# Learning Tree Structures from Leaves For Particle Decay Reconstruction

arXiv: https://arxiv.org/abs/2208.14924 · HTML: https://mlsanity.com/paper/2208.14924/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 31 Aug 2022.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Edge-labeling Graph Neural Network for Few-shot Learning](https://mlsanity.com/paper/1905.01436/) (2019)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Machine Learning in High Energy Physics Community White Paper](https://mlsanity.com/paper/1807.02876/) (2018)
- [MLPF: Efficient machine-learned particle-flow reconstruction using graph neural networks](https://mlsanity.com/paper/2101.08578/) (2021)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Performance of a Geometric Deep Learning Pipeline for HL-LHC Particle Tracking](https://mlsanity.com/paper/2103.06995/) (2021)
- [Hierarchical Message-Passing Graph Neural Networks](https://mlsanity.com/paper/2009.03717/) (2020)
- [Explaining machine-learned particle-flow reconstruction](https://mlsanity.com/paper/2111.12840/) (2021)
- [Tree Structure-Aware Graph Representation Learning via Integrated Hierarchical Aggregation and Relational Metric Learning](https://mlsanity.com/paper/2008.10003/) (2020)
- [Hierarchical Relational Inference](https://mlsanity.com/paper/2010.03635/) (2020)
- [Shared Data and Algorithms for Deep Learning in Fundamental Physics](https://mlsanity.com/paper/2107.00656/) (2021)

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

- [Improved particle-flow event reconstruction with scalable neural networks for current and future particle detectors](https://mlsanity.com/paper/2309.06782/) (2023)
- [PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction](https://mlsanity.com/paper/2402.11538/) (2024)
- [Sum-Product-Set Networks: Deep Tractable Models for Tree-Structured Graphs](https://mlsanity.com/paper/2408.07394/) (2024)

## Abstract (arXiv)

In this work, we present a neural approach to reconstructing rooted tree graphs describing hierarchical interactions, using a novel representation we term the Lowest Common Ancestor Generations (LCAG) matrix. This compact formulation is equivalent to the adjacency matrix, but enables learning a tree's structure from its leaves alone without the prior assumptions required if using the adjacency matrix directly. Employing the LCAG therefore enables the first end-to-end trainable solution which learns the hierarchical structure of varying tree sizes directly, using only the terminal tree leaves to do so. In the case of high-energy particle physics, a particle decay forms a hierarchical tree structure of which only the final products can be observed experimentally, and the large combinatorial space of possible trees makes an analytic solution intractable. We demonstrate the use of the LCAG as a target in the task of predicting simulated particle physics decay structures using both a Transformer encoder and a Neural Relational Inference encoder Graph Neural Network. With this approach, we are able to correctly predict the LCAG purely from leaf features for a maximum tree-depth of 8 in 92.5% of cases for trees up to 6 leaves (including) and 59.7% for trees up to 10 in our simulated dataset.