Abstract
We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, which also preserves existing parton splittings by using layer-skipping connections. By applying a shower merging procedure, the network can be evaluated on unshowered events produced by a matrix element calculation. The trained network behaves as a parton shower that qualitatively reproduces jet-based observables.
Highlights
JHEP12(2018)021 input pattern output pattern to recover the input data as the target
Building a deep learning network that can approximate the behaviour of QCD is a useful exercise for several reasons: such a network can help provide insights into why neural networks work so well for analysis tasks; the network can extract features and observables directly from data, which can be used to confront existing shower models; the evolution of the network parameters with depth in the network can provide some insight into the structure of showers; the trained autoencoder will not fit data that is different from that it is trained on, could be used to identify signal that differs from the QCD backgound; and the toy model trained directly on data can provide a useful comparison to existing methods for tuning Monte Carlo models
We have demonstrated that it is possible to encapsulate many of the features of a QCD parton shower in an autoencoding recursive convolutional neural-network, and that the number of trainable network parameters needed to do so is not large
Summary
2.1 Network structure The layout of the autoencoding CNN is shown in figure 2. The sequence of convolution followed by max-pooling is repeated until the output image size is k × k Note that if such a k × k image were again to be passed through the Conv2D and max-pooling layers, the result would be a single pixel. In the case that all Conv2D filters produce identical ( zero) output in the same pixel, the FilterMask randomly picks a single filter to activate according to its recorded probability This means that if a single active pixel is passed into the CNN, it will be propagated to the k × k bottleneck as a single pixel but reinflated using randomly activated Conv2DTranspose upscaling filters. The process of applying the stack of Conv2DTranspose filters, followed by merging with the corresponding FilterMask from the compression stage, is repeated until the image is the same size as the original input image. The code is available from [9]
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