# Know When To Fold 'Em: Token-Efficient LLM Synthetic Data Generation via Multi-Stage In-Flight Rejection

arXiv: https://arxiv.org/abs/2605.14062 · HTML: https://mlsanity.com/paper/2605.14062/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Code and instruction data synthesis, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Code and instruction data synthesis](https://mlsanity.com/synth/code-and-instruction-data-synthesis/)

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

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- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
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- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
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- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Sequence Tutor: Conservative Fine-Tuning of Sequence Generation Models with KL-control](https://mlsanity.com/paper/1611.02796/) (2016)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Synthetic Data Generation Using Large Language Models: Advances in Text and Code](https://mlsanity.com/paper/2503.14023/) (2025)
- [Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens](https://mlsanity.com/paper/2505.18237/) (2025)
- [FlashThink: An Early Exit Method For Efficient Reasoning](https://mlsanity.com/paper/2505.13949/) (2025)
- [Synthesizing Post-Training Data for LLMs through Multi-Agent Simulation](https://mlsanity.com/paper/2410.14251/) (2024)
- [Prune 'n Predict: Optimizing LLM Decision-making with Conformal Prediction](https://mlsanity.com/paper/2501.00555/) (2024)
- [Lost at the Beginning of Reasoning](https://mlsanity.com/paper/2506.22058/) (2025)
- [Abstain-R1: Calibrated Abstention and Post-Refusal Clarification via Verifiable RL](https://mlsanity.com/paper/2604.17073/) (2026)
- [SynthesizRR: Generating Diverse Datasets with Retrieval Augmentation](https://mlsanity.com/paper/2405.10040/) (2024)
- [Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning](https://mlsanity.com/paper/2604.18419/) (2026)
- [LYNX: Learning Dynamic Exits for Confidence-Controlled Reasoning](https://mlsanity.com/paper/2512.05325/) (2025)

## Abstract (arXiv)

While synthetic data generation with large language models (LLMs) is widely used in post-training pipelines, existing approaches typically generate full outputs before applying quality filters, leading to substantial token waste on samples that are ultimately discarded. To address this, we propose Multi-Stage In-Flight Rejection (MSIFR), a lightweight, training-free framework that detects and terminates low-quality generation trajectories at intermediate checkpoints before they reach full completion. MSIFR decomposes the generation process into sequential stages and applies fast rule-based validators to identify arithmetic inconsistencies, hallucination patterns, and formatting violations, enabling early rejection of faulty samples. We formalize in-flight rejection as a sequential decision process and show that any non-trivial discard policy reduces expected token consumption, with stage-wise savings increasing when rejection occurs earlier in the generation pipeline. We further demonstrate that conditional utility estimates form a martingale, ensuring that early, in-flight rejection does not bias the expected utility of retained samples. Across five instruction-tuned models and seven reasoning benchmarks, MSIFR reduces token consumption by 11%-77% as a standalone method, and up to 78.2% when combined with early-exit methods, while preserving or improving evaluation accuracy. These results confirm that MSIFR provides a practical mechanism for improving the efficiency of LLM-based synthetic data generation without additional training or architectural changes.