# Composition Collapse: Stable Factual Knowledge Does Not Imply Compositional Reasoning

arXiv: https://arxiv.org/abs/2605.26789 · HTML: https://mlsanity.com/paper/2605.26789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 9 of 9)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Do Large Language Models Perform Latent Multi-Hop Reasoning without Exploiting Shortcuts?](https://mlsanity.com/paper/2411.16679/) (2024)

## Built on by (most cited first, 1 of 1)

- [Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models](https://mlsanity.com/paper/2610.05472/) (2026)

## Abstract (arXiv)

Post-training is routinely evaluated through aggregate benchmark scores that treat multi-hop reasoning as a single capability -- as if a model that answers more questions correctly must be better at assembling facts. We show that this assumption can be misleading: recipes with statistically indistinguishable atomic knowledge produce composition behaviour separated by over 40 percentage points, a phenomenon we call composition collapse: the systematic failure to assemble stably-known facts into chains, invisible to aggregate metrics. We introduce a double-gate protocol that changes the estimand from an aggregate compositionality gap to residual composition failure conditioned on stable atomic access, decomposing post-training gains into three independent channels: atomic stability, residual composition, and critical depth. On a benchmark of temporal factual chains spanning depths 2--11 across four post-training recipes, this decomposition reveals that post-training objectives shift composition capability in directions that aggregate metrics mask, and suggests that claims about multi-hop reasoning improvement should be accompanied by atomic-gate-controlled composition metrics. Diagnostic probes further show that a substantial share of measured composition failure reflects generation-time computation constraints rather than permanent inability to compose.