLMs fail in multi-operand addition due to insufficient lookahead.

Tokenization strategies do not significantly improve multi-operand addition.

Inherent reliance on a one-digit lookahead heuristic limits LLMs' numerical reasoning.

Abstract

Autoregressive large language models (LLMs) exhibit impressive performance across various tasks but struggle with simple arithmetic, such as addition of two or more operands. We show that this struggle arises from LLMs' use of a simple one-digit lookahead heuristic, which works fairly well (but not perfect) for two-operand addition but fails in multi-operand cases, where the carry-over logic is more complex. Our probing experiments and digit-wise accuracy evaluation show that LLMs fail precisely where a one-digit lookahead is insufficient to account for cascading carries. We analyze the impact of tokenization strategies on arithmetic performance and show that all investigated models, regardless of tokenization, are inherently limited in the addition of multiple operands due to their reliance on a one-digit lookahead heuristic. Our findings reveal fundamental limitations that prevent LLMs from generalizing to more complex numerical reasoning.