# T1: Tool-integrated Verification for Test-time Compute Scaling in Small Language Models

arXiv: https://arxiv.org/abs/2504.04718 · HTML: https://mlsanity.com/paper/2504.04718/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Small Language Models: Survey, Measurements, and Insights](https://mlsanity.com/paper/2409.15790/) (2024)
- [START: Self-taught Reasoner with Tools](https://mlsanity.com/paper/2503.04625/) (2025)
- [When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning](https://mlsanity.com/paper/2504.01005/) (2025)
- [VersaPRM: Multi-Domain Process Reward Model via Synthetic Reasoning Data](https://mlsanity.com/paper/2502.06737/) (2025)
- [Mind the Gap: Examining the Self-Improvement Capabilities of Large Language Models](https://mlsanity.com/paper/2412.02674/) (2024)

## Built on by (most cited first, 13 of 13)

- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Distilling LLM Agent into Small Models with Retrieval and Code Tools](https://mlsanity.com/paper/2505.17612/) (2025)
- [Heimdall: test-time scaling on the generative verification](https://mlsanity.com/paper/2504.10337/) (2025)
- [LatentEvolve: Self-Evolving Test-Time Scaling in Latent Space](https://mlsanity.com/paper/2509.24771/) (2025)
- [Tool Verification for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2603.02203/) (2026)
- [Trust but Verify! A Survey on Verification Design for Test-time Scaling](https://mlsanity.com/paper/2508.16665/) (2025)
- [Gecko: A Simulation Environment with Stateful Feedback for Refining Agent Tool Calls](https://mlsanity.com/paper/2602.19218/) (2026)
- [Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling](https://mlsanity.com/paper/2606.19354/) (2026)
- [Mid-Harness: Scaling Actions Between Model and Harness for Terminal Agents](https://mlsanity.com/paper/2609.39982/) (2026)
- [Understanding Human Limits in Pattern Recognition: A Computational Model of Sequential Reasoning in Rock, Paper, Scissors](https://mlsanity.com/paper/2508.06503/) (2025)
- [Decoding the Critique Mechanism in Large Reasoning Models](https://mlsanity.com/paper/2603.16331/) (2026)
- [Physics as the label for measuring and correcting materials reasoning in multimodal models](https://mlsanity.com/paper/2609.12181/) (2026)
- [Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge](https://mlsanity.com/paper/2609.34327/) (2026)

## Abstract (arXiv)

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 verification by sLMs underexplored. In this work, we investigate whether sLMs can reliably verify the output candidates 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 verification (T1), a two-stage framework that first filters candidates with external tools and then uses an sLM for final verification, offloading memorization-heavy steps to tools such as a code interpreter. Within T1, we prove that offloading to external tools reduces the memorization burden on sLMs 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 improves the verification accuracy of both process reward models (PRMs) and critic models. Our findings highlight the potential of tool integration to substantially improve the verification abilities of sLMs.