# Breaking the Likelihood Trap: Variance-Calibrated Modulation for Large Language Model Decoding

arXiv: https://arxiv.org/abs/2606.22511 · HTML: https://mlsanity.com/paper/2606.22511/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 58 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 30 of 41)

- [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)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [A Contrastive Framework for Neural Text Generation](https://mlsanity.com/paper/2202.06417/) (2022)
- [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)
- [Stay on topic with Classifier-Free Guidance](https://mlsanity.com/paper/2306.17806/) (2023)
- [Do LLMs write like humans? Variation in grammatical and rhetorical styles](https://mlsanity.com/paper/2410.16107/) (2024)
- [Epsilon Sampling Rocks: Investigating Sampling Strategies for Minimum Bayes Risk Decoding for Machine Translation](https://mlsanity.com/paper/2305.09860/) (2023)
- [Understanding the Repeat Curse in Large Language Models from a Feature Perspective](https://mlsanity.com/paper/2504.14218/) (2025)
- [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)
- [Relating Neural Text Degeneration to Exposure Bias](https://mlsanity.com/paper/2109.08705/) (2021)
- [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)
- [Penalty Decoding: Well Suppress the Self-Reinforcement Effect in Open-Ended Text Generation](https://mlsanity.com/paper/2310.14971/) (2023)

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

- [Reference-Based Analysis of Coherence and Diversity in Open-Ended Text Generation](https://mlsanity.com/paper/2609.28080/) (2026)

## Abstract (arXiv)

In open-ended generation, LLMs frequently fall into the "likelihood trap", characterized by repetitive degeneration and vocabulary dullness, resulting in a discrepancy between machine-generated and human-written text. While post-hoc tail truncation (e.g., Top-p, Min-p) avoids sampling from the unreliable tail, it can misalign generation with human lexical preferences by over-sampling from the uncalibrated head; fixed scalar repetition penalties, in turn, ignore how the scale of the logit distribution varies across inference steps, which can disrupt semantic coherence. To address both shortcomings, we propose Variance-Calibrated Modulation (VCM), a training-free pre-decoding intervention. VCM directly reshapes the probability distribution prior to truncation via two dynamic mechanisms: (1) Contextual Searchlight via PMI, which naturally suppresses global stopwords and elevates context-evoked tokens, and (2) Adaptive Self-Debiasing, which utilizes real-time logit standard deviation to provide scale-invariant penalization. In experiments across open-ended generation, factual QA, and mathematical reasoning, we show that VCM consistently mitigates the likelihood trap. With negligible computational overhead, VCM integrates with existing decoding strategies, improving diversity and coherence and, particularly at higher decoding temperatures, reasoning accuracy. Our code is publicly available on GitHub: https://github.com/AetherDing/VCM