Interpretable Geometric Deep Learning via Learnable Randomness Injection
Authors: Siqi Miao
Yunan Luo
Mia Liu
Pan Li
Venue: ICLR 2023 poster (2023)
Keywords: Geometric Deep Learning
Interpretation
Graph Neural Networks

Abstract: Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learning (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models are often complicated and hardly interpretable, which poses concerns to scientists who are to deploy these models in scientific analysis and experiments. This work proposes a general mechanism, learnable randomness injection (LRI), which allows building inherently interpretable models based on general GDL backbones. LRI-induced models, once trained, can detect the points in the point cloud data that carry information indicative of the prediction label. We also propose four datasets from real scientific applications that cover the domains of high-energy physics and biochemistry to evaluate the LRI mechanism. Compared with previous post-hoc interpretation methods, the points detected by LRI align much better and stabler with the ground-truth patterns that have actual scientific meanings. LRI is grounded by the information bottleneck principle, and thus LRI-induced models are also more robust to distribution shifts between training and test scenarios. Our code and datasets are available at https://github.com/Graph-COM/LRI.

Published as a conference paper at ICLR 2023
INTERPRETABLE GEOMETRIC DEEP LEARNING VIA LEARNABLE RANDOMNESS INJECTION
Siqi Miao', Yunan Luo', Mia Liu", Pan Li
GGorgia Institute of Technology. "Purdue University
{siqi .iiao, yunar, pan1 panli]egatech. edu,
e (1iu3173, panli pet.:prrs..aanepuuuuuuu...e.
ABSTRACT
Point cloud data is ubiquitous in scientific fields. Recently, geometric deep learn- ing (GDL) has been widely applied to solve prediction tasks with such data. However, GDL models often complicated and hardly interpretable, which poses concerns to scientists who are to deploy these models in scientific analy- sis and experiments. This work proposes general mechanism, learnable ran- dommess injection (LRI), which allows building inherently interpretable models based on general GDL backbones. LRI-induced models, once trained, can de- tect the points in the point cloud data that carry information indicative of the prediction label. We also propose four datasets from real scientific applications that cover the domains of high-energ, physics and biochemistry to evaluate the LRI mechanism. Compared with previous post-hoc interpretation methods, the points detected by LRI align much better and stabler with the ground-truth pat- terns that have actual scientific meanings. LRI is grounded by the information bottleneck principle, and thus LRI-induced models are also more robust to dis- tribution shifts between training and test scenarios. Our code and datasets are available https:: httttp:://iithb...o http://wwwb..oocnaaaccc////////e
INTRODUCTION
The measurement of many scientific research objects can be represented as a point cloud, i.e., set of featured points in some geometric space. For example, in high energy physics (HEP), particles generated from collision experiments leave spacial signals on the detectors they pass through (Guest al. 2018): In biology, protein is often measured and represented as a collection of amino acids with spacial locations (Wang et al.) 2004 2005). Geometric quantities of such point cloud data often encode important properties of the research object, analyzing which researchers may expect to achieve new scientific discoveries (Tusnady & Simon
1998
Aad et al. 2012).
Recently, machine learning techniques have been employed to accelerate the procedure of scientific discovery (Butler al. 2018 Carleo et al.
2019). For geometric data above, geometrie deep learning (GDL) (Bronstein et al. 2017; 2021 has shown great promise and has been applied to the fields such HEP (Shlomi al. 2020 Qu & Gouskos 2020), biochemistry (Gainza et al., 2020 Townshend et al.) 2021) and so on. However, geometric data in practice is often irregular and high- dimensional. Think about a collision event in HEP that generates hundreds thousands of particles, or protein that consists of tens to hundreds of amino acids. Although each particle or each amino acid is located in low-dimensional space, the whole set of points eventually is extremely irregular and high-ding dinbbsiienii...... So. current research on GDL primarily focuses on designing neural network (NN) architectures for GDL models to deal with the above data challenge. GDL models have to preserve some symmetries of the system and incorporate the inductive biases reflected by geometric principles to guarantee their prediction quality (Cohen Welling 2016 Bogatskiy et 2020). and therefore often involve dedicated-desse -essignd complex NN architectures.
Albeit with outstanding prediction performance, the complication behind GDL models makes them bardly interpretable. However, in many scientific applications, interpretable models are in need (Roscher et al. 2020): For example, in drug discovery, compared with just predicting the bind- ing affinity of protein- -igand pair, it is more useful know which groups of amino acids determine the affinity and where can be the binding site, as the obtained knowledge may guide future research
directions (Gao al. 2018
Karimi et al. 2019 2020 Moreover, scientists tend only trust inter-

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Published as a conference paper at ICLR 2023
Unbranched
Protein
Alkane
Ligand
f
y
pileup
B = 21
Binding
Site
*X
Carbonyl
(a) ActSTrack
(b) Tau3mu
(c) SynMol
(d) PLBind
Figure 1: Illustrations of the four scientific datasets in this work to study interpretable GDL models.
pretable models in many scenarios, c.g., most applications in HEP, where data from real experiments lack labels and models have to be trained on simulation data (Nachman & Shimmin 2019). Here, model interpretation is used to verify if a model indeed captures the patterns that match scientific principles instead of some spurious correlation between the simulation environment and labels. Un- fortunately, to the best of our knowledge, there have been no studies on interpretable GDL models let alone their applications in scientific problems. Some previous post-hoe methods may be extended to interpret pre-trained GDL model while they suffer from some limitations to be reviewed in
Sec. 2 Morcover, recent works (Rudin) 2019] Laugel et al., 2019 Bordt et al. 2022 Miao et al.) 2022 have shown that the data patterns detected by post-hoc methods are often inconsistent across interpretation methods and pre- mre-trinee models, and may hardly offer reliable scientific insights.
To fill the gap, this work proposes to study interpretable GDL models. Inspired by the recent work (Miao et al., 2022), we first propose a general mechanism named Learnable Randommess Injection (LRI) that allows building inherently interpretable GDL models based on a broad range of GDL backbones. We then propose four datasets from real-world scientific applications in HEP and biochemistry and provide extensive comparison between LRI-induced GDL models and previous post-hoc interpretation approaches (after being adapted to GDL models) over these datasets.
Our LRI mechanism provides model interpretation by detecting a subset of points from the point cloud that is most likely to determine the label of interest. The idea of LRI is to inject learn- able randomness to each point, where, along with training the model for label prediction, injected randomness on the points that are important to prediction gets reduced. The convergent amounts of randomness on points essentially reveal the importance of the corresponding points for predic- tion. Specifically in GDL, as the importance of point may be indicated by either the existence of this point in the system or its geometric location, we propose to inject two types of random- ness, Bernoulli randomness, with the framework name LRI-Bernoulli to test existence importance of points and Gaussian randomness on geometric features, with the framework name -Rl-Gaussinn to test location importance of points. Moreover, by properly parameterized such Gaussian random- ness, we may tell for a point, how in different directions perturbing its location affects the prediction result more. With such fine-grained geometric information, we may estimate the direction of the particle velocity when analyzing particle collision data in HEP. LRI is theoretically sound as it es- sentially uses a variational objective derived from the information bottleneck principle (Tishby al.] 2000). LRI-induced models also show better robustness to the distribution shifts between training and test scenarios, which gives scientists more confidence in applying them practice.
We note that one obstacle to studying interpretable GDL models is the lack of valid datasets that consist of both classification labels and seientifically meaningful patterns verify the quality of interpretation. Therefore, another sigmificant contribution of this work is to prepare four bench- mark datasets grounded on real-world scientific applications to facilitate interpretable GDL research. These datasets cover important applications in HEP and biochemistry. We illustrate the four datasets in Fig. T and briefly introduce them below. More detailed descriptions can be found in Appendix C
Act.Track is a particle tracking dataset in HEP that used to reconstruct the properties, such as the kinematics of charged particle given set of position measurements from a tracking detector. Tracking is an indispensable step in analyzing HEP experimental data as well as particle tracking used in medical applications such as proton therapy (Schulte et al. 2004 Thomson
2013 Ai et al., 2022). Our task is formulated differently from traditional track reconstruction tasks: We predict the existence of a - nu decay and use the set of points from the μ to verify model interpretation, which can be used to reconstruct μ tracks. Act sTrack also provides a controllable environment (e.g., magnetic field strength) to study fine-grained geometric patterns.
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Tau3Mu, another application in HEP, is to detect challenging signature of charged lepton flavor violating decays, i.e., the r + Zun decay, given simulated muon detector hits in proton- proton collisions. Such decays are greatly suppressed in the Standard Model (SM) of particle physics (Oerter 2006; Blackstone et al. 2020), therefore, any detection of them is a clear signal of new physics beyond the Standard Model (Calibbi & Signorelli] [018 Collaboration 2021 Unfortunately, - puat contains particles of extremely low momentum, thus technologically impossible trigger with traditional human-engineered algorithms. Hence, online detection with advanced models that explores the correlations between signal hits on top of background hits is required to capture such decays at the Large Hadron Collider. Our task is to predict the existence of r junu and use the detector hits left by the ja's to verify model interpretation.
