# Knowing When to Quit: A Principled Framework for Dynamic Abstention in LLM Reasoning

arXiv: https://arxiv.org/abs/2604.18419 · HTML: https://mlsanity.com/paper/2604.18419/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 15 of 15)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [Adaptive Inference-Time Compute: LLMs Can Predict if They Can Do Better, Even Mid-Generation](https://mlsanity.com/paper/2410.02725/) (2024)
- [Knowledge of Knowledge: Exploring Known-Unknowns Uncertainty with Large Language Models](https://mlsanity.com/paper/2305.13712/) (2023)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [Value Augmented Sampling for Language Model Alignment and Personalization](https://mlsanity.com/paper/2405.06639/) (2024)
- [Check Yourself Before You Wreck Yourself: Selectively Quitting Improves LLM Agent Safety](https://mlsanity.com/paper/2510.16492/) (2025)

## Built on by (most cited first, 8 of 8)

- [Doomed from the Start: Early Abort of LLM Agent Episodes via a Recall-Controlled Probe Cascade](https://mlsanity.com/paper/2607.06503/) (2026)
- [Calibration is the Bottleneck: An Action-Class Diagnostic of Multi-Turn Tool-Calling](https://mlsanity.com/paper/2609.00949/) (2026)
- [Solving Without Stopping: On-Policy Distillation at Small Scale](https://mlsanity.com/paper/2609.37326/) (2026)
- [Nice Fold or Hero Call: Learning Budget-Efficient Thinking for Adaptive Reasoning](https://mlsanity.com/paper/2605.11625/) (2026)
- [Know When To Fold 'Em: Token-Efficient LLM Synthetic Data Generation via Multi-Stage In-Flight Rejection](https://mlsanity.com/paper/2605.14062/) (2026)
- [Selective Safety Steering via Value-Filtered Decoding](https://mlsanity.com/paper/2605.14746/) (2026)
- [ANTE: Anticipate, Then Execute -- Learning Internal World Models for Coding Agents from Verified Beliefs](https://mlsanity.com/paper/2610.15368/) (2026)
- [Training Language Models to Fail Gracefully](https://mlsanity.com/paper/2610.20401/) (2026)

## Abstract (arXiv)

LLMs utilizing chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning and toxicity avoidance tasks support our theory and demonstrate improved selective accuracy over existing methods.