# Beyond Single-Point Judgment: Distribution Alignment for LLM-as-a-Judge

arXiv: https://arxiv.org/abs/2505.12301 · HTML: https://mlsanity.com/paper/2505.12301/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 39 references that are in the map.
- First posted on arXiv 18 May 2025.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [Towards Measuring the Representation of Subjective Global Opinions in Language Models](https://mlsanity.com/paper/2306.16388/) (2023)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [Adversarial Training Methods for Semi-Supervised Text Classification](https://mlsanity.com/paper/1605.07725/) (2016)
- [WildBench: Benchmarking LLMs with Challenging Tasks from Real Users in the Wild](https://mlsanity.com/paper/2406.04770/) (2024)
- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [FLASK: Fine-grained Language Model Evaluation based on Alignment Skill Sets](https://mlsanity.com/paper/2307.10928/) (2023)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [Human-like Summarization Evaluation with ChatGPT](https://mlsanity.com/paper/2304.02554/) (2023)
- [Quantile Regression for Distributional Reward Models in RLHF](https://mlsanity.com/paper/2409.10164/) (2024)
- [Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning](https://mlsanity.com/paper/2306.02408/) (2023)
- [A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologies](https://mlsanity.com/paper/2203.14046/) (2022)
- [Improving LLM-as-a-Judge Inference with the Judgment Distribution](https://mlsanity.com/paper/2503.03064/) (2025)

## Built on by (most cited first, 4 of 4)

- [Probabilistic Calibration Is a Trainable Capability in Language Models](https://mlsanity.com/paper/2605.11845/) (2026)
- [From Uncertain Judgments to Calibrated Rankings: Conformal Elo Estimation for LLM Evaluation](https://mlsanity.com/paper/2606.13221/) (2026)
- [Order Matters: LVLMs as Judges for Temporal Reasoning in Image Sequences](https://mlsanity.com/paper/2608.10908/) (2026)
- [PACEShop: Evaluating Personalized, Actionable, Compositional, and Evidence-grounded Shopping Assistants](https://mlsanity.com/paper/2608.26180/) (2026)

## Abstract (arXiv)

LLMs have emerged as powerful evaluators in the LLM-as-a-Judge paradigm, offering significant efficiency and flexibility compared to human judgments. However, previous methods primarily rely on single-point evaluations, overlooking the inherent diversity and uncertainty in human evaluations. This approach leads to information loss and decreases the reliability of evaluations. To address this limitation, we propose a novel training framework that explicitly aligns the LLM-generated judgment distribution with empirical human distributions. Specifically, we propose a distributional alignment objective based on KL divergence, combined with an auxiliary cross-entropy regularization to stabilize the training process. Furthermore, considering that empirical distributions may derive from limited human annotations, we incorporate adversarial training to enhance model robustness against distribution perturbations. Extensive experiments across various LLM backbones and evaluation tasks demonstrate that our framework significantly outperforms existing closed-source LLMs and conventional single-point alignment methods, with improved alignment quality, evaluation accuracy, and robustness.