SynMol is molecular property prediction task. Although some works have studied model interpretability in such tasks (McCloskey et al. 2019; Sanchez-LLengeling et al., 2020), they limit their focus on the theemicl--bondgreee geometric features. In this work, we put focus on 3D molecular representations. Our task is to predict the property given by two functional groups carbonyl and unbranched alkane (McCloskey et 2019) and use atoms in these functional groups to verify model interpretation.
representations of molecules, and largely ignore their
PLBind is to predict pooeein-ligand binding affinities given the 3D structures of proteins and ligands, which is crucial step in drug discovery, because a high affinity is one of the major drug selecting criteria (Wang& & Zhang 2017 Karimi et al., 2019). Accurately predicting their affini- ties with interpretable models is useful for rational drug design and may help the understanding of the underlying biophysical mechanism that enables protein-ligand binding (Held et al. [0111] Du et al.) 2016 Cang & Wei, 2018). Our task to predict whether the affinity is above a given threshold and use amio acids in the binding site of the test protein to verify model interpretation.
We evaluate LRI with three popular GDL backbone models DGCNN (Wang et al. 2019), Point Transformer (Zhao et al., 202T), and EGNN (Satorras et al.] 2021 over the above datasets. We also extend five baseline interpretation methods to GDL for comparison. We find that interpretation results given by LRT align much better with the scientific facts than those of the baselines. Also, we observe over some datasets, I.RI-Gaussian outperforms LRI-Bernoulli while on others vice versa. This implics different GDL applications may have different interpretation requirements. Effective data patterns may vary regarding how the task depends on the geometric features of the points. Inter- estingly, we find LRI-Gaussian can discover some fine-grained geometric patterns, such as providing high-quality estimations of the directions of particle velocities in actsTraack and a high-quality estimation of the strength of the used magnetic field. Moreover, neither of LRI mechanisms de- grades the prediction performance of the used backbone models. LRI mechanisms even improve model generalization when there exist some distribution shifts from the training to test scenarios.
2 RELATED WORK
We review two categories of methods that can provide interpretability in the following.
Post-hoc Interpretation Methods. Interpretation methods falling into this category assume a pre- trained model is given and attempts further analyze it to provide post-hoc interpretation. Among them, gradient-based methods (Zhou et al., 2016 Selvaraju et al. 2017 [Sundararajan et al., 2017] Shrikumar et al.. 2017; Chattopadhay et al. 2018) may be extended to interpret geometric data by checking the gradients w.r.t. the input features or intermediate embeddings of each point. Some methods interpret graph neural networks can be applied to geometric data (Ying et al. 2019 Luo et al.) 2020;; Schlichtkrull et al. 2021 Yuan et al. (021). However, these methods need to mask graph structures pre- presconstde by geometric features and cannot fully evaluate the effectiveness of geometric features. Among other methods, Chen et al. (2018); Yoon et al. (2018) study pattern
selection for regular data, RRibeiro et al. ( Lundberg Lee (2017 : Huang et al. (2022) utilize a local surrogate model, and Lundberg & Lee (2017): Chen et al. (2019b); Ancona al. (2019); Lundberg et al. 2020) leverage the shapley value to evaluate feature importance. These methods either cannot utilize geometric features or cannot be easily applied to irregular geometric data.
Inherently Interpretable Models. Although vanilla attention mechanisms (Bahdanau et al. 2015 Vaswani al. 2017) were widely used for inherent interpretability. multiple recent studies show that they cannot provide reliable interpretation, especially for data with irregular structures (Serrano Luo et al. 2020). So, some works focusing
& Smith 2019 Jain & Wallace 2019: Ying al. 2019
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on improving the attention mechanism for better interpretability (Bai al. 2021 Miao al. 2022
some propose to identify representative prototypes during training (Li et al., 2018; Chen et al,
2019a), and some methods (Tagaanki et al.] 2020; Yu et al. 2021: Sun et al., 2022) adopt the information bottleneck principle (Tishby et al. 2000p. However, all these methods cannot analyze geometric features in GDL., Along another line, invariant learning methods (Arjovsky et al., 2019 Chang et al.) 2020; Krueger et al., [021] Wu et al.) [022] [Cen et al. (022) focusing on out-of- distribution generalization based on causality analysis may also provide some interpretability, but these methods are typically of great complexity and cannot analyze the geometric features as well.
3 PRELIMINARIES AND PROBLEM FORMULATION
In this section, we define some useful concepts and notations.
GDL Tasks. We consider a data sample is a point cloud C = (V, where V= {ur, V2. .... Un is a set of n points, X E Rx includes d-dimensional features for all points, and R=x3 denotes 3D spacial coordinates of points. In this work, we introduce our notations by assuming the points are in 3D euclidean space while our method can be generalized. We focus on building classification model 5 = ((C to predict the class label y of C. Regression tasks are left for future studies.
GDL Models. The first class of DGL models view each sample of points as an unordered set. It learns a dense representation Zy for each v E V. and then applies a permutation invariant function, e.g., sum/mean/max pooling, to aggregate all point representations
that they can handle irregular data (Zaheer et al. 2017, Charles et al. 2017). The second class of methods can better utilize geo- metric features and local information. These methods first construct a k-nn graph G over the points in each sample based on their distances, e.g., [|,, rull. and iteratively update the representation of point o via aggregation AGG u E Nv)))), where N(v) is the neighbours of point e in graph G and AGG is a permutation invariant function. Then, another function is used to aggregate all point representations to make predictions. Compared with graph neural networks (GNNs) (Kipf) & Welling, 2017: Xu et al.) 2019; Veličković et al. 2018) that encode graph-structured data without geometric features, GDL models often process geometric features carefully: Typically, these fea- tures transformed into some scalars such as distances, angles and used as features that some group (e.g., (3))) (3) invariances of the prediction can be kept (Fuchs et al. 22200] Gasteiger al., 2020 Beaini al. 2021 Satorras al. 202T Schütt al. [022]). Some models that perform 3D convolution over 3D data also belong to the second class because the convolution kernels can be viewed as one way define the distance scalars for graph construction and neighborhood aggre- gation (Schütt et al. 2017: Thomas et al. [0188] Wu et al., 2019). The third class will dynamically construct the k-nn graphs based on the hidden representations of points (Wang et al., 2019) Qu & Gouskos 2020 Zhao et al.) (02T). In this work, we focus on using the second class of models' architectures as the backbones because most scientific applications adopt this class of models.
Interpretable Patterns in GDL. Given sample C = -V,, X,r), r), our goal of building an inherently interpretable model is that the model by itself can identify a subset points C, = (V., X., rs) that best indicates the label y. Mostly, C, will have scientific meaning. For example, in the task to detect T + iii decay, our model should identify the detector hits left by the three jAs 's but not the hits from other particles. We consider two types of indications of the label given by a point: existence importance, i.e., whether the point exists in the cloud is important to determine the label, and location importance, i.e. whether the geometric location of the point is important determine the label. In the above example, the existence of the detector hits left by the three jis is of course important. On the other hand, the locations of these hits are also crucial because location features reflect the momentum of these particles when they pass through detectors, which should satisfy equations regarding certain invariant mass if they are indeed generated from a T + aid decay.
4 METHODOLOGY
In this section, we introduce our method Learnable Randomness Injection (LRI). In LRI, we have an interpreter and classifier f. g is to encode the original data and generate randomness to perturb the data. if is to encode the perturbed data and make predictions. g and f are trained together to make accurate predictions while providing interpretability. LRI can be applied to large class of GDL models to make them interpretable. We may choose a GDL model architecture as the backbone to build the data encoders in g and These encoders could share not share parameters. Below,
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Interpreter
Classifier f
h
Pv
0
Interpreter g
Classifier f
0
10
0.3
030
Figure 2: The architectures of LRI-Bernoulli (top) and LRI-Gaussian (bottom).
we introduce specifics about this procedure. We first describe LRI-Bernoulli, where Bernoulli ran- domness is injected to measure the existence important of points. Then, we introduce LRI- -RI-Gaussian, which injects Gaussian randomness into geometric features to test the location importance of points. Finally, we connect our objectives with the information bottleneck principle (Tishby et al. 2000).
4.1 URI-BERNOULLI TO TEST EXISTENCE IMPORTANCE
Pipeline. Given a sample - (V, X, r), we first construct a k-nn graph & based on the euclidean distance ||r, ru.l between every pair of points v, E V. As shown in the top of Fig. 2 the interpreter encodes C, generates a representation Zu for each point and uses the last component to map Zy Pv E [0, 1]. Here, h consists of an MLP plus sigmoid layer, and samples Bernoulli mask for each point via m,, ~ (p. The sampling is based on a reparameterization trick (Jang et al. 2017: Maddison et al. 2017) to make dmin. computable. The perturbed data Ö is yielded by removing the points with m. i C. The edges in G connected to these points are also masked and removed, which gives graph G. Finally, the classifier f takes as inputs Č' and I to make predictions.
dy.
Objective. Eq. 1 shows our objective for each sample C, where the first term is a cross-entropy loss for classification and the second term is a KL divergence regularizer. 3 is the regularization coefficient and Bern a) is predefined Bernoulli distribution with hyperparameter
1.
min (CE(f(C, (),
E (Bem(pp))]BBmmt NEV
Here, f is optimized via the first term. The interpreter g is optimized via the gradients that pass through the masks {myJoev contained in E and I in the first term, and {pr in the second term.
