Recent progress in applying machine learning for jet physics has been built upon an analogy between calorimeters and images. In this work, we present a novel class of recursive neural networks built instead upon an analogy between QCD and natural languages. In the analogy, four-momenta are like words and the clustering history of sequential recombination jet algorithms is like the parsing of a sentence. Our approach works directly with the four-momenta of a variable-length set of particles, and the jet-based tree structure varies on an event-by-event basis. Our experiments highlight the flexibility of our method for building task-specific jet embeddings and show that recursive architectures are significantly more accurate and data efficient than previous image-based networks. We extend the analogy from individual jets (sentences) to full events (paragraphs), and show for the first time an event-level classifier operating on all the stable particles produced in an LHC event.
Neural networks in particle physics have a long history. They have been used in the past for many tasks, including early work on quark-gluon discrimination @cite_24 @cite_7 , particle identification @cite_28 , Higgs tagging @cite_25 or track identification @cite_35 . In most of these, neural networks appear as shallow multi-layer perceptrons where input features were designed by experts to incorporate domain knowledge. More recently, the success of deep convolutional networks has triggered a new body of work in jet physics, shifting the paradigm from engineering input features to learning them automatically from raw data, e.g., as in these works treating jets as images @cite_13 @cite_39 @cite_6 @cite_3 @cite_1 @cite_12 @cite_34 @cite_10 . Our work builds instead upon an analogy between QCD and natural languages, hence complementing the set of algorithms for jet physics with techniques initially developed for natural language processing @cite_0 @cite_20 @cite_38 @cite_18 @cite_8 @cite_32 . In addition, our approach does not delegate the full modeling task to the machine. It allows to incorporate domain knowledge in terms of the network architecture, specifically by structuring the recursion stack for the embedding directly from QCD-inspired jet algorithms (see Sec. )
@cite_35 @cite_3 @cite_10 @cite_20 @cite_38 @cite_18 @cite_8 @cite_39 @cite_7 @cite_28 @cite_32 @cite_6 @cite_34 @cite_25 @cite_12 @cite_1 @cite_24 @cite_0 @cite_13
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We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark gluon discrimination, boosted W tagging, and boosted top tagging. The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods. Machine learning based on convolutional neural networks can be used to study jet images from the LHC. Top tagging in fat jets offers a well-defined framework to establish our DeepTop approach and compare its performance to QCD-based top taggers. We first optimize a network architecture to identify top quarks in Monte Carlo simulations of the Standard Model production channel. Using standard fat jets we then compare its performance to a multivariate QCD-based top tagger. We find that both approaches lead to comparable performance, establishing convolutional networks as a promising new approach for multivariate hypothesis-based top tagging. Recursive structure is commonly found in the inputs of different modalities such as natural scene images or natural language sentences. Discovering this recursive structure helps us to not only identify the units that an image or sentence contains but also how they interact to form a whole. We introduce a max-margin structure prediction architecture based on recursive neural networks that can successfully recover such structure both in complex scene images as well as sentences. The same algorithm can be used both to provide a competitive syntactic parser for natural language sentences from the Penn Treebank and to outperform alternative approaches for semantic scene segmentation, annotation and classification. For segmentation and annotation our algorithm obtains a new level of state-of-the-art performance on the Stanford background dataset (78.1 ). The features from the image parse tree outperform Gist descriptors for scene classification by 4 . We introduce a novel machine learning framework based on recursive autoencoders for sentence-level prediction of sentiment label distributions. Our method learns vector space representations for multi-word phrases. In sentiment prediction tasks these representations outperform other state-of-the-art approaches on commonly used datasets, such as movie reviews, without using any pre-defined sentiment lexica or polarity shifting rules. We also evaluate the model's ability to predict sentiment distributions on a new dataset based on confessions from the experience project. The dataset consists of personal user stories annotated with multiple labels which, when aggregated, form a multinomial distribution that captures emotional reactions. Our algorithm can more accurately predict distributions over such labels compared to several competitive baselines. Neural machine translation is a relatively new approach to statistical machine translation based purely on neural networks. The neural machine translation models often consist of an encoder and a decoder. The encoder extracts a fixed-length representation from a variable-length input sentence, and the decoder generates a correct translation from this representation. In this paper, we focus on analyzing the properties of the neural machine translation using