T1: Tool-integrated Self-verification for Test-time Compute Scaling in
  Small Language Models
Authors: name: Minki Kang, name: Jongwon Jeong, name: Jaewoong Cho

Recent studies have demonstrated that test-time compute scaling effectively
improves the performance of small language models (sLMs). However, prior
research has mainly examined test-time compute scaling with an additional
larger model as a verifier, leaving self-verification by sLMs underexplored. In
this work, we investigate whether sLMs can reliably self-verify their outputs
under test-time scaling. We find that even with knowledge distillation from
larger verifiers, sLMs struggle with verification tasks requiring memorization,
such as numerical calculations and fact-checking. To address this limitation,
we propose Tool-integrated self-verification (T1), which delegates
memorization-heavy verification steps to external tools, such as a code
interpreter. Our theoretical analysis shows that tool integration reduces
memorization demands and improves test-time scaling performance. Experiments on
the MATH benchmark demonstrate that, with T1, a Llama-3.2 1B model under
test-time scaling outperforms the significantly larger Llama-3.1 8B model.
Moreover, T1 generalizes effectively to both mathematical (MATH500) and
multi-domain knowledge-intensive tasks (MMLU-Pro). Our findings highlight the
potential of tool integration to substantially improve the self-verification
abilities of sLMs.