Interpretation Rationale. The interpretation is given by the competition between the two terms in Eq. The first term is to achieve good classification performance so it tends to denoise the data by reducing the randomness generated by g. i.e., Pe + The second term, on the other hand, tends to keep the level of randomness, i.e., Pe - a. After training, Pe will converge to some value. If the existence of point v important to the label y, then Pe should be close to 1. Otherwise, Pe is close to a. We use p, 's to rank the points v E V according to their existence importance.
4.2 LRI-GAUSSIAN TO TEST LOCATION IMPORTANCE
Pipeline. We start from the same graph G as LRI-Bernoulli. As shown in the bottom of Fig. here, the interpreter y will encode the data and map it to covariance matrix Σ, E 3x33 for each point c. Gaussian randomness 6, ~ (O, Σ.) is then sampled to perturb the geometric features F. = =r, + 6, of v. Note that, to test location importance, new k-nn graph is constructed based on perturbed distances ||F, - Full- Reconstructing ς is necessary because using the original graph g will leak information from the original geometric features r. Finally, the classifier f takes inputs the location-perturbele perturbed data C = (V, X, r) and & to make predictions.
Objective. Eq shows the objective of LRI-Gaussian for each sample C. Different from Eq. here the regularization is Gaussian N (0, II), where I is an identity matrix and is hyperparameter.
min Lox 9), + B Σ DKI.(N (O),)
(2)
VED
Again, the classifier f will be optimized via the first term. The interpreter g will be optimized via the gradients that pass through the perturbation {e implicitly contained in Ć and & in the first term, and vev in the second term. However, there technical difficulties to be addressed.
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Table 1: Statistics of the four datasets.
Classs
Featurs
Dinemsions
Samples
SuinteSunple
PeinteSumpl:
Clas Ratio
ActaTewck
2
5341
100.1
22.8
39/51
Ranakon
7015515
2
129087
16.9
5,5
2476
Random
711515
Sysetos
2
8663
21.9
6,6
18/92
Paraza
78911111
FL3ind
10891
399
132.3
24/1
Time
M2/N2
First, how to parameterize Σ, as it should be positive definite, and then how to make de- com- ZE.
putable? Our solution is to let the last component h in g map representation Z, not to Σg directly but to a dense matrix U, E RR33 via an MLP and two scalars 01, 02 E R+ via softplus layer. Then, the covariance matrix is computed by Σn ag U, + azI. Moreover, we find using E, and the reparameterization trick for multivariate Gaussian implemented by PyTorch is numerically unstable as it includes Cholesky decomposition. So. instead, we use the reparameterization trick e, - a, + +osss+/azlll Vazlsz, where $1, S2 IO) not hard to show that [[(,,""] E,.
Second, the construction of the k-nn graph based on Fy is not differentiable, which makes the gradients of hev that pass through the structure of & not computable. We address this issue by associating each edge v, u in @ with a weight wen E (0, 1) that monotonically decreases w.r.t. the distance, Weu = ofI Fu.ll ll. These weights are used in the neighborhood aggregation procedure in f. Specifically, for the central point v. f adopts aggregation AGG ( WWn, Zu и E (v)))) where zu the representation of the neighbor point u in the current layer. This design makes the structure of & differentiable. Moreover, because we set Wuv construct & is "conceptually" smaller than k. So, in practice, we choose slightly larger number (say 1.5k) of nearest neighbors construct & and adopt the above strategy.
the number of used nearest neighbors to
Interpretation Rationale. The interpretation rationale is similar to that of RRI-Bernuulli, i.e., given by the competition between the two terms in Eq. [ The first term is achieve good classification performance by reducing the randomness generated by The second term, on the other hand, tends to keep the level of randomness, i..., Σ. - aI. After training. the convergent determinant |Eel which characterizes the entropy of injected Gaussian randomness, indicates the location importance of point e. We use Σ., 's to rank the points v E V according to their location importance.
B
Fine-grained Interpretation on Location Importance. Interestingly, the con- vergent Σ. implies more fine fine-grained geometric information, i.e., how different directions of perturbations on point affect the prediction. This can be analyzed by checking the eigenvectors of Σ.. As illustrated in the figure on the right, Σ,, of point v at A is represented by the ellipses {x x² Exxx < 0} for different O's. It tells perturbing towards the direction B affects the prediction less than perturbing v towards the orthogonal direction. As a showcase, later, use such fine- grained information to conduct an in-depth analysis of HEP data.
4.3 CONNECTING LRI AND THE INFORMATION BOTTLENECK PRINCIPLE.
Our objectives Eq. T and Eq 2 are essentially variational upper bounds of the information bottleneck (IB) principle (Tishby et al. 2000, Alemi et al. 2017) whose goal is to reduce the mutual information between C and while keeping the mutual information between Ć and the label, i.e., min - -[(;; Y)+ C). We provide derivations in Appendix A Grounded on the IB principle, LRI tends to extract minimal sufficient information to make predictions and can be more robust to distribution shifts between training and test datasets (Achille & Soatto 2018 Wu et al. 2020
Miao et al. 2022).
5 BENCHMARKING INTERPRETABLE GDL
In this section, we will evaluate LRI-Bernoulli, LRI-Gaussian and some baseline methods extended to GDL over the proposed four datasets. Here, we briefly describe our setup and put more details on the datasets, hyperparameter tuning, and method implementations, in Appendix C and
respectively. A summary of datasct statistics shown in Table
Backbone Models include DGCNN (Wang al. 2019) Point Transformer (Zhao et al. 2021). and EGNN (Satorras et al. 2021) which have been widely used for scientific GDL (Qu & Gouskos Atz et al. 2021 Sagliardi et al.) 2022).
2020
Baseline interpretation methods include three masking- based methods BernMask, BernMask-P and PointMask, and two gradient-hasee methods GradGeo and GradGAM. Masking-based methods

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Table 2: Interpretation performance on the four datasets. The Bold!, Bold, and Underline highlight the first, second, and third best results, respectively. All results are reported with mean + std.
AccoTrook
Point Transfemerr
DGNN
ROC AUC
Psced8
24
ROC AUC
Poce9h112
ROC ALC
Prueth
Randon
50
21
21
50
21
21
21
21
Gaddiin
65.52
+ 1.55
50.71
1.16
50.20 + 1.07
65.52 + 1.01
51.76 + 1.04
30.00 + 1.52
67.57 + 0.65
51.09 + 1.37
30.87
1.21
RanaMaok
68.55
4.7.2
45.00=
7.14
12:72
7.91
76.94 + 1.00
71.17 + 1.60
07 07:100=:3:22 3.22
50.94 = 3.86
18.07
+:2.0
20.00 +: 3.13
BeraMask-P
88.16=
76.04
= 11.30
66.71 6.50
84.36 2.64
73.24 6:66
60:41 +
96.81 27.03
17.38 4: 82.06.
18.92 + 21.22
PointMask
20.55 6.11
21.05
4.67
21.54 2: 4.36
50.56 0.91
22. 11433::.33 1.78
20.68
a: 7.63
10.55 2 1.40
20.05 2: 1.14
20.00 1.01
GrdGAM
22.06:22.42
$4.20
= 2:20
08.04
2:306
88.07 4: 2.25
82.13
4: 0.92
64.64
2: 1,80
70.44 6: 2.62
78.05 4:
02:50 1,33
90.29
1.80
60.36
1:200
74.50
1.25
87 00 2.40
$6.71 9:55
65 1.22
28.02 +: 3.84
61.66 +: 1:33
55 29 1.90
LRI Glussian
06.40
0.34
92 40
0.64
79.9T
= 0.72
P0.11 1:350
88.30 24336
74.71
1.90
04.34 1.700
91.54
11.49
70.78
à 11811
Tou3Ma
DGCNN
Point Transformer
BGNN
ROC AUC
ProcuR3
ROC AUC
P
Piz
ROC AUC
Prou
0r
Random
35
35
50
35
35
35
GrdGGe
80.76 1: 0.31
10.80
0.33
56.05
0.34
79 62
0.33
67. 96
0.49
35.13 4. 0.24
28.03 1.13
64.72
2.00
3.1.2
0.7%
Bernbaakk
56.28
1.15
50,88
1:64
12:11
0.94
30 1-0.00
12:68
0.38
18.11 1: 0.22
72:27
8: 2:45
61.27
3:68
31.91
6.153
BernMask--P
$4.90
14.00
03.56
13.50
39
9.10
78 4.05
50:39
4.78
55.41
3.300
70:00
+555
56.35
0.008
50.00
4.44
PointMask
02.02
2.56
20.55
2:27
38.71
1,48
57.33 2.25
44.00
1.51
35.53
2:
35.90
37.05
4.74
GndGAM
09.42
11 4.04
51.82
8.02
40.78
4. 3.00
80.911
1: 0.33
61.14
2: 1.46
54.36
3. 0.67
75.84
1.45
02.003
1. 2.41
53.11
1,52
RRI-Bernndli
27.58
70.00
0.00
55.91
0.77
77.22 1.62
07.73
2.50
74
1.15
78.71
0.06
08
0.81
55
0.57
LRI Gaussian
81.
