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Jet Flavor Classification in High-Energy Physics with Deep Neural Networks
Daniel Guest, Julian Collado, Pierre Baldi, Shih-Chieh Hsu, Gregor Urban, Daniel Whiteson
TL;DR
Jet-flavor classification is difficult because tracking detectors provide large, variable-dimensional data while standard taggers rely on expert dimensionality reduction. The paper compares deep networks using track, vertex, and expert representations, finding that lower-level information can improve on expert-only taggers, while track-only classification remains challenging. Combining low-level information with expert features gives the best performance in the studied setting.
Problem
Jet-flavor classification must infer whether jets come from light- or heavy-flavor quarks despite large, variable-dimensional tracking data and reliance on expert dimensionality reduction.
Method
The paper applies deep networks to structured track, vertex, and expert representations arranged as strict processing functions of one another.
Results
Combining low-level information with expert features has the best performance, while track-only networks remain below higher-level networks and track-plus-vertex networks outperform expert-only networks.
Takeaways & Limitations
Lower-level track and vertex information can match or exceed expert-only state-of-the-art performance, while expert guidance remains useful for achieving the strongest results.
Takeaways & Limitations
The conclusions apply to the expert strategies considered and to the simulated environment studied, which the authors regard as representative of current state of the art.
Abstract
from arXiv · showhide
Classification of jets as originating from light-flavor or heavy-flavor quarks is an important task for inferring the nature of particles produced in high-energy collisions. The large and variable dimensionality of the data provided by the tracking detectors makes this task difficult. The current state-of-the-art tools require expert data-reduction to convert the data into a fixed low-dimensional form that can be effectively managed by shallow classifiers. We study the application of deep networks to this task, attempting classification at several levels of data, starting from a raw list of tracks. We find that the highest-level lowest-dimensionality expert information sacrifices information needed for classification, that the performance of current state-of-the-art taggers can be matched or slightly exceeded by deep-network-based taggers using only track and vertex information, that classification using only lowest-level highest-dimensionality tracking information remains a difficult task for deep networks, and that adding lower-level track and vertex information to the classifiers provides a significant boost in performance compared to the state-of-the-art.
INTRODUCTION
Jet-flavor classification helps identify heavy-flavor signals and suppress light-flavor backgrounds, but detector tracking data are large, variable, and unordered. The paper investigates deep networks across progressively processed representations to assess information loss and classification performance.
- Jet-flavor classification distinguishes jets from light-flavor and heavy-flavor quarks to identify heavy-flavor signals and reduce light-flavor backgrounds.
- Heavy-flavor jets tend to contain displaced decays, whose vertices are reconstructed from charged-particle trajectories.
- Variable particle counts and unordered tracks create a high-dimensional classification problem without a natural ordering.
- Traditional approaches reduce dimensionality before applying shallow machine-learning techniques, partly because of historical limits on handling high- and variable-dimensional data.
- The paper applies deep learning to track, vertex, and expert representations that form a strict processing hierarchy.
- The layered dataset enables analysis of information loss during processing and the ability of classifiers to learn from lower- and higher-dimensional data.
CLASSIFICATION AND DIMENSIONALITY
The classifier must compress potentially very high-dimensional detector data into a single discriminating value, but direct likelihood estimation is impractical and lower-dimensional processing may discard useful information. Structured representations therefore provide benchmarks for testing how completely classifiers extract information from lower-level inputs.
- The ML task is to map observed data at a chosen processing level from IR^N to a scalar containing classification-relevant information.
- The theoretical upper bound is classification based on the true heavy-flavor-to-light-flavor likelihood ratio in the high-dimensional domain.
- Directly estimating the unknown likelihood in the original high-dimensional space would require enormous amounts of labeled data.
- For spaces above approximately 50 dimensions, extracting the relevant information remains difficult even with deep learning and can require large training samples.
- Structured datasets with multiple processing levels let higher-level representations serve as performance benchmarks when the true likelihood is unknown.
- If lower-level tools underperform higher-level tools, they have not extracted all relevant information; if they exceed them, higher-level data may omit relevant information.
DATA
The study uses simulated jets labeled by flavor and organizes detector information into track, vertex, and expert levels with decreasing dimensionality and increasing expert preprocessing. This setup supports comparisons of raw tracking information, reconstructed vertices, and conventional expert features.
- Light-flavor jets originate from u, d, s quarks or gluons, charm jets from c quarks, and heavy-flavor jets from b quarks.
- The study assumes pileup will not alter relative method performance and uses a simplified tracking model without material interactions or strange-hadron removal.
- Secondary vertices are reconstructed iteratively with adaptive vertex fitting, including repeated fitting to account for multiple vertices in b-hadron decay chains.
- The intermediate representation contains vertex mass, associated-track count, energy fraction, displacement measures, and angular separations from the jet axis.
- The highest-level representation models current experimental inputs with fourteen expert features, including track significances, JetProb, jet widths, vertex significance, vertex counts, and decay-chain quantities.
