Classification of jets with deep learning has gained significant attention in recent times. However, the performance of deep neural networks is often achieved at the cost of interpretability. Here we propose an interpretable network trained on the jet spectrum $S_{2}(R)$ which is a two-point correlation function of the jet constituents. The spectrum can be derived from a functional Taylor series of an arbitrary jet classifier function of energy flows. An interpretable network can be obtained by truncating the series. The intermediate feature of the network is an infrared and collinear safe C-correlator which allows us to estimate the importance of a $S_{2}(R)$ deposit at an angular scale R in the classification. The performance of the architecture is comparable to that of a convolutional neural network (CNN) trained on jet images, although the number of inputs and complexity of architecture is significantly simpler than the CNN classifier. We consider two examples: one is the classification of two-prong jets which differ in color charge of the mother particle, and the other is a comparison between Pythia 8 and Herwig 7 generated jets.

At multi TeV pp colliders such as the LHC, boosted heavy particles can be produced and form a single collimated cluster of particles. Such a localized cluster is distinguished from QCD jets from quarks or gluons by the substructures of the cluster [1]. For this purpose, consistent definitions of substructures of jets have been studied extensively. There are various methods for identifying the jet substructures, such as strategies based on cluster decomposition [1-8] and shape variables [9-13]. These methods focus on different features of jet substructures to maximize the discrimination power. For the case of Higgs, W, and Z boson decaying hadronically into two quarks, a critical feature is a two-prong substructure inside. Because the key features depend on nature of the parent particle of a jet, there are several frameworks that can be applied to jets [14-18]. In this paper, we propose a new framework to identify jet substructures using a spectral function similar to the angular structure function [14, 19, 20]. Spectral analysis is widely used technique to explore quantum worlds.