# XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction

arXiv: https://arxiv.org/abs/2605.05866 · HTML: https://mlsanity.com/paper/2605.05866/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 62 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Permutation Invariant Training of Deep Models for Speaker-Independent Multi-talker Speech Separation](https://mlsanity.com/paper/1607.00325/) (2016)
- [Attention is All You Need in Speech Separation](https://mlsanity.com/paper/2010.13154/) (2020)
- [Multi-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks](https://mlsanity.com/paper/1703.06284/) (2017)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)
- [A probabilistic deep learning approach to automate the interpretation of multi-phase diffraction spectra](https://mlsanity.com/paper/2103.16664/) (2021)
- [End-to-End Crystal Structure Prediction from Powder X-Ray Diffraction](https://mlsanity.com/paper/2401.03862/) (2024)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [Exploring Supervised Machine Learning for Multi-Phase Identification and Quantification from Powder X-Ray Diffraction Spectra](https://mlsanity.com/paper/2211.08591/) (2022)
- [Dara: Automated multiple-hypothesis phase identification and refinement from powder X-ray diffraction](https://mlsanity.com/paper/2510.19667/) (2025)
- [AI-Driven Structure Refinement of X-ray Diffraction](https://mlsanity.com/paper/2602.16372/) (2026)

## Built on by (most cited first, 3 of 3)

- [PhaseMatcher: Autoregressive Phase-Set Identification with Spectral Decomposition](https://mlsanity.com/paper/2610.05844/) (2026)
- [A self-learning scientific agent for X-ray diffraction](https://mlsanity.com/paper/2610.07862/) (2026)
- [PXRD-Bench: How Close Are We to Determining Crystal Structures from Powder Diffraction?](https://mlsanity.com/paper/2610.16480/) (2026)

## Abstract (arXiv)

Multiphase powder X-ray diffraction (PXRD) analysis remains a fundamental bottleneck in structure identification, as real-world synthesis often produces complex mixtures whose constituent phases (components) cannot be reliably disentangled. While recent advances in representation-based crystal retrieval and generation suggest the possibility of inferring structures directly from PXRD, existing approaches largely assume single-phase inputs and break down in multiphase settings. Here, we present XDecomposer, a prior-free framework for joint decomposition and identification of multiphase XRD patterns without requiring candidate phase lists, structural templates, or prior knowledge of phase number. We formulate multiphase diffraction analysis as a set prediction problem, where the model infers an unordered set of phase-resolved components, their mixture proportions, and corresponding structural representations within a unified architecture. A phase-query-driven decomposition mechanism, together with diffraction-consistent physical reconstruction, enables accurate source separation while preserving crystallographic fidelity. Extensive experiments on both simulated and experimental datasets show that XDecomposer substantially improves reconstruction accuracy and phase identification across diverse chemical systems, while maintaining strong generalization to unseen mixtures. These results provide a practical route toward data-driven, source-resolved multiphase XRD analysis and reduce long-standing dependence on prior-guided iteratively phase matching. The code is openly available at https://github.com/Licht0812/XDecomposer