Equivariant Flow-Based Sampling for Lattice Gauge Theory

Kanwar, Gurtej; Albergo, Michael S.; Boyda, Denis; Cranmer, K.; Hackett, Daniel C.; Racanière, Sébastien; Rezende, Danilo Jimenez; Shanahan, Phiala E.

doi:10.1103/physrevlett.125.121601

Cited by 180 publications

(212 citation statements)

References 54 publications

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“…As we have shown, it successfully improves the problem of topology freezing and exponentially-growing autocorrelation times in the 2D model considered -both with and without fermion content. The integrated autocorrelation time of wHMC in the pure gauge case is very similar to the one obtained in machine-learned flow-based sampling algorithms [14,15], however without the additional training cost.…”

Section: Discussionsupporting

confidence: 63%

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Topological sampling through windings

Albandea¹,

Hernández²,

Ramos³

et al. 2021

Eur. Phys. J. C

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We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

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Section: Discussionsupporting

confidence: 63%

“…We will test our algorithm in the U (1) gauge theory in 2D with and without fermion content. This model has been recently used as benchmark in machine-learned flowbased sampling algorithms [14,15], as well as in tensor network approaches [16,17] (see Ref. [18] for a review).…”

Section: Introductionmentioning

confidence: 99%

Topological sampling through windings

Albandea¹,

Hernández²,

Ramos³

et al. 2021

Eur. Phys. J. C

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“…Normalizing flows allow for the latent space to be irregular and not necessarily Gaussian. While the exact deep learning architecture is not critical, we focus on normalizing flow since it has been shown as a powerful tool for representing physical models [11,[35][36][37][38][39][40][41][42][43][44][45]. In the QUAK construction, our signal choices can be thought of as "approximate-priors" since they help direct the space of searches towards signals with similar features.…”

Section: Conceptmentioning

confidence: 99%

Quasi anomalous knowledge: searching for new physics with embedded knowledge

Park

Rankin

Udrescu

et al. 2021

J. High Energ. Phys.

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Discoveries of new phenomena often involve a dedicated search for a hypothetical physics signature. Recently, novel deep learning techniques have emerged for anomaly detection in the absence of a signal prior. However, by ignoring signal priors, the sensitivity of these approaches is significantly reduced. We present a new strategy dubbed Quasi Anomalous Knowledge (QUAK), whereby we introduce alternative signal priors that capture some of the salient features of new physics signatures, allowing for the recovery of sensitivity even when the alternative signal is incorrect. This approach can be applied to a broad range of physics models and neural network architectures. In this paper, we apply QUAK to anomaly detection of new physics events at the CERN Large Hadron Collider utilizing variational autoencoders with normalizing flow.

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“…3 In fact, it is somewhat surprising that autoencoders appear to perform worse on the nominally easier task of a bump hunt in leptons than on the superficially much more complicated task of jet image recognition and classification, since leptons live on a phase space of fixed dimension. The increasing prominence of "physics-inspired neural networks" -where networks with important symmetry principles (such as gauge equivariance and Lorentz symmetry) hard-coded into the network architecture perform better than networks which are forced to learn these principles from scratch [54][55][56] -suggests that knowledge of the topology may in fact be necessary to appropriately interpret the autoencoder performance. We illustrate this point with the low-dimensional examples described above, and speculate on how these principles might be applied in the context of phase space.…”

Section: Jhep04(2021)280mentioning

confidence: 99%

Topological obstructions to autoencoding

Batson¹,

Haaf

Kahn

et al. 2021

J. High Energ. Phys.

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Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock “bump hunt” in which the autoencoder fails to identify an anomalous “signal” for reasons tied to the intrinsic topology of n-particle phase space.

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Equivariant Flow-Based Sampling for Lattice Gauge Theory

Cited by 180 publications

References 54 publications

Topological sampling through windings

Topological sampling through windings

Quasi anomalous knowledge: searching for new physics with embedded knowledge

Topological obstructions to autoencoding

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