# textttSPECS: Faster Test-Time Scaling through Speculative Drafts

arXiv: https://arxiv.org/abs/2506.15733 · HTML: https://mlsanity.com/paper/2506.15733/

## Key facts

- Cited by 3 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 32 of its 59 references that are in the map.
- First posted on arXiv 15 Jun 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, 30 of 32)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Language Model Cascades](https://mlsanity.com/paper/2207.10342/) (2022)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [Sequoia: Scalable, Robust, and Hardware-aware Speculative Decoding](https://mlsanity.com/paper/2402.12374/) (2024)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [Asymptotics of Language Model Alignment](https://mlsanity.com/paper/2404.01730/) (2024)
- [Faster Cascades via Speculative Decoding](https://mlsanity.com/paper/2405.19261/) (2024)
- [Soft Best-of-n Sampling for Model Alignment](https://mlsanity.com/paper/2505.03156/) (2025)
- [QuantSpec: Self-Speculative Decoding with Hierarchical Quantized KV Cache](https://mlsanity.com/paper/2502.10424/) (2025)
- [Accelerating RL for LLM Reasoning with Optimal Advantage Regression](https://mlsanity.com/paper/2505.20686/) (2025)
- [Qsharp: Provably Optimal Distributional RL for LLM Post-Training](https://mlsanity.com/paper/2502.20548/) (2025)

## Built on by (most cited first, 3 of 3)

- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Off-the-Shelf LLMs as Process Scorers: Training-Free Alternative to PRMs for Mathematical Reasoning](https://mlsanity.com/paper/2606.01682/) (2026)
- [Taming Speculative Search for Test-Time Scaling in LLM Serving](https://mlsanity.com/paper/2609.39334/) (2026)

## Abstract (arXiv)

Scaling test-time compute has driven the recent advances in the reasoning capabilities of large language models (LLMs), typically by allocating additional computation for more thorough exploration. However, increased compute often comes at the expense of higher user-facing latency, directly impacting user experience. Current test-time scaling methods primarily optimize for accuracy based on total compute resources (FLOPS), often overlooking latency constraints. To address this gap, we propose textttSPECS, a latency-aware test-time scaling method inspired by speculative decoding. textttSPECS~uses a smaller, faster model to generate candidate sequences efficiently, and evaluates these candidates using signals from both a larger target model and a dedicated reward model. We introduce new integration strategies, including reward-guided soft verification and a reward-based deferral mechanism. Empirical results on MATH500, AMC23 and OlympiadBench datasets show that textttSPECS~matches or surpasses beam search accuracy while reducing latency by up to ~19.1%. Our theoretical analysis shows that our algorithm converges to the solution of a KL-regularized reinforcement learning objective with increasing beam width.