A Detailed Study of Interpretability of Deep Neural Network based Top Taggers Ayush Khot1 Mark S. Neubauer1 and Avik Roy1

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A Detailed Study of Interpretability of Deep Neural

Network based Top Taggers

Ayush Khot1, Mark S. Neubauer1, and Avik Roy1‡

1Department of Physics & National Center for Supercomputing Applications

(NCSA), University of Illinois at Urbana-Champaign, Urbana, IL 61801

E-mail: avroy@illinois.edu

June 2023

Abstract. Recent developments in the methods of explainable AI (XAI) allow

researchers to explore the inner workings of deep neural networks (DNNs), revealing

crucial information about input-output relationships and realizing how data connects

with machine learning models. In this paper we explore interpretability of DNN models

designed to identify jets coming from top quark decay in high energy proton-proton

collisions at the Large Hadron Collider (LHC). We review a subset of existing top tagger

models and explore diﬀerent quantitative methods to identify which features play the

most important roles in identifying the top jets. We also investigate how and why

feature importance varies across diﬀerent XAI metrics, how correlations among features

impact their explainability, and how latent space representations encode information

as well as correlate with physically meaningful quantities. Our studies uncover some

major pitfalls of existing XAI methods and illustrate how they can be overcome to

obtain consistent and meaningful interpretation of these models. We additionally

illustrate the activity of hidden layers as Neural Activation Pattern (NAP) diagrams

and demonstrate how they can be used to understand how DNNs relay information

across the layers and how this understanding can help to make such models signiﬁcantly

simpler by allowing eﬀective model reoptimization and hyperparameter tuning. These

studies not only facilitate a methodological approach to interpreting models but also

unveil new insights about what these models learn. Incorporating these observations

into augmented model design, we propose the Particle Flow Interaction Network

(PFIN) model and demonstrate how interpretability-inspired model augmentation can

improve top tagging performance.

Keywords: Explainable AI, interpretable machine learning, jet classiﬁcation with deep

learning

‡corresponding author

arXiv:2210.04371v4 [hep-ex] 5 Jul 2023

A Detailed Study of Interpretability of Deep Neural Network based Top Taggers 2

1. Introduction

Machine learning (ML) models are ubiquitous in experimental High Energy Physics

(HEP). With an ever increasing volume of data coupled with complex detector

phenomenology, these models are useful to ﬁnd meaningful information from these

large datasets. Over time, machine learning models have grown in complexity and

simpler regression and classiﬁcation models have been replaced by intricate and deep

neural networks. Owing to their intractably large number of trainable parameters and

arbitrarily complex non-linear nature, deep neural networks (DNNs) have often been

treated as black boxes. It has always been challenging to understand how diﬀerent input

features contribute to the network’s computational process and how the inter-connected

neural pathways convey information. In recent years, advances in explainable Artiﬁcial

Intelligence (XAI) [1] have made it possible to build intelligible relationship between

an AI model’s inputs, architecture, and predictions [2, 3, 4]. While some methods

remain model agnostic, a substantial subset of these methods have been developed

to infer interpretability of computer vision models where an intuitive reasoning can

be extracted from human-annotated datasets to validate XAI techniques. However, in

other data structures such as large tabular data or relational data constructs like graphs,

use of XAI methods are still quite novel [5, 6]. In recent times, XAI has been successful

in learning the underlying physics of a number of problems in high energy detectors [7],

including parton showers at the Large Hadron Collider (LHC) [8] and jet reconstruction

using particle ﬂow algorithms [9].

One of the major applications of ML in the ﬁeld of HEP is classiﬁcation of jets,

which is referred to as jet tagging. Jets represent hadronic showers observed as conical

spray of particles originating from quarks and gluons produced in the high energy

collisions at a collider experiment like the LHC. Identifying jets that originate from

decay products of a particle such as the top quark (t) and being able to separate them

from other jet categories, such as jets originating from the quantum chromodynamics

(QCD) background, is an important challenge in many physics analyses. Traditional top

tagging algorithms based on kinematic features of jets and clustering of jet constituents

(see Refs. [10, 11, 12, 13] for example) have been used in particle phenomenology research

as well as by the ATLAS and CMS experiments and their predecessors. In Run 1 physics

analyses, these top tagging algorithms along with low-complexity statistical models like

decision trees took the center stage in dealing with top tagging [14, 15, 16]. However,

owing to their superior performance, models based on DNNs started becoming popular

in Run 2 at a higher center-of-mass energy of 13 TeV [17, 18].

