# KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2604.17621 · HTML: https://mlsanity.com/paper/2604.17621/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 19 Apr 2026.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [RQ-RAG: Learning to Refine Queries for Retrieval Augmented Generation](https://mlsanity.com/paper/2404.00610/) (2024)
- [Multidimensional Consistency Improves Reasoning in Language Models](https://mlsanity.com/paper/2503.02670/) (2025)
- [OntoURL: A Benchmark for Evaluating Large Language Models on Symbolic Ontological Understanding, Reasoning and Learning](https://mlsanity.com/paper/2505.11031/) (2025)

## Abstract (arXiv)

Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term "the tip of the iceberg." We formalize this challenge through two orthogonal dimensions: knowledge width, the cardinality of the required universe, and reasoning depth, the number of compositional set operations. We introduce KnowledgeBerg, a benchmark of 4,800 multiple-choice questions derived from 1,183 enumeration seeds spanning 10 domains and 17 languages, with universes grounded in authoritative sources to ensure reproducibility. Representative open-source LLMs demonstrate severe limitations, achieving only 5.26-36.88 F1 on universe enumeration and 16.00-44.19 accuracy on knowledge-grounded reasoning. Diagnostic analyses reveal three stages of failure: completeness, or missing knowledge; awareness, or failure to identify requirements; and application, or incorrect reasoning execution. This pattern persists across languages and model scales. Although test-time compute and retrieval augmentation yield measurable gains -- up to 4.35 and 3.78 points, respectively -- substantial gaps remain, exposing limitations in how current LLMs organize structured knowledge and execute compositional reasoning over bounded domains. The dataset is available at https://huggingface.co/datasets/2npc/KnowledgeBerg