# CryptoX : Compositional Reasoning Evaluation of Large Language Models

arXiv: https://arxiv.org/abs/2502.07813 · HTML: https://mlsanity.com/paper/2502.07813/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 8 Feb 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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 Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [CREAK: A Dataset for Commonsense Reasoning over Entity Knowledge](https://mlsanity.com/paper/2109.01653/) (2021)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [KOR-Bench: Benchmarking Language Models on Knowledge-Orthogonal Reasoning Tasks](https://mlsanity.com/paper/2410.06526/) (2024)
- [MAP-Neo: Highly Capable and Transparent Bilingual Large Language Model Series](https://mlsanity.com/paper/2405.19327/) (2024)
- [Jamba-1.5: Hybrid Transformer-Mamba Models at Scale](https://mlsanity.com/paper/2408.12570/) (2024)
- [Understanding and Patching Compositional Reasoning in LLMs](https://mlsanity.com/paper/2402.14328/) (2024)
- [COM2SENSE: A Commonsense Reasoning Benchmark with Complementary Sentences](https://mlsanity.com/paper/2106.00969/) (2021)
- [Evaluating and Aligning CodeLLMs on Human Preference](https://mlsanity.com/paper/2412.05210/) (2024)
- [Memory Injections: Correcting Multi-Hop Reasoning Failures during Inference in Transformer-Based Language Models](https://mlsanity.com/paper/2309.05605/) (2023)
- [ExecRepoBench: Multi-level Executable Code Completion Evaluation](https://mlsanity.com/paper/2412.11990/) (2024)
- [LogicGame: Benchmarking Rule-Based Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2408.15778/) (2024)
- [MdEval: Massively Multilingual Code Debugging](https://mlsanity.com/paper/2411.02310/) (2024)
- [Understanding the Interplay between Parametric and Contextual Knowledge for Large Language Models](https://mlsanity.com/paper/2410.08414/) (2024)
- [Getting More from Less: Large Language Models are Good Spontaneous Multilingual Learners](https://mlsanity.com/paper/2405.13816/) (2024)

## Built on by (most cited first, 5 of 5)

- [From Code Foundation Models to Agents and Applications: A Comprehensive Survey and Practical Guide to Code Intelligence](https://mlsanity.com/paper/2511.18538/) (2025)
- [Agentic Deep Graph Reasoning Yields Self-Organizing Knowledge Networks](https://mlsanity.com/paper/2502.13025/) (2025)
- [KORGym: A Dynamic Game Platform for LLM Reasoning Evaluation](https://mlsanity.com/paper/2505.14552/) (2025)
- [Chain of Event-Centric Causal Thought for Physically Plausible Video Generation](https://mlsanity.com/paper/2603.09094/) (2026)
- [JT-SAFE-V2: Safety-by-Design Foundation Model with World-Context Data](https://mlsanity.com/paper/2605.24414/) (2026)

## Abstract (arXiv)

The compositional reasoning capacity has long been regarded as critical to the generalization and intelligence emergence of large language models LLMs. However, despite numerous reasoning-related benchmarks, the compositional reasoning capacity of LLMs is rarely studied or quantified in the existing benchmarks. In this paper, we introduce CryptoX, an evaluation framework that, for the first time, combines existing benchmarks and cryptographic, to quantify the compositional reasoning capacity of LLMs. Building upon CryptoX, we construct CryptoBench, which integrates these principles into several benchmarks for systematic evaluation. We conduct detailed experiments on widely used open-source and closed-source LLMs using CryptoBench, revealing a huge gap between open-source and closed-source LLMs. We further conduct thorough mechanical interpretability experiments to reveal the inner mechanism of LLMs' compositional reasoning, involving subproblem decomposition, subproblem inference, and summarizing subproblem conclusions. Through analysis based on CryptoBench, we highlight the value of independently studying compositional reasoning and emphasize the need to enhance the compositional reasoning capabilities of LLMs.