0.02
T3.13' d: 1.30
58.28'
= 0.59
70 1: 0.66
70.32
0.7.7
57.05
0.53
80.02|
0.30
71.30'
1: 3.003
57.07 0.41
Synito1
DGCNN
Point Transformer
DGNN
ROC AUC
P
Pi
ROC AUC
Proce 5
Pr
ROC AUC
Procdh
Pm
Gnddlen
72.10-+-9.00
8:70
1.45
55
1-905
BernMaok
+-.22
32.15
7.61
25, 00.088
7.25
ResMMak-P
70.51 30.52
03,02 95.15
52.55
30.33
67.23 6.07
75.39
05:00
68
PointMask
70.22
4.27
G8.18 2.56
72.06 2.10
06.13
2:25
3.05
GudGAAM
+ 5.54
78.90
6.67
5.56
1.19
90.04
1.58
64.38
88.56
41.30 6.05
L LRd-
96
96.05 + 1.51
8T.11 +:5.1
74.57
+
91. 00.00 1.52
82.72
2:30
68.55 57
1.11
90.04 5:30
71.06 + +.5.7
08.08 1.18
LRI-Gasssian
99.00
0.33
97
0.34
77.04
06.33
00.001
72.20
1.40
97.281 0.66
91.62
+1.25
74.06
1.18
F18ind
DGCNN
Poim Trunsfones
BGNN
ROC AUC
PSce
Praz5h40
ROC AUC
Poc
Practh40
BOC ALC
Proc0i-0
Random
50
45
45
50
45
45
50
45
45
Orddieo
52.33 4.63
X5.8
2:47
53.79
1,51
38 08.
2,83
19.30 à 3:13
$7.85 d:
57.75! 1.2.1
61.02 2.24
00.11 1,70
BasMaak
48.18
3:32
48.00
3.40
69.73 73
56.90 3:09
8::56
11:99
2.82
BeraMask-P
42.70 8:17
7.58
56.47 2.77
56,86
54.58
00.65 7:55
57
6.4.1
PointMask
1.91
1.52
52.92 3.83
44.34 à 3.50
44.50
0.00
0,00
GndGAM
53.76
3.38
56,00 4.85
54.25
4.42
56.51 3.32
56,54
40.73
56.02 6.63
52.96 1.3,33
LRI Bernoulli
55.
5.38
61.02
5.68
59. 10.533.1 1.94
72.98|
67.83
2.08
67.07
73.22/ 2.00
66 2.07
LRI Guussian
31.51
3.24
63,88
60:37
54.05
2.94
02.76
5.50
5,02
30,52
1.44
attempt to learn a mask E [o, 1] for each point and may help to test existence importance of points. Among them, BernMask and BernMask-P are post-hoe extended from two previous methods on graph-structured data, i.e., Ying et al. (2019) and Luo et al. (2020). BernMask and BernMask-I dif- fer in the way they generate the masks, where BernMask-P utilizes a parameterized mask generator while BernMask optimizes a randomly initialized mask with no other parameterization. PointMask an inherently interpretable model adopted from Taghanaki et al. (2020). Thus, they are the base- GradGeo is extended from Shrikumar al. (017)) and checks the gradients w.r.t. geometric features, which may help with testing location importance, and thus is a bascline of LRI-Gaussian. GradGAM is extended from /Selarajju et al. (017) and leverages the gradients w.r.t. the learned representations of points, which also reflects the importance of points to the prediction.
lines of
Metrics. On each dataset, the model is trained based on the prediction (binary classification) task. Then, we compare interpretation labels (E {0, 1}) of points with the learned point importance scores to measure interpretation performance. We report two metrics: interpretation ROC AUC and precision @ m. Beyond interpretation, the model prediction performance is also measured in ROC AUC and reported in Sec. 5.5] which is make sure that all models are pre-trained well for those post-hoc baselines and to verify that LRI-induced models also have good prediction accuracy.
Hyperparameter Tuning. Gradient-based methods have no hyperparameters to tune, while all other methods are tuned based on the validation prediction performance for a fair comparison, because tuning on interpretation performance is impossible in a real-world setting. For LRI- LRI-Bernulll, a is tuned in {0.5, 0.7); for LRI-Gaussian, as the geometric features in our datasets are all centered at the origin, a is tuned based on the 5th and 10th percentiles of entries of abs(r). And, , is tuned in (1.0, 0.1, 0.01} for both methods after normalization based on the total number of points.
5.1 ACTSTRACK: END-TO-END PATTERN RECOGNITION AND TRACK RECONSTRUCTION
Here, we are to predict whether a collision event contains a 2 + paf decay. Each point in a point cloud sample is detector hit where a particle passes through. We use the hits from the decay to
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Published as a conference paper at ICLR 2023
Table 3: The angle ( mtd between the velocity and the first principal component of >g (uRI-Gaussian) v.s. between the velocity and the direction orthogonal to the gradient of re in x-y space (GradGeo) under different magnetic field strengths (T).
41
RT
14T
Random Grndiin
45
45
45
45
45
45
22.89 2.455
18.55 + 1.29
51.79 + 2.12
53.67 2.50
30.27 + +.5.1
57.22 11-22+-311
3-18
38.01 + 5.2
30.25 + 1.00
38.01 3.80
96.25 + 5,34
1 RRI-Guasim
5.0 + 0.97
5.17 +
5.05 + 1.05
667
1.17
5.50 + 1.71
6.06 + 1:25
7.50 2.577
7.39 1.00
7.57 = 1.20
7.80 1.08
test interpretation performance. We evaluate all methods on the data generated with a magnetic field B = 2T parallel to the z axis (see Fig. Ta.. ( the results, where LRI-Gaussian works consistently the best on all backbones and metrics, and LRI-Bernoulli achieves the second best performance. This indicates that both the existence and locations of those detector hits left by the utss are important to predictions. GradGAM is also competitive baseline, which even outperforms both BernMask and BermMask-P. While BernMask-P performs decently on two backbones, it fails to provide interpretability for EGNN and its results have high variances, probably due the unstable issue of post-hoe interpretations, as described in Miao et al. (2022). BernMask, PointMask, and GradGeo seem unable to provide valid interpretability for Acts AcakTrack.
Fine-grained Geometric Patterns. We find LRI-Gaussian can discover fine-grained geometric patterns. Intuitively, slight per- turbation of each point along the underlying track direction will affects the model prediction less than the same level of perturba- tion orthogonal to the track. Therefore, the principal component of Eg in x-y space, i.e., the space orthogonal to the direction of the background magnetic field, give estimation of the the evaluation of track di-
Correlation: 0.995
Sigem-Rario
022
track direction at v. rection (velocity direction) estimation based on analyzing E,. Here, we test the background magnetic field changing from 2T to 20T. LRI-Gaussian is far more accurate than GradGeo. The latter uses the gradients of different coordinates to compute the most sensitive direction. Moreover, the ratio between the lengths of two principal components of E. in x-y space gives estimation of the curvature of the track at v, which is proportional to the strength of the magnetic field B up to a constant multiplier (due to the law Lorentz force F' x B). Therefore, we can estimate B by analyzing E. Fig. 3 shows this approach provides an almost accurate estimation of B up to a constant multiplier. Fig, 4 provides vi- sualizations of the yielded fine-grained patterns, and detailed analysis of the obtained fineggrained interpretation patterns can be found in Appendix B
01
Magnetic Field Strength
Figure 3: Eigen-ratio of Σ, v.s. magnetic field strength B (T).
5.2 TAU3MU: + nht DECAY DETECTION IN PROTON-PROTON COLLISIONS
This task is to predict whether proton-proton collision event contains 7 puu decay, which is similar to ActsTrack, while Tau 3Mu the j's are a lot softer, and only the hits from the first layer of detectors are used. Each point in a point cloud sample is detector hit associated with local bending angle and 2D coordinate in the pseudorapidity-azimutt (17-² space. We use the hits generated from this decay test interpretation performance. As shown Table [ LRI-Gaussian still works the best. LRI-Bernoulli and GradGeo are close, and both are the second best. While GradGAM still works well on some backbones, all masking- based methods do not perform well.
5.3 SYNMOL: MOLECULAR PROPERTY PREDICTION WITH SYNTHETIC PROPERTIES
This task is to predict whether a molecule contains both functional groups branched alkanes and car- bonyl, which together give certain synthetic properties (MeCloskey et al. 2019) Sanchez-Lengelinn et al. 2020). Each point in a point cloud sample is an atom associated with 3D coordinate and a categorical feature indicating the atom type. We use the atoms in these two functional groups to test interpretation performance. As shown in Table 2 LRI-Gaussian performs consistently the best by only perturbing geometric features in molecules, and -el-Bolnlllli works the second best and achieves comparable performance with LRI-Gaussian on Point Transformer. This shows that both the existence and locations of atoms are critical and further validates the benefit of using 3D representations of molecules in the tasks like molecular property prediction. Among other methods,
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Table 4: Generalization performance LRI. Classification AUC on test sets are reported with tsd for all backbones on the four datasets.
DOCSS
Thea Tranchemme
DONN
DOCON
BONS
Trasivee
20035
Pee Tranlerar
2301
0E08 2.24
96 23796 R:1
07.88 B1A82
$2.34 JUB
20 2.55
86 26.-2211
1648 2:4.5
8638 842
1887 LUB
SUST
03:3 1.
16.17 324
96 94 6M4
96.88 6:446
1610 6.:
96IT 916
1646 6488
99915 930
5986 WID
$6.6 938
Table 5: Generalization performance of LRI with distribution shifts. The column name d1 d1-d2 de- notes the models are validated and tested samples with d1 and d2 tracks, respectively.
