# VBF Event Classification with Recurrent Neural Networks at ATLAS's LHC Experiment
## 2 An Example of a Combinatorial Problem: The VBF Categorization Task  
The standard model of particle physics is the theoretical framework describing the current knowledge of fundamental interactions. In this context and in its extension involving beyond standard model (BSM) theories, boson particles can be produced through several mechanisms: gluon-gluon fusion (GGF), Drell-Yan (DY) and vector-boson fusion (VBF) are some of the most common mechanisms that can take place at the LHC. In the case of the SM Higgs boson, the GGF is the dominating production mechanism, which occurs \(\sim\)90% of the time, while the VBF is the second one with less than 10% of the production rate. Examples of Feynman diagrams are shown in Figure 1 for GGF and VBF high-mass particle X productions. In these diagrams the X resonance decays into two vector bosons.  
According to the theory expectation, each production mechanism is characterised by a different set of physics objects that are involved in the process and that are reconstructed in the final state of the event. In particular, the VBF mechanism is expected to have two extra jets in the event with distinct features with respect to the GGF mechanism. In addition, given the complexity of the interactions occurring at a hadronic collider, and the detector effects, each event has a different jet multiplicity, that may vary up to about tens of jets. Indeed, besides the main physics process, summarised by the Feynman diagram (hard process), many other interactions could take place, such as interactions among the spectator partons (quark/gluon inside the protons) named as _underlying processes_ and interactions between protons from different bunches of the proton beams running in the LHC pipelines, known as _pile-up interactions_.  
The classification of such VBF events was strongly driven in the past by the identification of two jets among the reconstructed ones in the events that are directly related to the topology of the process. This represents a combinatorial problem in which all the possible pairs of objects may diverge quickly as the total amount of objects (\(N\)) available increases.  
Figure 1: Feynman diagrams of the production of a high-mass particle X that decays into a diboson system; ggF (**left**) and VBF (**right**) are the two dominant channels.  
For instance, with \(N=3\) only 3 pairs are possible, but with \(N=6\) the number of possible pairs increases to 15 (Figure 2).  
Of course, the misidentification rate of an algorithm will definitely affect the outcome of the combinatorial problem as much as jet multiplicity increments. Furthermore, given the geometrical acceptance of the ATLAS detector, during object reconstruction, one or more jets might be completely lost or wrongly identified, and this will contribute to a further increase of the misidentification (Figure 3).  
In such a situation, since many traditional pairing algorithms based on physics quantities yield low accuracy, it is obvious that a machine learning approach was expected to be beneficial. In particular, rather than trying to solve the combinatorial problem that fails by definition in a significant amount of events since the true pair is not present in the data at all, it was found that the best way was to not solve the combinatorial problem and let an ML approach maximize all the information that is coded in the data.