For top quarks produced with large momenta, the decay products can be packed

close to one another and be reconstructed as a single jet. For such boosted jets,

top tagging can be particularly challenging and require a better analysis of jet

substructures, a collection of constituents and their derivative properties that can oﬀer

better discrimination between jet classes. DNNs have proven to be useful to exploit

the jet substructure properties in performing jet classiﬁcation. A wide variety of deep

A Detailed Study of Interpretability of Deep Neural Network based Top Taggers 3

learning models have been developed to optimize top tagging [19, 20, 21, 22, 23, 24, 25,

26, 27, 28, 29, 30, 31, 32, 33]. A comprehensive review and comparison of many of these

models is given in Ref. [34]. Some of these models have exploited DNN’s capacity to

approximate arbitrary non-linear functions [35] and their huge success with problems

in the ﬁeld of computer vision, other models have been inspired by the underlying

physics information like jet clustering history [22], physical symmetries [23] and physics-

inspired feature engineering [27]. These eﬀorts have inspired novel model architectures

and feature engineering by creating or augmenting input feature spaces with physically

meaningful quantities [27, 36, 37].

The rich history of physics-inspired model development makes the problem of top

tagging an excellent playground to better understand the modern XAI tools themselves.

This allows us to traverse a rare two-way bridge in exploring the relationship between

data and models- our physics knowledge will allow us to better understand the inner

workings of modern XAI tools and perfect them while those improved tools would allow

us to take a deeper look at the models- paving ways for analyzing and reoptimizing

them. As it has been pointed out in Ref. [38], such insights into explainability of

DNN-based models are important to validate them, to make them reliable and reusable.

Additionally, the broader scope of uncertainty quantiﬁcation in association with ML

models relies on developing robust explanations [39] and in the ﬁeld of HEP for

problems like top tagging will require dedicated understanding of how robust as well as

interpretable these models are [40].

Yet another remarkable application of interpretability is to understand how the

model conveys information and in doing so, which parts of a DNN most actively engage

in forward propagation of information. Such studies could be useful to understand

and reoptimize model complexity. Given DNNs have shown remarkable success in jet

and event classiﬁcation, recent work has placed emphasis on developing DNN-enabled

FPGAs for trigger-level applications at the LHC [41, 42, 43]. As resource consumption

and latency of FPGAs directly depend on the size of the network to be implemented,

it is deﬁnitely easier to embed simpler networks on these devices. Hence, methods that

allow interpreting a network’s response patterns as well as provide critical insights about

model optimization without compromising its performance can greatly beneﬁt these new

budding ﬁelds of ML applications, especially for online event selection and jet tagging

at current and future high energy colliders.

Application of state-of-the-art explainability techniques for interpreting jet tagger

models is receiving more attention recently [37, 44, 45, 46] and has been demonstrated

to be successful in identifying feature importance for models like the Interaction

Network [47]. In this paper, we study the interpretability of a subset of existing ML-

based top tagging models. The models we have chosen use multi-layer perceptrons

(MLPs) as underlying neural architecture. Choosing simpler neural architecture allows

us to elucidate the applicability and limitations of existing XAI methods and develop

new tools to examine them without convoluting these eﬀorts with the complexity of

larger models or unorthodox data structures. To compare our results for diﬀerent

A Detailed Study of Interpretability of Deep Neural Network based Top Taggers 4

models as well as with existing benchmarks in published literature, we use the dataset

developed by the authors of Ref. [23] and later used in the top tagger model review in

Ref. [34]. The models explored in this paper along with the dataset have been reviewed

in section 2. The model hyperparameters explained in this section will constitute the

baseline model in each category. Variants of each model are studied to better understand

their interpretability where the underlying architecture remains the same but model

hyperparameters, input features, or data preprocessing might be changed. Section 3

reviews modern XAI methods that we will use in investigating the explainability of top

tagger models. In section 4, we analyze the results of applying XAI methods on diﬀerent

top tagger models. Section 6 summarizes our ﬁndings and illustrates new dimensions

to explore in the conjunction of XAI and HEP.

2. Review of Top Tagging Dataset and Models

The dataset used in this paper has been used to perform model benchmarking studies

in Ref. [34] and publicly available at Ref. [48]. This dataset consists of 1 million top

(signal) jets and 1 million QCD (background) jets genetated with Pythia8 [49] with its

default tune at 14 TeV center of mass energy for proton-proton collisions. The detector

simulation was performed with Delphes [50] and jets were reconstructed using the

anti −ktalgorithm [51] with a jet radius of R= 0.8using FastJet [52]. Only jets

with transverse momenta within the range of 550 and 650 GeV are considered. For

each jet, the dataset contains the four momenta of up to 200 constituents with zero-

padded entries for missing constituents. The dataset is divided into traning, validation,

and testing sets with a 6:2:2 split. Some characteristic jet features from a random

subsample of the training data are shown in Figure 1.