ActaTrack
10-10
15-20
20-30
25-40
30-50
35-60
40-70
ERM
96.33 +: 0.65
93.83
0.34
91.14 1.07
87.85
1.12
85.90 + 1.74
84.19
154
82.87 :: 0.74
LRI-Bemoulli
97.05 + 0.71
94.66 # 0.75
93.08 + 0.94
90.93 + 0.76
89.95 + 1.31
86.11 + 143
86.95 + 1.46
LRI- RRI-Gaussian
97.51 +: 0.76
95.69 + 0.80
93.64 + 1.39
91.12 # 2.97
89.89 + 1.15
87.45 + 1.47
88.13 = 0.63
GradGAM, BernMask-P and PointMask are unstable and can only provide some interpretability for one or two backbones, while GradGeo and BernMask seem to fail to perform well on SynMol.
5.4 PLBIND: PROTEIN-LIGANI BINDING AFFINITY PREDICTION
This task is to predict whether a protein-ligand pair is of affinity KD < 10 nM. Each point in a protein an amino acid associated with 3D coordinate, a categorical feature indicating the amino acid type, and two scalar features. Each point in a ligand is an atom associated with a 3D coordinate, a categorical feature indicating the atom type, and a scalar feature. Different from other datasets, each sample in P PLBind contains two sets of points. So, for each sample, two encoders will be used to encode the ligand and the protein separately, and the obtained two embeddings will be added to make prediction. As shown in Table 2 LRI-Bernoulli outperforms all other methods, while LRI-Gaussian achieves comparable performance on EGNN. This might indicate that to make good predictions PLBind, the existence of certain groups of amino acids is more important than their exact locations. Interestingly, all other methods do not seem to perform well on P PLBind. Moreover, all methods have low ROC AUC, which suggests only part of but not the entire binding site is important to decide the binding affinity.
5.5 GENERALIZATION PERFORMANCE. AND ABLATION STUDIES OF LRI
LRI-induced models can generalize better while being interpretable. As shown in Table both LRI- induced models never degrade prediction performance and sometimes may even boost it compared with models trained without LRI, i.c., using empirical risk minimization (ERM). Moreover, LRI- induced models are more robust to distribution shifts as LRI is grounded on the IB principle. Table shows study with shifts the numbers of particle tracks, where all models trained samples with 10 particle tracks, and tested on samples with a different number of (from 10 to 70) tracks. We observe LRI-induced models work consistently better than models trained naively. We also conduct ablation studies on the differentiable graph reconstruction module proposed specifically for geometric data in LRI-Gaussial we find that without this module the interpretation performance of URI-Gaussian may be reduced up to 49% on ActssTe sectsrrac and up to 23% on SynMol, which shows the significance of this module. More details of the ablation study can be found in Appendix F.I
CONCLUSION
This work systematically studies interpretable GDL models by proposing framework Learnable Randomness Injection (LRI) and four datasets with ground-truth interpretation labels from real- world scientific applications. We have studied interpretability existence importance and location importance of points, and instantiated LRI with LRI-Bernoulli and -II-Gaussian to test the two types of importance, respectively. We observe LRI-induced models provide interpretation best aligning with scientific facts, especially LRI- that tests location importance. Grounded on the IB principle, LRI never degrades model prediction performance, and may often improve it when there exist distribution shifts between the training and test scenarios.
GDL from the perspectives of

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Published as a conference paper at ICLR 2023
ACKNOWLEDGMENTS
We greatly thank the actionable suggestions given by reviewers. S. Miao and M. Liu are supported by the National Science Foundation (NSF) award OAC-2117997. Y. Luo is partially supported by 2022 Seed Grant Program of the Molecule Maker Lab Institute, an NSF AI Institute (grant no. 2019897) at the University of Illinois Urbana- Shaana--happainn P. Li is supported by the JPMorgan Faculty Award.
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A VARIATIONAL BOUNDS OF THE IB PRINCIPLE
Let's assume the sample with its label (c, Y) ~ Pexx. We ignore the 9 our objectives to keep the notation simple, then, the IB objective is:
min -IC;)) BI(C,C)
(3)
where č is the perturbed sample, and .(: denotes the mutual information between two random variables.
For the first term -I(Č) Y), by definition we have:
P(Y C)
I(C)Y) EE log
(4)
IY(Y)
We introduce a variational approximation PY(Y C) for PYY ()) as intractable. Then, we yield a variational upper bound:
PY(Y (c) P(Y)
-T(C, -EErr
log
Ee (PL( () [&)]
log PY (Õ)
P(Y)
-Ee log Po [6]] H(Y),
(5)
where H(Y is the entropy of which a constant. We use the prediction model f paired with the cross-entropy loss (CE(S(O), Y) to represent -Fay logg Po Ct}. minimizing which is thus equivalent to minimizing variational upper bound of YTC
For the second term C(;;C), because č = g(C). Suppose ø is the parameter of By definition, we have:
Po(C c)) I(,,C) = EEcc log TP(C) {0]
As IP(C) is intractable, we introduce variational approximation Q(C). Then, yield variational upper bound:
T(C:C)= = Be,c log Pa(CIC) DEL (PIÕ)IQ(C) Q(C)
S Ec DKI. (Po(CIC))IQ(C)) [C)1Q(C))]
For LRI-Bernoulli, 9n takes as input v E V. Then, it samples my ~ Bern and yields ? by removing all points with m, = in C. This procedure gives ( C) = II P(m,lpp)) which essentially makes m, condi- tionally independent across different points given the input point cloud C. In this case, define QCC) follows. For every point cloud C Pc, sample mi, Ber((a), where
(V,X,r) and first outputs p.. [0, 1] for each point
[0, 1] is a hyperparameter. We remove all points in and add points when their m = 1. This procedure gives Q(²) Ee Pmmm CCP(C). As m' is independent from C given its size n, Q(C) Σn P'm') = n) Pm)) IT IP(m)), where P(n) is constant. Then, we yield:
DKL (P&(C Q)))(()) = Σ DKI(Bemmpp)) Ber((a)) (Bmm(a)) + c(n,a),
(8)
where c(n, a) does not contain parameters to be optimized. Therefore, minimizing the second term of is equivalent to minimizing variational upper bound of I [CC:C). Now, we can conclude that the objective of LRI-Bernoulli variational upper bound of the IB principle.
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IiI
0: 301
Yn
-75
250
130 255 230
100
Figure 4: Visualizing interpretable patterns discovered by LRI-Gaussian for ActsTrack, where the origins (0, are the centers of the collisions. Points are plotted x-y plane (mm) with magnetic fields perpendicular
the plane, only points colored black/red indicate the two tracks of the two p's from the 2 > μu decay, and the blue contour superimposed on each point v is the shape of the (scaled) learned Gaussian (0, E,), where E 400E i.e. each element is multiplied by 400, otherwise the contour would be hardly visible. For figures in the top row, the number next to each point v is Eul; for figures in the bottom row, the number next to each point is the angle between the true track direction and the learned direction, and non-critical points not plotted for better visualization.
For LRI-Gaussian, I4 now takes as input C = X,, r) and first outputs covariance matrix E. E 33x3 for each point E V. Then, it samples 6, _N(0, E,) and yields Č (V,X.r c), where is vector containing e, for each point. This procedure gives PC(C C) Ie P(c, Ew), which essentially makes 6, conditionally independent across different points given the input point cloud C. In this case, we define (CC) as follows. For every point cloud
Ic,, we sample é, ~ NO oI) and yield Č = (V, VVX,r r E'), where a is hyperparameter. Similarly, we obtain (C) P(n) IT P(C.), where ((n) is constant. Finally, for this case, we have:
DKL. (Po(C ( (((I))()())
Σ Dw.,N((, (O) + c(n, a:),
where c(n, at) is constant, therefore, minimizing the second term LRI-Gaussian is equivalent to minimizing a variational upper bound of T(C:C). Hence, the objective of LRI-Gaussian is also variational upper bound of the IB principle.
B INTERPRETATION VISUALIZATION
AetsTrack. Figure shows the interpretable patterns discovered by LRI-Gaussian. The top row shows that the randomness of the learned Gaussian noise (O Σ.) indicates the importance of each point e, and thus Egl can measure the importance quantitatively as it characterizes the entropy of Gaussian. In the examples, non-critical points learn isotropic Gaussian close to (000, aI) as regularized by the KL divergence Eq. 2 while critical points left by the p's produced by the -> pi decay learn multivariate Gaussian with small randomness, i.e., small |E,], because high
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randomness these points would greatly affect model prediction and the prediction loss in Eq. would not allow this to happen. As shown quantitatively in Table 2 |ze] measures the importance of each point very well and can provide the best interpretation AUC in most cases.
The bottom row of Figure shows that LRI-Gaussian is also capable of discovering fine- ane-grained geometric patterns. In the examples, small perturbation each point along the underlying track direction may not even affect the model prediction (because the track radius may not change a lot by such perturbations). Therefore, the principal component (i.e., the eigenvector that corresponds the largest eigenvalue) of ,., in x-y space can give an estimation of the track direction at v. As shown quantitatively in Table []] the principal component can actually estimate the track direction very well. Meanwhile, we can also see that the ratio between the lengths of two principal components
(i.e.. 2dd Largest Eigenvaluc, ) of ,,, varies when the strength of the background magnetic field B changes, Largest Eigenvalue
and as shown quantitatively in Figure 3] this ratio provides an almost accurate estimation of B up to constant multiplier. This is because the direction orthogonal to the track direction is the direction of Lorentz force, and when the principal component of E. in x-y space indicates the track direction, the second principal component in x-y space would be the direction of Lorentz force. Since Lorentz force F x B and the properties of u's (e.g., momentum) from the - pi decay is independent of magnetic field strength, the ratio magnetic field.
