Tau lepton reconstruction: t-SNE visualization of tau jets and embeddings

[jpata]

Use the t-SNE method: https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding
to visualize the space of tau lepton jets, both in terms of the raw features and in neural network embeddings.

The dataset can be found here: https://zenodo.org/records/13881061.
Specifically, take https://zenodo.org/records/13881061/files/z_train.parquet?download=1 which contains tau jets.

Part 1: raw jet features

From the dataset, take the particle constituents reco_cand_p4s of tau jets and map each jet to 2D space using https://scikit-learn.org/1.5/modules/generated/sklearn.manifold.TSNE.html.

jet 1: momenta of the particles 1-N in the jet p1, p2, p3, ..., pN
map the jet into a 2D embedding with t-SNE: f(jet) = f(p1, p2, p3, ..., pN) -> (x,y)

Give each jet in the 2D scatterplot a color according to the true tau decay mode gen_jet_tau_decaymode.
Do the jets with a different gen_jet_tau_decaymode cluster together in similar regions?

Part 2: neural network embeddings

We can have a neural network to transform the jet into e.g. 128 numbers (an embedding) before the t-SNE function.

jet 1: momenta of the particles 1-N in the jet p1, p2, p3, ..., pN
map the jet using a neural network embedding: nn(p1, p2, p3, ..., pN) -> R^128
map the jet neural network embeddings into a 2D embedding with t-SNE: f(R^128) -> (x,y)

For the embedding, use the neural network from https://github.com/HEP-KBFI/ml-tau-en-reg.

References

• https://arxiv.org/pdf/2407.06788
• https://arxiv.org/pdf/2307.07747