An Exploration of Learnt Representations of W Jets

Abstract

I present a Variational Autoencoder (VAE) trained on collider physics data (specifically boosted W jets), with reconstruction error given by an approximation to the Earth Movers Distance (EMD) between input and output jets. This VAE learns a concrete representation of the data manifold, with semantically meaningful and interpretable latent space directions which are hierarchically organized in terms of their relation to physical EMD scales in the underlying physical generative process. A hyperparameter β controls the resolution at which the VAE is sensitive to structures in the data manifold. The variation of the latent space structure with β, and the scaling of some VAE properties, provide insight into scale dependent structure of the dataset and its information complexity. I introduce two measures of the dimensionality of the learnt representation that are calculated from this scaling. Data, Architecture, and TrainingA sample of 6 × 10 5 W jets were simulated with momenta in the range 500 -600 GeV using a standard pipeline of Madgraph [10], Pythia8 [11], and Delphes [12]. The simulated jets typically contain O(100) particles, and the 50 largest-momentum particles are selected and stored as 3-vectors Preprint. Under review.

Challenges for Unsupervised Anomaly Detection in Particle Physics

“…In order to understand what a VAE is learning, we study its latent space. In particular, we look at distance between events in VAE latent space (see [48,63] for other studies of VAE latent spaces in particle physics). Since we can think of the VAE anomaly score as a "distance" encoding how far any given event is from the background distribution, it is also natural to ask about the distances between individual events.…”

Challenges for unsupervised anomaly detection in particle physics

“…In order to understand what a VAE is learning, we study its latent space. In particular, we look at the distance between events in VAE latent space (see [48,64] for other studies of VAE latent spaces in particle physics). Since we can think of the VAE anomaly score as a "distance" encoding how far any given event is from the background distribution, it is also natural to ask about the distances between individual events.…”

“…[27] finds the optimal size to be around 20-34 for their top-tagging data. We chose the latent space size by preforming a small scan over latent dimension sizes [2,4,8,16,32,64] on the "The Machine Learning Landscape of Top Taggers" data [82] and found that the larger latent space yielded better top tagging. We then changed to the current data set, as there are more signals to consider (i.e.…”

Which Metric on the Space of Collider Events?

“…( 8), computing the linearized distance between all pairs of events E and Ẽ using pluOT only requires O(N 2 evt ) computations of the weighted Euclidean metric; see eq. (12). Given that computing a weighted Euclidean metric is several orders of magnitude faster than computing the Hellinger-Kantorovich metric, our approach using pluOT offers a substantial computational advantage compared to computing the exact Hellinger-Kantorovich distance between all pairs of events.…”

“…In [2], the EMD formed the foundation of a unified approach to collider observables based on the distance between an event and a manifold on the space of events, recasting decades of collider physics in the language of optimal transport. Optimal transport also un-derlies a number of recently-developed machine learning frameworks for anomaly detection and event generation at the LHC [7][8][9][10][11][12].…”