# Trajectory-Retrieval Speculative Decoding: When Does a Model's Own History Help?

arXiv: https://arxiv.org/abs/2610.07350 · HTML: https://mlsanity.com/paper/2610.07350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 17 of 17)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [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)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [Sequoia: Scalable, Robust, and Hardware-aware Speculative Decoding](https://mlsanity.com/paper/2402.12374/) (2024)
- [SpecDec++: Boosting Speculative Decoding via Adaptive Candidate Lengths](https://mlsanity.com/paper/2405.19715/) (2024)
- [Inference with Reference: Lossless Acceleration of Large Language Models](https://mlsanity.com/paper/2304.04487/) (2023)
- [Dynamic Speculation Lookahead Accelerates Speculative Decoding of Large Language Models](https://mlsanity.com/paper/2405.04304/) (2024)
- [Accelerating Large Language Model Reasoning via Speculative Search](https://mlsanity.com/paper/2505.02865/) (2025)
- [RAPID: Long-Context Inference with Retrieval-Augmented Speculative Decoding](https://mlsanity.com/paper/2502.20330/) (2025)
- [Token-Driven GammaTune: Adaptive Calibration for Enhanced Speculative Decoding](https://mlsanity.com/paper/2504.00030/) (2025)
- [ReasonOps: Operator Segmentation for LLM Reasoning Traces](https://mlsanity.com/paper/2605.29192/) (2026)
- [The Shape of Overthinking: Backtracking Bursts in Long Reasoning Traces](https://mlsanity.com/paper/2605.27965/) (2026)

## Abstract (arXiv)

Long chain-of-thought reasoning increases sequential decoding cost while creating a growing history of potentially reusable continuations. We investigate when this history supplies useful drafts and complements an existing drafter. Controlled source comparisons reveal trajectory-specific reuse, motivating our method Trajectory-Local Adaptive Retrieval (TLAR). TLAR retrieves approximately matched continuations from the current trajectory and uses recent verification outcomes to adapt retrieval activation and candidate width. TLAR combines retrieved continuations with model-generated drafts in a shared candidate tree, preserving the target model's output distribution through exact verification. Across code debugging, mathematics, and open-ended writing, our evaluation connects source reuse, incremental acceptance, and execution cost. Combining TLAR with strong retrieval baselines improves token acceptance under matched verification budgets and increases end-to-end throughput over the draft-model baseline. These findings support generated trajectories as runtime memory for adaptive inference.