2 Largest Eigenvalue Largest Eigenvalue
can imply the strength of the background
C DETAILS OF THE DATASETS
C.I BACKGROUND AND TASKS
We describe the background and tasks of our datasets in more detail in this section.
AetsTrack. As illustrated in Fig. La protons will collide at the center of the detectors, and a number of interactions will happen, where different interactions may produce different particles, e.g., z + in decay produces two j's. The produced particles will then fly through multiple layers of detectors with magnetic field, and Fig. shows example that has four layers of ring detectors with a 2T magnetic field parallel to z-axis. When a particle flies through such detectors, the detectors will record where the particle hits the detector (i.e., geometric coordinates) and measure certain properties of the particle (e.g.. momentum) depending on the type of the detector. And if the particle charged, then its track space may be curved due to the magnetic field. As such, each particle will leave set of points on the detectors with some measured properties, and all particles produced from the collision will then form a point cloud, where a point is just particle hit on detector. However, we are only interested in a certain interaction, i.e., the 2 - nil decay, and do not care other interactions (these interactions are called pileup interactions or background events). Fortunately, the particle hits in the point cloud will reveal the information about the interactions happened in the collision. For example, if z + uu decay just happened, then there should be two sets of points in the point cloud that are left by the two μ's just produced from the decay. In principle. it is possible to reconstruct the type of a particle based on its tracks and/or some other measured properties in magnetic field, and once can find that there are two tracks that must be caused by two y's (with certain invariant mass), then we would know a z + jy decay just happened in the collision. Therefore, the classification task of Act sTrack is to predict if there exists a - pup decay or not in the collision given the point cloud measured by the detectors. Each positive sample contains particle hits from both a = + uıfe decay and some pileup interactions, while each negative sample has only hits from pileup interactions. In principle. if a classifier can successfully predict the existence of a > pu decay, it should be aware of which sets of points in the point cloud represent the tracks of the p's. Therefore, the particle hits left by the two n's are labeled as ground-truth interpretation, and we expect an interpretable model to highlight these points as important points for the classification task.
Tau3Mu. Even though MMu has a similar basic HEP setup as Tau3Mu now has a different configuration of the detectors and the magnetic field. Besides, the underlying physics process of interest is different and the task is with a different physics motivation (as shown in [). The formulation of the machine learning task is classification task to predict if there exists a T - dait decay or not given point cloud. Each positive sample contains both a T > zuu decay and some pileup interactions, while each negative sample has only pileup interactions.
as shown in Fig. Ib
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Likewise, if a classifier can successfully prediet whether there is a hin decay or not, expect those particle hits left by the three jás produced by the r + tui decay to be the important points for the classification task, and an interpretable model should be able to highlight these points.
SynMol. Different from typical molecular property prediction tasks, SynMol provides 3D repre- sentations of molecules instead of 2D chemical bond graphs. Namely, each molecule is represented as a 3D point cloud with each point being an atom in space. 'he classification task of SynMol 1 is to predict if a molecule has a certain property or not. As shown in Fig. [c] we know that the property of interest is determined by two certain functional groups (i.e., specific groupings of atoms). There- fore, we expect an interpretable model that can successfully predict the property should be able to highlight those atoms in the two functional groups as the important points for the classification task.
The classification task of PLBind is to predict if a pair of protein and ligand can bind together (with a high affinity) or not given the 3D structures of proteins and ligands. Notably, Fig.Td [nly shows the surface of protein for better visualization, and actually proteins in PLBind represented as 3D point clouds, where each point is just amino acid in the protein. Similarly, ligands are just small molecules, and they are also represented as 3D point clouds, where each point is an atom in the ligand. In principle, as shown in Fig. d a high binding affinity should largely depend on the amino acids of the protein that are near the binding site. Therefore, we label those amino acids near the binding site as ground-truth interpretation, and we expect interpretable classifier that can successfully predict the high-affinity pairs should be able to highlight those amino acids as important points for the classification task.
PLBind.
C.2 DATASET COLLECTION
We elaborate how we collect the four datasets in this section. The statistics of the four datasets are shown in Table
Basic Settings. 1) For each sample in the four datasets, all points are centered at the origin. 2) Only positive samples in our datasets have ground-truth interpretation labels, so we only evaluate interpretation performance on positive samples. 3) For any pair of points and u in the four datasets, they have an edge feature of ([r,, rull: [r. if they are connected in the constructed k-nn graph.
ActsTrack. z pa events are simulated with PYTHIA generator (Bierlich al. 2022 overlaid with soft QCD pilcup events, and particle tracks are simulated using Acts Common Tracking Soft- ware (Ai et al. 2022). For all samples, ten pileup interactions are generated with a center-of-mass energy of 14TeV V. and the additional hard scatter interaction is only generated for positive samples. Particle tracks are simulated with a magnetic field parallel to the axis, and the default Act Tra ck is simulated with B- 2T To make sure both 'ss from the decay are properly measured, we cal- culate the invariant mass my for every pair of p's in the generated data using Eq, |0 so that every positive sample in our dataset has at least pair of μ² with an invariant mass close to 91.19 GeV, ie., the mass of the z bosons.
1 2 mij
m² + (vm2 v2. Ph, + P2.4 Vm² 2 p2. + r2g + p3.3)
-Pa,s Pa.j Py. Pv.j + Pz,i Pz.j).
(10)
Then, those detector hits left by the jts from the - um decay is labeled as ground-truth interpre- tation. As our focus is on model interpretation performance, we only keep 10 tracks in each sample to train and test models to reduce classification difficulty, while raw files with all tracks are also provided. In the future works, we will study more extensive evaluation of different approaches over the samples with all tracks. Each point in a sample a detector hit left by some particle, and it is associated with 3D coordinate. As points in ActsTrack do not have any features in X, we use a dummy X with all ones when training models. Momenta of particles measured by the detectors are also provided, which can help evaluate fine-grained geometric patterns in the data, but it is not used for model training. Because each particle on average leaves 12 hits and a model may classify samples well if it captures the track of any one of the jt's from the decay, we report both precision @ 12 and precision @ 24. Finally, we randomly split the dataset into sets with ratio of 70: 15: 15.
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Tau3Mu. The leptons produced in decays of D and B mesons simulated by the PYTHIA gen- erator (Bierlich et al. 2022) are used to generate the signal samples. The background events are generated with multiple soft QCD interactions modeled by the PYTHIA generator with a setting that resembles the collider environment at the High Luminosity LHC. The generated muons' inter- actions with the material in the endcap muon chambers are simulated including multiple scattering effects that resemble the CMS detector. The signal sample is mixed with the background samples at per-event level (per point cloud), with the ground-truth labels preserved for the interpretation stud- ies. The hits left by the j's from the T + riil decay are labeled as ground-truth interpretation. We only use hits on the first layer of detectors to train models and make sure every sample in the dataset has at least three detector hits. Each point in the sample contains measurements of local bending angle and 2D coordinate in the pseudorapidity-zzime model only needs to capture hits from each μu, we report precision @3. And because 80% of positive samples have less than hits labeled as ground-truth interpretation. we also report precision 7. Finally, we randomly split the dataset into training/validatioonesst sets with a ratio of 70 15 15.
(1-12 space. Because in the best case the
SynMol. We utilize the molecules in ZINC (Irwin et al. 2012), and follow McCloskey et al. (2019) and Lengelez-Lengeling et al. (2020) to create synthetic properties based on the existence of certain functional groups. Specifically, ly, if a molecule contains both the unbranched alkane and carbonyl, then we label it as a positive sample; otherwise it is labeled as a negative sample. So, the atoms in branched alkanes and carbonyl are labeled as ground-truth interpretation. Instead of 2D represen- tations of molecules, we associate each atom a 3D coordinate by generating a conformer for each molecule. To do this, we first add hydrogens to the molecule and apply the ETKDG method (Riniker) & Landrum 2013). After that, the generated structures are cleaned up using the MMFF94 force hield (Halgren 1999) with a maximum iteration of 1000, and the added hydrogens are removed once it is finished. Both ETKDG and MMFF94 are implemented using RDKit. Besides a 3D coordi- nate, each point in sample also has categorical feature indicating the atom type. Even though the two functional groups may only have five atoms in total, some molecules may contain multiple such functional groups. So, report both precision@5 @5 and precision @8 (80% of positive sam- ples have less than 8 atoms labeled as ground-truth interpretation). Finally, we split the dataset into wraiiing/validationneest sets in way that the number of molecules with without either of these functional groups is uniformly distributed following (McCloskey et al. 2019) so that the dataset bias is minimized.
