# Learning Compact Representations of LLM Abilities via Item Response Theory

arXiv: https://arxiv.org/abs/2510.00844 · HTML: https://mlsanity.com/paper/2510.00844/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 31 of its 34 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 30 of 31)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learning](https://mlsanity.com/paper/2010.15875/) (2020)
- [Large Language Model Routing with Benchmark Datasets](https://mlsanity.com/paper/2309.15789/) (2023)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [Routing to the Expert: Efficient Reward-guided Ensemble of Large Language Models](https://mlsanity.com/paper/2311.08692/) (2023)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [Anchor Points: Benchmarking Models with Much Fewer Examples](https://mlsanity.com/paper/2309.08638/) (2023)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [MixLLM: Dynamic Routing in Mixed Large Language Models](https://mlsanity.com/paper/2502.18482/) (2025)
- [EmbedLLM: Learning Compact Representations of Large Language Models](https://mlsanity.com/paper/2410.02223/) (2024)
- [Harnessing the Power of Multiple Minds: Lessons Learned from LLM Routing](https://mlsanity.com/paper/2405.00467/) (2024)
- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [Beyond GPT-5: Making LLMs Cheaper and Better via Performance-Efficiency Optimized Routing](https://mlsanity.com/paper/2508.12631/) (2025)
- [Prompt-to-Leaderboard](https://mlsanity.com/paper/2502.14855/) (2025)
- [How Benchmark Prediction from Fewer Data Misses the Mark](https://mlsanity.com/paper/2506.07673/) (2025)
- [Capability Instruction Tuning: A New Paradigm for Dynamic LLM Routing](https://mlsanity.com/paper/2502.17282/) (2025)
- [Route to Reason: Adaptive Routing for LLM and Reasoning Strategy Selection](https://mlsanity.com/paper/2505.19435/) (2025)

## Built on by (most cited first, 10 of 10)

- [Agent psychometrics: Task-level performance prediction in agentic coding benchmarks](https://mlsanity.com/paper/2604.00594/) (2026)
- [Can We Trust Item Response Theory for AI Evaluation?](https://mlsanity.com/paper/2607.15190/) (2026)
- [LOCUS: Low-Dimensional Model Embeddings for Efficient Model Exploration, Comparison, and Selection](https://mlsanity.com/paper/2601.21082/) (2026)
- [Consistent and Distinctive: LLM Benchmark Efficiency via Maximum Independent Set Prompt Selection on Similarity Graphs](https://mlsanity.com/paper/2606.01400/) (2026)
- [Mind the Delay: Latency-aware Query Routing for Heterogeneous LLM pools](https://mlsanity.com/paper/2607.18253/) (2026)
- [Are Near-Tied LLM Rankings Robust to Family-DIF-Guided Benchmark Recomposition?](https://mlsanity.com/paper/2609.00482/) (2026)
- [RSI-Router: Evolving Subtask-Level LLM Routing and Skills for Cost-Efficient Agents](https://mlsanity.com/paper/2609.34712/) (2026)
- [DepthCharge: A Domain-Agnostic Framework for Measuring Depth-Dependent Knowledge in Large Language Models](https://mlsanity.com/paper/2603.23514/) (2026)
- [Balance of Benchmarks: Semantic Density Reweighting for Task-Conditioned Model Comparison](https://mlsanity.com/paper/2608.30044/) (2026)
- [You're Hired: Strategic Model Selection for LLM Collaboration](https://mlsanity.com/paper/2609.38816/) (2026)

## Abstract (arXiv)

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.