# FutureBridge: Token Selection Beyond Local Preference in Collaborative Decoding

arXiv: https://arxiv.org/abs/2608.06819 · HTML: https://mlsanity.com/paper/2608.06819/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [SpecReason: Fast and Accurate Inference-Time Compute via Speculative Reasoning](https://mlsanity.com/paper/2504.07891/) (2025)
- [CITER: Collaborative Inference for Efficient Large Language Model Decoding with Token-Level Routing](https://mlsanity.com/paper/2502.01976/) (2025)
- [R2R: Efficiently Navigating Divergent Reasoning Paths with Small-Large Model Token Routing](https://mlsanity.com/paper/2505.21600/) (2025)
- [GlimpRouter: Efficient Collaborative Inference by Glimpsing One Token of Thoughts](https://mlsanity.com/paper/2601.05110/) (2026)
- [Confidence-Guided Stepwise Model Routing for Cost-Efficient Reasoning](https://mlsanity.com/paper/2511.06190/) (2025)
- [RelayLLM: Efficient Reasoning via Collaborative Decoding](https://mlsanity.com/paper/2601.05167/) (2026)
- [Confidence-Calibrated Small-Large Language Model Collaboration for Cost-Efficient Reasoning](https://mlsanity.com/paper/2603.03752/) (2026)
- [Select to Think: Unlocking SLM Potential with Local Sufficiency](https://mlsanity.com/paper/2604.26940/) (2026)
- [Pay for Hints, Not Answers: LLM Shepherding for Cost-Efficient Inference](https://mlsanity.com/paper/2601.22132/) (2026)
- [Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing](https://mlsanity.com/paper/2606.25354/) (2026)

## Built on by (most cited first, 1 of 1)

- [From Candidate Tokens to Final Outcomes: Decoding Relative Long-Horizon Candidate Value from Reasoning Model Representations](https://mlsanity.com/paper/2610.15412/) (2026)

## Abstract (arXiv)

Token-level collaboration allows a large language model (LLM) to assist a small language model (SLM) when their predictions diverge. Existing methods either use LLM-generated intervention tokens or rank candidates with the LLM's next-token probabilities. Both rely on the LLM's local preference, even though an LLM-selected token may be difficult for the SLM to build on. We present FutureBridge, which ranks joint LLM-SLM token candidates according to how well they support the SLM's subsequent reasoning. During training, an answer-verified LLM trajectory supplies a fixed shared future, and a frozen SLM evaluates every candidate under this common context. The resulting counterfactual scores supervise a lightweight token reranker that observes only the current state and candidate token. At inference, FutureBridge uses the LLM only to expand the candidate pool, selects one token, and returns generation to the SLM without generating or appending a future suffix. Across five mathematical reasoning benchmarks, FutureBridge improves the Qwen3-1.7B SLM's Math Avg. by 35.1% relative to greedy SLM decoding. These results indicate that token selection benefits from modeling whether the receiving SLM can use each candidate to continue reasoning, rather than relying on the LLM's local preference alone.