- The dataset contains simulated light-flavor, charm, and heavy-flavor jets produced with particle-physics event, showering, hadronization, and detector-simulation tools.
METHODS
The experiments convert the three flavor labels into a binary bottom-versus-nonbottom task and evaluate light-quark and charm-quark rejection separately.
- The three labels are mapped to binary targets by assigning bottom quarks to one and charm and light quarks to zero.
- The study evaluates light-quark and charm-quark rejection separately.
Machine Learning Approaches
Variable-sized, unordered track and vertex sets challenge fixed-input machine learning methods. The study addresses these challenges with several deep-learning approaches while examining high-level jet-flavor information.
- Track and vertex data have variable size, making them challenging inputs for machine-learning models.The associated sets are also unordered, although elements are often listed in an arbitrary order.
- High-level jet-flavor variables are distributions used to discriminate light-flavor from heavy-flavor quark jets.
- The paper evaluates feedforward, LSTM recurrent, and outer recursive neural networks for this classification problem.
Feedforward Neural Networks
Feedforward networks require variable-sized track and vertex inputs to be ordered, capped, and padded. The architecture uses shared first-layer weights for track-level structure before fully connected processing.
- Feedforward networks require arbitrary ordering, input-size capping, and zero padding for variable-sized track and vertex sets.
- Tracks are sorted by decreasing absolute d0 significance, which outperformed random ordering and helps retain secondary-vertex tracks under capping.
- 15 tracks are retained, preserving all original tracks in 99.97% of samples; jets with fewer tracks are zero-padded.
- The networks were trained for 100 epochs, with model selection based on validation error and hyperparameters manually optimized.
- The feedforward networks use shared weights for each track object in the first layer, followed by fully connected layers.
LSTM Networks
LSTM networks process ordered sequences of track, vertex, and expert features for variable-sized inputs. Their sequence-processing design avoids zero padding, while the models retain a 15-track maximum for comparability.
- LSTM inputs are sequences of concatenated track, vertex, and expert features sorted by absolute d0 significance.
- Unlike feedforward models, LSTMs handle arbitrary-length sequences without zero padding.
- The LSTM models nevertheless retain a maximum of 15 tracks to enable comparison with the fully connected models.
- The architecture combines one LSTM layer with a feedforward network that produces the final predictions.
Outer Recursive Networks
The outer recursive approach handles track sets by applying a shared network to track pairs and then combining the pair outputs with a multilayer perceptron.
- The outer recursive architecture processes all possible track pairs with a single shared nonlinear network.
- With up to 15 tracks, the model forms 105 unordered or 210 ordered pairs.
- Pair outputs are concatenated and passed to a multilayer perceptron with one to four hidden layers.
Hardware and Software Implementations
The study used multicore CPU machines and NVIDIA Titan GPUs, with neural networks trained through Theano and, for feedforward networks, Keras.
- Computations used machines with 16 Intel Xeon cores, NVIDIA Titan graphics processors, and 64 GB memory.
- Neural networks were trained using the GPU-accelerated Theano library, with Keras also used for feedforward networks.
RESULTS
The results compare neural-network architectures and feature levels using AUC and efficiency-based evaluations. Combined lower-level information can outperform expert-only inputs, while feedforward networks most often perform best and event distributions provide an additional comparison of classifier behavior.
- The best LSTM models use hidden states of about 70 units, while the MLP size has secondary importance for overall performance.
- The AUC metric measures performance, with larger values indicating better classification; signal efficiency and background rejection are examined across kinematic conditions.
- Networks combining expert-level information with track and/or vertex information outperform the expert-only benchmark, sometimes by a significant margin.
- Track-only or vertex-only networks do not match expert-only performance, whereas networks using both tracking and vertexing slightly exceed it.
- Feedforward deep networks most often perform best for a given feature set, although their margin over LSTM models is sometimes small.
- Selected event distributions are compared at equivalent background rejection to examine how classifiers with and without lower-level information classify events.
DISCUSSION
The experiments find that expert-level dimensional reduction can discard useful information, while combining low-level tracks and vertices with expert features gives the strongest performance. However, lower-level information alone remains difficult for deep networks and requires careful simulation validation.
- Expert strategies for dimensional reduction sacrifice or distort useful information needed for jet-flavor classification.
- Networks using tracks and vertices outperform those using only vertices, while track-only networks outperform vertex-only networks but remain below high-level-feature networks.The lower-level feature space is more difficult for networks to learn from despite containing a superset of the high-level information.
- The conclusions are limited to the expert strategies studied and the simulated environment, while high-dimensional inputs require careful validation of simulation models.Suggested validation combines one-dimensional feature checks with network-output validation in control samples.
- Networks using tracks and vertices outperform expert-only networks, except at high signal efficiency (> 75%), where expert-only networks perform better.
- Combining expert features with low-level information significantly outperforms state-of-the-art expert-only networks.Expert features provide low-dimensional guidance while retaining lower-level information, and may steer learning toward well-understood discrimination strategies.
- These improvements can provide important boosts to physics studies that rely on identifying jet flavor.