Towards novel insights in lattice field theory with explainable machine learning

Blücher, Stefan; Kades, Lukas; Pawlowski, Jan M.; Strodthoff, Nils; Urban, Julian M.

doi:10.1103/physrevd.101.094507

Cited by 50 publications

(39 citation statements)

References 32 publications

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“…We obtain 96.56% accuracy, but the formulae are not obviously interpretable 18. Layer-wise relevance propagation has not been widely applied in the physics context, but see[35] for an example.…”

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confidence: 99%

Disentangling a deep learned volume formula

Craven

Jejjala

Kar

2021

J. High Energ. Phys.

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We present a simple phenomenological formula which approximates the hyperbolic volume of a knot using only a single evaluation of its Jones polynomial at a root of unity. The average error is just 2.86% on the first 1.7 million knots, which represents a large improvement over previous formulas of this kind. To find the approximation formula, we use layer-wise relevance propagation to reverse engineer a black box neural network which achieves a similar average error for the same approximation task when trained on 10% of the total dataset. The particular roots of unity which appear in our analysis cannot be written as e2πi/(k+2) with integer k; therefore, the relevant Jones polynomial evaluations are not given by unknot-normalized expectation values of Wilson loop operators in conventional SU(2) Chern-Simons theory with level k. Instead, they correspond to an analytic continuation of such expectation values to fractional level. We briefly review the continuation procedure and comment on the presence of certain Lefschetz thimbles, to which our approximation formula is sensitive, in the analytically continued Chern-Simons integration cycle.

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confidence: 99%

Disentangling a deep learned volume formula

Craven

Jejjala

Kar

2021

J. High Energ. Phys.

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“…For training, we use L1 loss in addition to the standard cross-entropy loss, i.e., L train ðy;ŷÞ Àylogŷ À ð1 À yÞlog ð1 ÀŷÞ þ γ ∑ α;k;a f α;k ðaÞ; ð4Þ where y = {0, 1} is the label of the snapshot, and γ is the L1 regularization strength. The role of the L1 loss is to promote sparsity in the filter patterns by turning off pixels which are unnecessary 10,11 .…”

Section: Resultsmentioning

confidence: 99%

“…The path to surmounting both of these issues is to obtain some form of interpretability in our models. To date, most efforts at interpretable ML on scientific data have relied on manual inspection and translation of learned features from training standard architectures [9][10][11] . Instead, here we propose an approach designed from the ground-up to automatically learn information that is meaningful within the framework of physics.…”

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confidence: 99%

Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

Miles

Bohrdt

et al. 2021

Nat Commun

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Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data.

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“…Likewise, tools from statistical mechanics have brought new conceptual advances to the field of deep learning where questions about expressiveness of deep neural networks, their information propagation capabilities, their generalization properties have been studied [19,284,285]. Tangentially, work the intersection between physics and machine learning may aid interpretability more broadly since this has been a central topic in the physics context [47,94,[286][287][288][289][290].…”

Section: Discussionmentioning

confidence: 99%

Machine learning for quantum matter

Carrasquilla

2020

Advances in Physics: X

178

111

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Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.

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Towards novel insights in lattice field theory with explainable machine learning

Cited by 50 publications

References 32 publications

Disentangling a deep learned volume formula

Disentangling a deep learned volume formula

Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

Machine learning for quantum matter

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