PLBind. We utilize protein-ligand complexes from PDBBind (Liu et al. 2017), which annotates binding affinities for subset of complexes in the Protein Data Bank (PDB) (Berman et al., 2000). In PDBBind, each protein-ligand pair is annotated with a dissociation constant Ka, which measures the binding affinity between a pair of protein and ligand. We use a threshold of 10 nM on K₂ to obtain a binary classification task, and the model interpretability is studied on the protein-ligand pairs with high affinities. To augment negative data, during training, there is a 10% change of switching the ligand of complex to a random ligand, and the new protein-ligand pair will be labeled as a negative sample, i.e., low affinity. The ground-truth interpretation labels consist of two parts. First, as shown in previous studies (Liu et al., 2022). using the part of the protein that is within 15A of the ligand is enough to even learn to generate ligands that bind to a certain protein, so, we define the amino acids that are within 15A of the ligand to be the binding site and label them as ground- ground-truth interpretation. Second, we retrieve all atomic contacts (hydrogen bond and hydrophobic contact) for every protein-ligand pair from PDBsum (Laskowski et al., 2018) and label the corresponding amino acids in the protein as the ground-truth interpretation. Each amino acid in a protein is associated with a 3D coordinate, the amono acid type, solvent accessible surface area (SASA), and the B-factor. Each atom in a ligand is associated with 3D coordinate, the atom type, and Gasteiger charges. Finally, we split the dataset into training/validationnes. sets according to the year the complexes are discovered following Stärk et al. (2022).
D DETAILS ON HYPERPARAMETER TUNING
All hyperparameters are tuned based on validation classification AUC for a fair comparison. All settings are trained with 5 different seeds and the average performance on the 5 seeds are reported.
Basic Settings. We use a batch size of 128 on all datasets, except on Tau3Mu we use a batch size of 256 due to its large dataset size. The Adam (Kingma & Ba 2015) optimizer with learning rate
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Table 6: Ablation studies on the effect of the differentiable graph reconstruction module in LRI- Gaussian on ActsTrack and SynMol.
NetoTeack
DGCNN
Point Transfomer
EGNN
ROC: AUX
Picce9
ROC AUC
Phoc
Ph
ROC AUC
Pree0112
Pree0k24
w/ Grapph Roceess
04.24 0.66
91.01 + 1.02
78.47 +088
91.89 2.07
8500 2.74
74.00
3.01
96 0.75
90.85
0.66
70.42+0.80 0.80
w/o Graph Recons.
67.00 1.82
36.00 2.111
41.52
0.79
00.6 1:50
39.16 1 2.67
32.54
1.42
82,50 1 0.54
78.71
1388
59.02
1 137
SynMMol
DGCNN
Point Transfumer
EGNK
ROC: AUC
Proc
Prec88
ROC AUC
ProceS
Pres
ROC AUC
Prec
Graphh Regenss
88 0.63
05.01 + 1.75
70.95
+-0.2
96.81 1.42
8961 + 3.50
2.11
96.88 1.25
89.17 + 5.05
74,47 + 1.05
w/o Graph Recens.
08.65 0.39
85.06
1.45
70.58
+
90.00 + 1,51
79.00 + 0.50
64.25 + 1.31
78.59 + 36.27
66.26 + 36.02
08.79 + 30.07
of 1.0 x 10 3 and a weight decay of 1.0 x 10-6 5 are used, Act scrakk,ck, SynMol, and PLBind
construct k-nn graphs with & being 5; Tau constructs the graph by drawing edges for any pair of points with a distance less than 1. For fair comparison, all models will be trained with 300 epochs on Acts and SynMo1 and will be trained with 100 epochs on Tau and PLBind, so that all models are converged. For post-hoc methods, a classifier will be first pretrained with the epochs mentioned above, and those methods will further work on the model from the epoch with the best validation classification AUC during pretraining.
LRI-Bernoulli. 3 is tuned from {1.0, 0.1, 0.01} after normalizing the summation of the KL diver- gence by the total number of points. a is tuned from {0.5, 0.7}. Note that a should not be less than 0.5, because (0.5().5) injects the most randomness from an information ifformation-thhorrtie perspective. For Acc.sTrack and SynMol, we either train with 200 epochs and then train both and g with 100 epochs (also based on the best validation prediction performance). Similarly, for TMu3Mu and PLBind, we either train it 100 epochs from scratch or first pre-train f by 50 epochs and then train both f and by 50 epochs. The temperature in the Gumbel-softtax trick is not tuned and is set to 1.
300 epochs from scratch or first pre-train
ARI-Gaussian. 3 and the training time is tuned in the same way as for ORI-Bernoulli. Instead of directly tuning a, we tune it by rescaling the magnitude of the geometric features to make sure the KL divergence stable for optimization, because the magnitude of r may vary significantly across different datasets, e.g., extremely small or large. Specifically, we keep o = and rescale r by multiplying a constant с on it so that 1 would be roughly the 5th or 10th percentile of the entries in abs(c- r). In this way, e tuned from (200, 300} for ActsTrack, {10, 15) for SynMol, 113 for Tau3Mu, and (0.9, 1.2} for PLBind.
BernMask. This approach generalizes GNNExplainer (Ying et al. 2019) and learns a node mask m E [0, 1j for each sample C. Similar to GNNExplainer, there are two regularizers in its loss function, that is, mask size and entropy constraints. Specifically, the coefficient of the l penalty on the normalized mask size, i.e. ||ll is tuned from {1.0, 0.1, 0.01). Element-wise entropy of m is applied, i.c., 1 - log m, (1 - m.) log(1 - m,) and m, is the 2th entry of m, to encourage generating discrete masks, and the coefficient of this entropy constraint tuned from (1.0, 0.1, 0.01}. After pretraining the classifier, we set the number of iterations to learn masks per sample as 500 and tune the learning rate for each iteration from {0.1, 0.0013.
BernMask-P. This approach generalizes PGExplainer (Luo et al. 2020) and learns node mask m E [o, 1] for each sample Similar to BernMask, also has mask size and entropy constraints in its loss function, and their coefficients are both tuned from {1.0, 0,1, 0.01} as well. After pre- training the classifier, the explainer module in BernMask-P -P will be trained with extra 100 epochs on ActsTrack and SynMol and with extra 50 epochs Tau3Mu and PLBind. The temperature in the Gumbel-softmax trick is set to 1.
PointMask (Taghanaki et al. 2020). It is trained with 300 epochs TrtsTrack and SynMol, and with 100 epochs on Tau3MM and PLBind. It has two hyperparameters as specified in their paper, i.e., and i, where is tuned from {1.0, 0.1, 0.01} and / is tuned from (0.2, 0.5, 0.8).
E IMPLEMENTATION DETAILS
Backbone Models. All backbone models have layers with hidden size of 64. Batch normal- ization (Toffe& & Szegedy 2015) and ReLU activation (Nair & Hinton| (010)) are used. All MLP layers use dropout (Srivastava al. 2014) ratio of 0.2. SUM pooling is used generate point
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cloud embeddings to make predictions. All backbone models utilize implementations available in (PyG) (Fey & Lenssen 2019).
LRI-Bernoulli. Directly removing points from to yield Ć makes it non-differentiable. We provide two differentiable ways to approximate this step. The first way is to use another MLP to map the raw point features X to latent feature space H, and yield C (V, (m1 inn?') @ H.r). Here is vector containing my for each point v E V. is a vector of all ones, and C denotes glement-wise product. This is because masking X or is inappropriate as values in them have specific physical meanings. When the backbone model is implemented by using a message passing scheme, e.g., using PyG, another possible way is We find both ways can work well and we adopt the second way in our experiments.
to mask the message sent by the points be removed.
LRI-Gaussian, We a softplus layer to output ai and 02 parameterize the Gaussian distribu- tion. To make it numerically stable we clip the results of the softplus layer to [1.0 x 10-6 6,-6, 1.0 x 10%]- For & in the differentiable graph reconstruction module, we find it empirically a simple MLP can work well enough and thus we adopt it to implement Φ.
Baseline Methods. BernMask extended from Ying the implementation available in PyG. BernMask-P is extended from Luo et al. (2020) based on the authors' code and a recent PR in PyG. PointMask is reproduced based on the authors' code.
(0119) based the authors' code and
GradGAM and GradGeo are extended based on the code from Gildenblat & contributors (202T).
Discussions on LRI. We note that both f and g LRI needs permutation equivariant encoder to learn point representations, and we find for simple tasks these two encoders can share parame- ters to reduce model size without degrading interpretation performance, while for challenging tasks using two different encoders may be beneficial. In experiments ActsTrack, Tau3Mu, and SynMol, and use two different encoders for PLBind. size is not concern, using two encoders can be good starting point. The other thing is that of the key components LRI is the perturbation function h, as shown in Fig. [] and we have shown two ways design h. i.e., Bernoulli perturbation and Gaussian perturbation. Nonetheless, h can be generalized in many different ways. For example, is where one can incorporate domain knowledge and provide contextualized interpretation results, i.e., human understandable results. For instance, instead of perturbing molecules in the atom level, it is possible to perturb molecules in the func- tional group level, e.g., by averaging the learned perturbation in each functional group, so that the interpretation results can be more contextualized and more human understandable. In this work, we experiment this feature on PLBin by replacing the learned {Pa hee)(e) Uv or (E.) (ee)ee))) U in neighbourhood with the minimum p or with the Σ having the maximum determinant in that neighbourhood, which encourages either aggressively perturbing all amino acids in a neighborhood or not perturbing any amino acids in the neighborhood, and we find this can better help discover binding sites for PLBind.
the same encoder for
the model
F SUPPLEMENTARY EXPERIMENTS
F.1 ABLATION STUDIES
Table shows the effect of the differentiable graph reconstruction module in LRI-Gaussian, where e is set to 200 on Act Track and to 5 on SynMol so that large perturbations are encouraged to better show the significance of this module, is set 0.01, and f is first trained by 200 epochs and then f and g are trained together by 100 epochs. We observe significant drops when LRI-Gaussinn trained without differentiable graph reconstruction, which matches our expectations and validates the necessity of the proposed module.
