Jet substructure classification in high-energy physics with deep neural networks

At the extreme energies of the Large Hadron Collider, massive particles can be produced at such high velocities that their hadronic decays are collimated and the resulting jets overlap. Deducing whether the substructure of an observed jet is due to a low-mass single particle or due to multiple decay objects of a massive particle is an important problem in the analysis of collider data. Traditional approaches have relied on expert features designed to detect energy deposition patterns in the calorimeter, but the complexity of the data make this task an excellent candidate for the application of machine learning tools. The data collected by the detector can be treated as a two-dimensional image, lending itself to the natural application of image classification techniques. In this work, we apply deep neural networks with a mixture of locally connected and fully connected nodes. Our experiments demonstrate that without the aid of expert features, such networks match or modestly outperform the current state-of-the-art approach for discriminating between jets from single hadronic particles and overlapping jets from pairs of collimated hadronic particles, and that such performance gains persist in the presence of pileup interactions.

Figure 1

Distributions in simulated samples of high-level jet substructure variables widely used to discriminate between jets due to collimated decays of massive objects ($W\to qq$) and jets due to individual quarks or gluons (QCD). Two cases are shown: with and without the presence of additional in-time $pp$ interactions, included at the level of an average of 50 such interactions per collision.

Figure 2

Typical jet images from class 1 (single QCD jet from $q$ or $g$) on the left, and class 2 (two overlapping jets from $W\to q{q}^{\prime }$) on the right, after preprocessing as described in the text.

Figure 3

Average of 100,000 jet images from class 1 (single QCD jet from $q$ or $g$) on the left, and class 2 (two overlapping jets from $W\to q{q}^{\prime }$) on the right, after preprocessing.

Figure 4

Signal efficiency versus background rejection (inverse of efficiency) for deep networks trained on the images and boosted decision trees trained on the expert features, both with (bottom) and without pileup (top). Typical choices of signal efficiency in real applications are in the 0.5–0.7 range. Also shown are the performance of jet mass individually as well as two expert variables in conjunction with a mass window.

Figure 5

Distributions in simulated samples without pileup of high-level jet substructure variables for pure signal ($W\to qq$) and pure background (QCD) events. To explore the decision surface of the ML algorithms, also shown are background events with various levels of rejection for deep networks trained on the images and boosted decision trees trained on the expert features. Both algorithms preferentially select jets with values near the peak signal values. Note, however, that while the BDT has been supplied with these features as an input, the DNN has learned this on its own.

Figure 6

Distributions in simulated samples with pileup of high-level jet substructure variables for pure signal ($W\to qq$) and pure background (QCD) events. To explore the decision surface of the ML algorithms, also shown are background events with various levels of rejection for deep networks trained on the images and boosted decision trees trained on the expert features. Both algorithms preferentially select jets with values near the peak signal values. Note, however, that while the BDT has been supplied with these features as an input, the DNN has learned this on its own.