(a) (b) (c)

Figure 1. Distribution of (a) number of constituent particles, (b) jet transverse

momentum (pT,J ), and (c) jet mass (mJ) for background (QCD) and signal (top)

jets

In this paper we consider three diﬀerent NN-based models for top tagging. Given

the tagger distinguishes between two jet classes, minimizing the standard binary cross-

A Detailed Study of Interpretability of Deep Neural Network based Top Taggers 5

entropy (BCE) loss has been used as the training objective for all models. The training

is done using the Adam optimizer with minibatches. All networks showed comparable

performance with diﬀerent batchsizes. The architecture, hyperparameters, and data

preprocessing for each of the baseline models is summarized below-

TopoDNN [19, 17]: The simplest top tagging model we consider is a fully connected

multi-layer perceptron (MLP) trained with transverse momentum (pT), azimuthal

angle (ϕ), and pseudorapidity (η) of the 30 most energetic particles. Usually referred

to as TopoDNN, this model represents a quintessential MLP network. Although

TopoDNN is outperformed by many other ML-models for top tagging, its simple

architecture allows us to explore diﬀerent XAI metrics, their limitations, and the best

practices to overcome them. Since MLPs are still widely used in HEP for a wide variety

of applications, our studies of modern XAI for this model will also illustrate the best

practices to interpret the input-output relations for such models.

TopoDNN is trained on preprocessed data where (i) the jet is rotated on the η−ϕ

plane to have the most energetic component aligned along the central coordinate (0,0),

(ii) the second most energetic component falls along the negative-ϕaxis, and (iii) all

momenta are scaled with an arbitrarily chosen factor of 1/1700. The transformations

(i) and (ii) take advantage of the underlying Lorentz invariance of collider physics and

(iii) converts the momenta into unitless quantities and scales them down to a numerical

range comparable to those of η, ϕ quantities. The baseline model is constructed with

4 hidden layers with 300, 102, 12, and 6 nodes respectively and ReLU activation

function. The output layer consists of a single node which is converted by the sigmoid

function to represent the probability of the jet being classiﬁed as a signal jet.

Multi-body N-subjettiness (MBNS) [20, 21]: Top-tagging with N-subjettiness

variables uses an MLP as the underlying trainable architecture. However, the input

to the network is diﬀerent from the usual kinematic variables. It uses the multi-body

N-subjettiness variables [53], deﬁned as

τ(β)

n=1

pT,J X

pT,i min n∆Rβ

1i,∆Rβ

2i, ..., ∆Rβ

nio(1)

where pT,J and pT,i represent the transverse momenta of the jet and its i-th constituent

and ∆Rki is the distance between the k-th jet axis and the i-th particle constituent.

The njet axes chosen for claculating τ(β)

nare obtained using the ktalgorithm [54]

with E-scheme recombination [55]. Figure 2 shows the distribution of some of the τ

variables for QCD and top jets. The input to MBNS tagger is the set of subjettiness

variables

nτ(0.5)

1, τ(1)

1, τ(2)

1, τ(0.5)

2, τ(1)

2, τ(2)

2, ..., τ(0.5)

N−2, τ(1)

N−2, τ(2)

N−2, τ(1)

N−1, τ(2)

N−1o[{pT,J , mJ}(2)

where, besides the subjettiness variables, the jet pTand jet mass (mJ)variables are

used as inputs to provide a kinematic scale for the jet event. However, the latter inputs

are scaled by a factor of 1/1000 to mitigate the several orders of magnitude gap between

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ADetailedStudyofInterpretabilityofDeepNeuralNetworkbasedTopTaggersAyushKhot1,MarkS.Neubauer1,andAvikRoy1‡1DepartmentofPhysics&NationalCenterforSupercomputingApplications(NCSA),UniversityofIllinoisatUrbana-Champaign,Urbana,IL61801E-mail:avroy@illinois.eduJune2023Abstract.Recentdevelopmentsinthemethod...

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A Detailed Study of Interpretability of Deep Neural Network based Top Taggers Ayush Khot1 Mark S. Neubauer1 and Avik Roy1

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