This autoencoder model exploits the symmetry of the Lorentz Group, a Lie group that represents a fundamental symmetry of spacetime and describes the dynamics of relativistic objects such as elementary particles in a particle physics experiment. The model is built using the architecture of the LGN introduced by Bogatskiy et al. in arXiv:2006.04780 (see the README file in each directory for more details). A preprint is available on arXiv:2212.07347. Published on The European Physical Journal C.
To achieve Lorentz equivariance, the model works on the irreducible representations of the Lorentz group
To download data:
- Install
JetNet:pip3 install jetnet; - Run
preprocess.pypython utils/data/preprocess.py \ --jet-types g q t w z \ --save-dir "./data"
An example training looks like this.
mkdir -p results;
python -u main.py \
--data-paths "./data/g_jets_30p_p4.pt" "./data/q_jets_30p_p4.pt" \
--test-data-paths "./data/g_jets_30p_p4.pt" "./data/q_jets_30p_p4.pt" \
-j QCD \
-e 50 \
-bs 512 \
--train-fraction 0.75 \
--lr 0.0005 \
--loss-choice chamfer \
--get-real-method sum \
--tau-latent-vectors 8 \
--tau-latent-scalars 1 \
--maxdim 2 \
--l1-lambda 1e-8 \
--l2-lambda 0 \
--map-to-latent "min&max" \
--mlp-width 6 \
--mlp-depth 6 \
--encoder-num-channels 3 3 4 4 \
--decoder-num-channels 4 4 3 3 \
--patience 1000 \
--plot-freq 100 \
--save-freq 200 \
--plot-start-epoch 50 \
--equivariance-test \
--num-test-batch 1024 \
--save-dir "results" \
| tee "results/training-log.txt"
-bs(batch-size): batch size.-tbs(--test-batch-size): test batch size.-j(--jet-type): the jet type used for training (mainly used for naming files).-e(--num-epochs): number of epochs to train.--loss-choice: loss function to use.--train-fraction: fraction of the data used for training.--data-paths: paths to the training data.--test-data-paths: paths to the test data.--map-to-latent: aggregation method to the latent space.- For
min&max, min and max will be concatenated. - For
min+max, min and max will be added. - For
mix, a Lorentz group equivariant linear layer will mix the irreps to the latent space.
- For
--maxdim: maximum weight of representation to keep in training (recommended: 2 or 3).--tau-latent-scalars: number of (complexified) Lorentz scalars to keep in the latent space.--tau-latent-vectors: number of (complexified) 4-vectors to keep in the latent space.--encoder-num-channels: the number of channels for each representation in the encoder.--decoder-num-channels: the number of channels for each representation in the decoder.--plot-freq: frequency of plotting (plotting / epoch).--plot-start-epoch: epoch number at which to start plotting (for better GPU usage in the beginning).--save-dir: directory to save the trained model and plots.--equivariance-test: whether to test the model for equivariance.
The test includes reconstruction and can include Lorentz group equivariance test and anomaly detection. An example test looks like this.
python test.py \
-tbs 512 \
--num-test-batch 200 \
-j QCD \
--maxdim 2 \
--tau-latent-vectors 8 \
--tau-latent-scalars 1 \
--loss-choice chamfer \
--get-real-method sum \
--map-to-latent "min&max" \
--mlp-width 6 \
--mlp-depth 6 \
--encoder-num-channels 3 3 4 4 \
--decoder-num-channels 4 4 3 3 \
--model-path "results/LGNAutoencoder_QCDJet_min&max_tauLS1_tauLV1_encoder3344_decoder4433" \
--data-paths "data/g_jets_30p_p4.pt" "data/q_jets_30p_p4.pt" \
--test-data-paths "data/g_jets_30p_p4.pt" "data/q_jets_30p_p4.pt" \
--anomaly-detection \
--signal-paths "data/t_jets_30p_p4.pt" "data/w_jets_30p_p4.pt" "data/z_jets_30p_p4.pt" \
--signal-types t w z \
--equivariance-test \
| tee -a "results/test-log.txt"
Boost and rotational equivariance tests were done on the model. The rotation angles range from
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- F. Marc et al., "A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups", arXiv:2104.09459. Repository: A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups.
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