two models; RNN Encoder--Decoder and a newly proposed gated recursive convolutional neural network. We show that the neural machine translation performs relatively well on short sentences without unknown words, but its performance degrades rapidly as the length of the sentence and the number of unknown words increase. Furthermore, we find that the proposed gated recursive convolutional network learns a grammatical structure of a sentence automatically. In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder-Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases. Recently, neural network based sentence modeling methods have achieved great progress. Among these methods, the recursive neural networks (RecNNs) can effectively model the combination of the words in sentence. However, RecNNs need a given external topological structure, like syntactic tree. In this paper, we propose a gated recursive neural network (GRNN) to model sentences, which employs a full binary tree (FBT) structure to control the combinations in recursive structure. By introducing two kinds of gates, our model can better model the complicated combinations of features. Experiments on three text classification datasets show the effectiveness of our model. We introduce a new and highly efficient tagger for hadronically decaying top quarks, based on a deep neural network working with Lorentz vectors and the Minkowski metric. With its novel machine learning setup and architecture it allows us to identify boosted top quarks not only from calorimeter towers, but also including tracking information. We show how the performance of our tagger compares with QCD-inspired and image-recognition approaches and find that it significantly increases the performance for strongly boosted top quarks. Artificial intelligence offers the potential to automate challenging data-processing tasks in collider physics. To establish its prospects, we explore to what extent deep learning with convolutional neural networks can discriminate quark and gluon jets better than observables designed by physicists. Our approach builds upon the paradigm that a jet can be treated as an image, with intensity given by the local calorimeter deposits. We supplement this construction by adding color to the images, with red, green and blue intensities given by the transverse momentum in charged particles, transverse momentum in neutral particles, and pixel-level charged particle counts. Overall, the deep networks match or outperform traditional jet variables. We also find that, while various simulations produce different quark and gluon jets, the neural networks are surprisingly insensitive to these differences, similar to traditional observables. This suggests that the networks can extract robust physical information from imperfect simulations. Jets from boosted heavy particles have a typical angular scale which can be used to distinguish it from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The angular spectrum allows us to scan energy deposits over the angle between a pair of particles in a highly visual way. We set up an artificial neural network (ANN) to find out characteristic shapes of the spectra of the jets from heavy particle decays. By taking the discrimination of Higgs jets from QCD jets as an example, we show that the ANN based on the angular spectrum has similar performance to existing taggers. In addition, some improvement is seen in the case that additional extra radiations occur. Notably, the new algorithm automatically combines the information of the multi-point correlations in the jet. Using a neural-network classifier we are able to separate gluon from quark jets originating from Monte Carlo--generated ital e sup + ital e sup minus events with 85 --90 accuracy. While neural networks are very successfully applied to the processing of fixed-length vectors and variable-length sequences, the current state of the art does not allow the efficient processing of structured objects of arbitrary shape (like logical terms, trees or graphs). We present a connectionist architecture together with a novel supervised learning scheme which is capable of solving inductive inference tasks on complex symbolic structures of arbitrary size. The most general structures that can be handled are labeled directed acyclic graphs. The major difference of our approach compared to others is that the structure-representations are exclusively tuned for the intended inference task. Our method is applied to tasks consisting in the classification of logical terms. These range from the detection of a certain subterm to the satisfaction of a specific unification pattern. Compared to previously known approaches we obtained superior results in that domain. We introduce a novel approach to jet tagging and classification through the use of techniques inspired by computer vision. Drawing parallels to the problem of facial recognition in images, we define a jet-image using calorimeter towers as the elements of the image and establish jet-image preprocessing methods. For the jet-image processing step, we develop a discriminant for classifying the jet-images derived using Fisher discriminant analysis. The effectiveness of the technique is shown within the context of identifying boosted hadronic W boson decays with respect to a background of quark- and gluon- initiated jets. Using Monte Carlo simulation, we demonstrate that the performance of this technique introduces additional discriminating power over other substructure approaches, and gives significant insight into the internal structure of jets.