# Min-k Sampling: Decoupling Truncation from Temperature Scaling via Relative Logit Dynamics

arXiv: https://arxiv.org/abs/2604.11012 · HTML: https://mlsanity.com/paper/2604.11012/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 18 of 18)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [Truncation Sampling as Language Model Desmoothing](https://mlsanity.com/paper/2210.15191/) (2022)
- [Probing the Creativity of Large Language Models: Can models produce divergent semantic association?](https://mlsanity.com/paper/2310.11158/) (2023)
- [Adaptive Contrastive Search: Uncertainty-Guided Decoding for Open-Ended Text Generation](https://mlsanity.com/paper/2407.18698/) (2024)
- [Decoding Decoded: Understanding Hyperparameter Effects in Open-Ended Text Generation](https://mlsanity.com/paper/2410.06097/) (2024)
- [Improving Open-Ended Text Generation via Adaptive Decoding](https://mlsanity.com/paper/2402.18223/) (2024)
- [Balancing Diversity and Risk in LLM Sampling: How to Select Your Method and Parameter for Open-Ended Text Generation](https://mlsanity.com/paper/2408.13586/) (2024)
- [G2: Guided Generation for Enhanced Output Diversity in LLMs](https://mlsanity.com/paper/2511.00432/) (2025)
- [REAL Sampling: Boosting Factuality and Diversity of Open-Ended Generation via Asymptotic Entropy](https://mlsanity.com/paper/2406.07735/) (2024)

## Built on by (most cited first, 9 of 9)

- [Beyond Temperature: Hyperfitting as a Late-Stage Geometric Expansion](https://mlsanity.com/paper/2605.22579/) (2026)
- [Lost in Sampling: Assessing Lexical Reachability in LLMs via the Word Coverage Score (WCS)](https://mlsanity.com/paper/2605.27268/) (2026)
- [Breaking the Likelihood Trap: Variance-Calibrated Modulation for Large Language Model Decoding](https://mlsanity.com/paper/2606.22511/) (2026)
- [Beyond the Hivemind: Escaping LLM Homogeneity via Meta-Persona Anchoring and Sequential Temperature Scaling](https://mlsanity.com/paper/2608.02618/) (2026)
- [On the Diversity of Analogy Making in Large Language Models](https://mlsanity.com/paper/2608.03233/) (2026)
- [Temperature Fragility and the Conditional Benefits of Truncation Sampling](https://mlsanity.com/paper/2609.15476/) (2026)
- [Reference-Based Analysis of Coherence and Diversity in Open-Ended Text Generation](https://mlsanity.com/paper/2609.28080/) (2026)
- [Composable Decoding on the Probability Simplex: Theory and Implementation](https://mlsanity.com/paper/2609.34992/) (2026)
- [Truncation Samplers Are Nested: Comparing Decoding Rules Is a Measurement Problem](https://mlsanity.com/paper/2610.15570/) (2026)

## Abstract (arXiv)

The quality of text generated by large language models depends critically on the decoding sampling strategy. While mainstream methods such as Top-k, Top-p, and Min-p achieve a balance between diversity and accuracy through probability-space truncation, they share an inherent limitation: extreme sensitivity to the temperature parameter. Recent logit-space approaches like Top-nσ achieve temperature invariance but rely on global statistics that are susceptible to long-tail noise, failing to capture fine-grained confidence structures among top candidates. We propose Min-k Sampling, a novel dynamic truncation strategy that analyzes the local shape of the sorted logit distribution to identify "semantic cliffs": sharp transitions from high-confidence core tokens to uncertain long-tail tokens. By computing a position-weighted relative decay rate, Min-k dynamically determines truncation boundaries at each generation step. We formally prove that Min-k achieves strict temperature invariance and empirically demonstrate its low sensitivity to hyperparameter choices. Experiments on multiple reasoning benchmarks, creative writing tasks, and human evaluation show that Min-k consistently improves text quality, maintaining robust performance even under extreme temperature settings where probability-based methods collapse. We make our code, models, and analysis tools publicly available.