# Test-Time Speculation

arXiv: https://arxiv.org/abs/2605.09329 · HTML: https://mlsanity.com/paper/2605.09329/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 33 of its 40 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [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)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [CodeSearchNet Challenge: Evaluating the State of Semantic Code Search](https://mlsanity.com/paper/1909.09436/) (2019)
- [Taming Throughput-Latency Tradeoff in LLM Inference with Sarathi-Serve](https://mlsanity.com/paper/2403.02310/) (2024)
- [LMSYS-Chat-1M: A Large-Scale Real-World LLM Conversation Dataset](https://mlsanity.com/paper/2309.11998/) (2023)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [Mooncake: A KVCache-centric Disaggregated Architecture for LLM Serving](https://mlsanity.com/paper/2407.00079/) (2024)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [LongWriter: Unleashing 10,000+ Word Generation from Long Context LLMs](https://mlsanity.com/paper/2408.07055/) (2024)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [Online Speculative Decoding](https://mlsanity.com/paper/2310.07177/) (2023)
- [PARD: Accelerating LLM Inference with Low-Cost PARallel Draft Model Adaptation](https://mlsanity.com/paper/2504.18583/) (2025)

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

- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [SpecRoll: Fast-Slow Verifier-Feedback Adaptation for Speculative Reinforcement Learning Rollouts](https://mlsanity.com/paper/2608.04962/) (2026)
- [SharpDraft: Accelerating Long-Context Speculative Decoding with Cardinality-Aware Query Scaling](https://mlsanity.com/paper/2610.05106/) (2026)

## Abstract (arXiv)

Speculative decoding accelerates LLM inference by using a fast draft model to generate tokens and a more accurate target model to verify them. Its performance depends on the textitacceptance length, or number of draft tokens accepted by the target. Our studies show that the acceptance length of even state-of-the-art speculators, like DFlash, EAGLE-3 and PARD degrade with generation length, reaching values close to 1 (i.e. no speedup) within just a few thousand output tokens, making speculators ineffective for long-response tasks. Acceptance lengths decline because most speculators are trained offline on short sequences, but are forced to match the target model on much longer outputs at inference, well beyond their training distribution. To address this issue, we propose textitTest-Time Speculation (TTS), an online distillation approach that continuously adapts the speculator at test-time. TTS leverages the key insight that the token verification step already invokes the target model for each draft token, providing the training signal needed to adapt the draft at no additional cost. Treating the draft as the student and the target as a teacher, TTS adjusts the draft over several speculation rounds, with each update improving the draft's accuracy as generation proceeds. Our results across multiple models from the Qwen-3, Qwen-3.5, and Llama3.1 families show that TTS improves acceptance lengths over state-of-the-art speculators by up to 72% and 41% on average, with the benefits scaling with increased generation lengths.