# An Interpretable and Scalable Framework for Evaluating Large Language Models

arXiv: https://arxiv.org/abs/2605.07046 · HTML: https://mlsanity.com/paper/2605.07046/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 64 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 46)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [MuSR: Testing the Limits of Chain-of-thought with Multistep Soft Reasoning](https://mlsanity.com/paper/2310.16049/) (2023)
- [Survey of Vulnerabilities in Large Language Models Revealed by Adversarial Attacks](https://mlsanity.com/paper/2310.10844/) (2023)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [A Survey on Large Language Models for Critical Societal Domains: Finance, Healthcare, and Law](https://mlsanity.com/paper/2405.01769/) (2024)
- [Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models](https://mlsanity.com/paper/2310.17567/) (2023)
- [Can We Trust AI Benchmarks? An Interdisciplinary Review of Current Issues in AI Evaluation](https://mlsanity.com/paper/2502.06559/) (2025)
- [Estimating Contamination via Perplexity: Quantifying Memorisation in Language Model Evaluation](https://mlsanity.com/paper/2309.10677/) (2023)
- [PromptBench: A Unified Library for Evaluation of Large Language Models](https://mlsanity.com/paper/2312.07910/) (2023)

## Abstract (arXiv)

Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item Response Theory (IRT) offers a principled framework for modeling latent model abilities and item characteristics, but conventional methods are computationally expensive and numerically unstable, limiting large-scale implementations. To address these challenges, we propose an interpretable and scalable framework for LLM evaluation based on the majorization-minimization principle. Our approach reformulates the problem as a sequence of constrained matrix factorization subproblems, enabling stable and efficient parameter estimation with theoretical guarantees for identifiability and convergence. Experiments on synthetic and real-world datasets, including MATH-500 and six Open LLM Leaderboard benchmarks, demonstrate that our method achieves superior scalability and interpretability. It delivers orders-of-magnitude speedups over competing methods while maintaining comparable or even higher estimation accuracy. Our results align with established scaling laws and offer insights into item difficulty and discrimination, informing more principled benchmark design.