F.2 FINE-GRAINED GEOMETRIC PATTERN LEARNING
To discover fine-grained geometric information in ActsTrach using LRI-Gaussian as shown in Table 3 we conduct experiments based on DGCNN, where / is first trained with 100 epochs, and then g is further trained with 500 epochs while f is finetuned with a learning rate of 1e-8. f and use two different encoders, 3 is set to 10, e is 100. all dropout ratio is set to 0, and F-_ is used as
[r
22

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Published as a conference paper at ICLR 2023
point features. Finally, let directly output covariance matrix E, E R2x² i..., in x-y space, to only perturb the first two dimensions of r.
G LIMITATIONS AND FUTURE DIRECTIONS OF LRI
Current LRI provides interpretation results at point-level, while cannot find geometric pat- terns shared by a group of points (e.g., some set of points may be allowed to rotate around reference point in space).
Although Gaussian noise help capture some fine- fine-grained geometrie patterns, if the underly- ing geometric patterns get too complicated, LRI-Gaussian may degrade to only offer a ranking of point importance and have limited capability capture meaningful fine-grained geometric patterns. It may be possible to design customized noise with prior knowledge to detect different types of geometric patterns (e.g., what if some points can be freely moved along a curve without affecting prediction loss?), and can we even not use a fixed noise distribution (i.e., Gaussian or Bernoulli) and also make it trainable? Meanwhile, current LRT would need specific tuning to yield fine-grained interpretation results, which may be improved with better training strategies.
Current LRI may provide interpretation results that are not contextualized enough to guide sci- entists for further research. For example, chemists may prefer an interpretable model to tell them directly which functional groups are important instead of which atoms are important.
23


Reviews:
[{"review_id": "zl7_x__MSLy", "reviewer": "Reviewer_HwR5", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes two training schemas for fostering interpretability in Geometric Deep Learning by considering two properties: the relevance of a point presence and the relevance of a point location. A backbone classifier network is trained in an adversarial way where an Interpreter modifies the input data with a given amount of point-wise noise (either by removing points or perturbing their position). Then, the classifier module tries to improve the score by removing the noise while the Interpreter attempts to redistribute the amount of noise. In the end, the noise should be located at non-relevant points, while important points are kept unchanged. The method is tested across four different datasets from physic and chemistry, outperforming baselines in most cases.", "summary_of_the_review": "While some aspects in the discussion and experiments of the results could be improved, I have a positive opinion of the work: the contribution is interesting, well-validated, and based on straightforward principles. ", "strength_and_weaknesses": "STRENGHT\n=========\nS1) NOVELTY AND RELEVANCE: While similar principles have been proposed in the past to study neural network interpretability (on graphs: Miao et al. 2022; on images: \"U-noise: Learnable Noise Masks For Interpretable Image Segmentation\", Koker et al., 2021), I am not aware of similar approaches in the field of 3D point clouds. The formulation looks straightforward and applicable also in contexts outside the datasets proposed in the paper. Improving interpretability in Geometric Deep learning is an active research field, and I believe the proposed methods might have a relevant impact.\n\nS2) EXPERIMENTS: The two approaches are carefully tested with different backbones networks on several datasets, and also provide ablation and explanations of hyperparameter choices. \n\nWEAKNESSES\n========\nW1) LIMITATIONS AND DISCUSSION: The paper does not offer an overview of methods limitations, nor discussion or visualization of the achieved interoperability for the different tasks. Some sentences are spread across the text, pointing to how to exploit the covariance matrix to obtain fine-grained geometric patterns, but without showing examples. Clarify the interpretability analysis and clearly stating the outcomes could strengthen the paper message.\n\nW2) GEOMETRICAL DIVERSITY OF THE DATASETS: The proposed datasets present similar characteristics. The number of points for each sample is similar (between 15 and 340), with a similar proportion of importance points (between 20% and 30% of the entire point cloud) and the same number of classes (2 for all the datasets). It is also not clear if the different datasets face different points distribution (i.e., the density of the point clouds). I would suggest testing on data from different domains, coming from Computer Vision and Graphics (e.g., LiDAR, body scans, ShapeNet rigid objects), and also providing a measure about the density of the points w.r.t. the occupied space. \n\n\nMINOR\n=======\nM1) Can LBI-Bernoulli and LBI-Gaussian be trained together? Does it introduce instability in training? I think that if no technical limitations exist, it would be an interesting validation.\nM2) I think the methods can potentially work also on other domains (e.g., images, graphs), up to a minor reformulation of the two strategies. Is it correct? In that case, it might be mentioned as possible future work.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "iUXs3WPYLFO", "reviewer": "Reviewer_sW6V", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The submission develops two setups for building interpretable classifiers for geometric data and carefully applies them on four different test scenarios (from physics and medicine). The proposed models performs sensitivity analysis wrt either point inclusion (Bernoulli model) or point perturbation (Gaussian model). The proposed models are simple and can easily bee integrated with existing classifier models. The proposed models and classifier backbones are jointly trained. The paper also contributes benchmark datasets by collecting data from pretty diverse application settings and demonstrates the utility of the proposed framework. \n\nI liked this submission as it demonstrates applications on non-standard dataset with potential implication beyond our immediate field. ", "summary_of_the_review": "Overall a good paper and I would be supportive of acceptance. ", "strength_and_weaknesses": "+ Important topic and a simple clean framework\n+ End-to-end trainable wrt interpretability and classification\n+ Benchmark datasets and good evaluation\n\nThe following are some of the weaknesses that can be explored in future works. \n- Correlation across points is not considered. In many situation, this can be quite an important factor. \n- Performance in adversarial setting is not discussed/explored. \n- GradGAM, one of the gradient-based baselines, turns out to be a pretty good post-optimization approach. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "_mDExhfnJd8", "reviewer": "Reviewer_Wziv", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a framework for Learnable Randomness Injection (LRI) to train inherently interpretable geometric deep-learning models for scientific data. It perturbed data by learnable Bernoulli and Gaussian randomness masks in terms of existence and location importance. Furthermore, four scientific datasets with ground truth interpretation are proposed. ", "summary_of_the_review": "My major concern is the insufficient justification of technical contributions, computational cost analysis, and missing ablation study.", "strength_and_weaknesses": "Strengths:\n+ The paper is well-organized, written, and easy to follow.\n\n+ The proposed research is well-motivated and appealing.\n\n+ The proposed methods are simple and technically sound.\n\n+ Four scientific datasets with interpretation ground truth will be released, which will benefit a large research community.\n\nWeaknesses: \n- Insufficient justification of technical contributions. Although the proposed methods, namely LRI-Bernoulli and LRI-Gaussian, are technically sound, it is hard to tell the technical contributions compared with existing works. For instance, PointMark, BernMask (GNNExplainer), GradGeo (DeepLIFT) are intensionally selected for comparison. How are they related to the proposed methods? What are the key differences/improvements from the proposed methods and previous mask-based methods (e.g., PointMark)? \n\n- Computation overhead. Constructing KNN graphs is very time-consuming. The proposed LRI-Gaussian has to perform graph reconstruction after each round of perturbations. However, there is no discussion about computational cost either analytically or empirically.\n\n- Missing ablation study. Without ablation studies, it is hard to tell whether the prediction and interpretation gains result from more parameters and additional computations.\nThe authors claim that existing interpretation methods cannot handle irregular geometric data. However, there is limited evidence to show that the proposed methods can handle it. \nThe authors claim that most existing methods can only provide either the existence or location importance. However, is this really a significant problem? \nCan the proposed LRI-Bernoulli and LRI-Gaussian work together? \n\nMinor Issues:\n- The structures of g and f is unclear, how the f take points and 3D spatial coordinates to make predictions? \n- How is the $| \\Sigma_v|$ is used to rank the location importance?\n- How the eigenvectors of $| \\Sigma_v|$ is calculated?\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "LrTf91fFng9", "reviewer": "Reviewer_vQZw", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This work studies designing interpretable geometric deep learning via learnable randomness injection with 4 proposed datasets, ActsTrack, Tau3mu, SynMol, and PLBind.  They show that using LRI mechanisms could improve the prediction performance of the backbone models, and even could improve model generalization.", "summary_of_the_review": "At the current stage, I think it seems to be interesting research.  I would be willing to reconsider when the other review and the author's responses are available. ", "strength_and_weaknesses": "Strength:\n1. It is interesting to study using interpretable learning mechanisms for point cloud data, especially for proteins that often consist of hundreds of amino acids.\n2. It is also good to establish 4 benchmark datasets to facilitate interpretable GDL research.\n3. Their experimental results show appealing properties.\n\nWeaknesses:\n1. The paper is not well-organized, and also is not easy to read.  I would suggest moving the dataset introduction part to a later section, and could better prepare a full system overview to better illustrate how the full system work. \n2. According to Table 1, all 4 datasets seem to be not large-scale, and each dataset only has 2 classes.  I am not sure if that is sufficient for a classification benchmark.  The number of points in each sample seems to be not large either (i.e., the largest is 339.8), which should be much less than a normal visual point cloud scan (e.g., at least 1024 in ModelNet40).  Maybe the authors could explain more in the response.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster