Can Large Language Models put 2 and 2 together? Probing for Entailed Arithmetical Relationships

TL;DR

This paper investigates whether large language models can genuinely reason about arithmetical relationships, finding that their capabilities are limited to statistical inference and do not reflect true reasoning skills.

Contribution

The study introduces a simple probing setup to evaluate LLMs' reasoning about implicit knowledge, revealing their limitations in handling combinatorial and arithmetical reasoning.

Findings

LLMs improve in knowledge and pseudo-reasoning but remain limited to statistical inference.

Pure statistical learning struggles with combinatorial and arithmetical reasoning tasks.

Increasing model size does not necessarily enhance genuine reasoning abilities.

Abstract

Two major areas of interest in the era of Large Language Models regard questions of what do LLMs know, and if and how they may be able to reason (or rather, approximately reason). Since to date these lines of work progressed largely in parallel (with notable exceptions), we are interested in investigating the intersection: probing for reasoning about the implicitly-held knowledge. Suspecting the performance to be lacking in this area, we use a very simple set-up of comparisons between cardinalities associated with elements of various subjects (e.g. the number of legs a bird has versus the number of wheels on a tricycle). We empirically demonstrate that although LLMs make steady progress in knowledge acquisition and (pseudo)reasoning with each new GPT release, their capabilities are limited to statistical inference only. It is difficult to argue that pure statistical learning can cope with the combinatorial explosion inherent in many commonsense reasoning tasks, especially once arithmetical notions are involved. Further, we argue that bigger is not always better and chasing purely statistical improvements is flawed at the core, since it only exacerbates the dangerous conflation of the production of correct answers with genuine reasoning ability.