Provable Benefits of In-Tool Learning for Large Language Models
Authors: name: Sam Houliston, name: Ambroise Odonnat, name: Charles Arnal, name: Vivien Cabannes

Tool-augmented language models, equipped with retrieval, memory, or external
APIs, are reshaping AI, yet their theoretical advantages remain underexplored.
In this paper, we address this question by demonstrating the benefits of
in-tool learning (external retrieval) over in-weight learning (memorization)
for factual recall. We show that the number of facts a model can memorize
solely in its weights is fundamentally limited by its parameter count. In
contrast, we prove that tool-use enables unbounded factual recall via a simple
and efficient circuit construction. These results are validated in controlled
experiments, where tool-using models consistently outperform memorizing ones.
We further show that for pretrained large language models, teaching tool-use
and general rules is more effective than finetuning facts into memory. Our work
provides both a theoretical and empirical foundation, establishing why
tool-augmented workflows are not just practical, but provably more scalable.