# Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning

arXiv: https://arxiv.org/abs/2003.01504 · HTML: https://mlsanity.com/paper/2003.01504/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2020.

## Built on by (most cited first, 12 of 12)

- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://mlsanity.com/paper/2207.00283/) (2022)
- [Decoupling Pixel Flipping and Occlusion Strategy for Consistent XAI Benchmarks](https://mlsanity.com/paper/2401.06654/) (2024)
- [Stochastic normalizing flows as non-equilibrium transformations](https://mlsanity.com/paper/2201.08862/) (2022)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [Quantum field-theoretic machine learning](https://mlsanity.com/paper/2102.09449/) (2021)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
- [Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics](https://mlsanity.com/paper/2501.05580/) (2025)
- [Geometrical aspects of lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2303.11448/) (2023)
- [Machine Learning in Nuclear Physics](https://mlsanity.com/paper/2112.02309/) (2021)

## Abstract (arXiv)

Machine learning has the potential to aid our understanding of phase structures in lattice quantum field theories through the statistical analysis of Monte Carlo samples. Available algorithms, in particular those based on deep learning, often demonstrate remarkable performance in the search for previously unidentified features, but tend to lack transparency if applied naively. To address these shortcomings, we propose representation learning in combination with interpretability methods as a framework for the identification of observables. More specifically, we investigate action parameter regression as a pretext task while using layer-wise relevance propagation (LRP) to identify the most important observables depending on the location in the phase diagram. The approach is put to work in the context of a scalar Yukawa model in (2+1)d. First, we investigate a multilayer perceptron to determine an importance hierarchy of several predefined, standard observables. The method is then applied directly to the raw field configurations using a convolutional network, demonstrating the ability to reconstruct all order parameters from the learned filter weights. Based on our results, we argue that due to its broad applicability, attribution methods such as LRP could prove a useful and versatile tool in our search for new physical insights. In the case of the Yukawa model, it facilitates the construction of an observable that characterises the symmetric phase.