Explainable Graph Learning for Particle Accelerator Operations
Authors: Song Wang
Chris Tennant
Jundong Li
Venue: Accepted by TMLR ()

Abstract: Particle accelerators are vital tools in physics, medicine, and industry, requiring precise tuning to ensure optimal beam performance. However, real-world deviations from idealized simulations make beam tuning a time-consuming and error-prone process. In this work, we propose an explanation-driven framework for providing actionable insight into beamline operations, with a focus on the injector beamline at the Continuous Electron Beam Accelerator Facility (CEBAF). We represent beamline configurations as heterogeneous graphs, where setting nodes represent elements that human operators can actively adjust during beam tuning, and reading nodes passively provide diagnostic feedback. To identify the most influential setting nodes responsible for differences between any two beamline configurations, our approach first predicts the resulting changes in reading nodes caused by variations in settings, and then learns importance scores that capture the joint influence of multiple setting nodes. Experimental results on real-world CEBAF injector data demonstrate the framework’s ability to generate interpretable insights that can assist human operators in beamline tuning and reduce operational overhead.

Published in Transactions on Machine Learning Research (01/2026)
Explainable Graph Learning for Particle Accelerator Opera- tions
Song Wang
suShun@virgniaa.edy
Deportment of Electrical and Computer Engineering University of Virginia
Christopher Tennant
Comaandujjla. ory
Thomas Jefferson National Accelerator Facility
Jundong
edu
Department of Electrical and Computer Engineering University of Virginia
Reviewed on OpenReview: http::///orrrriieeee///////////r
Abstract
Particle accelerators are vital tools in physics, medicine, and industry, requiring precise tuning to ensure optimal beam performance. However, real-world deviations from idealized simulations make beam tuning a time-consuming and error-prone process. In this work, we propose an explanation-driven framework for actionable insight into beamline operations, focusing the injector beamline at the Continuous Electron Beam Accelcrator Facility heterogeneous graphs, where setting
(CEBAF). We represent beamline configurations actively adjust during beam tuning, nodes represent elements that human operators can and reading nodes passively provide diagnostic feedback. To identify the most influential setting nodes responsible for differences between any two beamline configurations, our ap- proach first. predicts the resulting changes in reading nodes caused by variations settings, and then learns importance scores that capture the joint influence of multiple setting nodes. Experimental results on real-world CEBAF injector data demonstrate the framework's abil- ity to generate interpretable insights that assist human operators in beamline tuning and reduce operational overhead.
1 Introduction
Particle accelerators complex scientific instruments designed to accelerate charged particles, such protons and electrons, to high energies (Wille) 2000 Conte & MacKay 2008 Sessler 2014 Wiedemann 2015 Appleby et al. 2020). These devices have found application in broad range of disciplines, such as particle physics, nuclear physics, and materials science, which contribute to uncovering the fundamental propertics of matter and the universe (Brüning & Myers 2016). Accelerators can probe nuclear structure (Leemann al.
2001 Willeke Beebe- Beebe-Wang 2021). characterize material propertics, and support medical fields through radiation therapy and advanced imaging technologies (Peach et. al.) 2011 Podgoršak 2014 Flanz 2015).
As some of the most advanced and complex machines engineered, particle accelerators demand precise operation [Kutsacy 2021 Friedrich et al. 2017). High-fidelity beamline simulations are commonly used to assist human operators in managing accelerator performance. However, these simulations are idealized and often differ from the complexities real-world implementations. This mismatch necessitates beam tuning, an itcrative process that socks align operational parameters with simulated performance. Beam tuning is frequently timo-consuming and challenging, contributing significantly to machine downtime. The current reliance limited diagnosties and simulation interactions compounds this inefficiency.

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In this work, we introduce novel explanation-driven framework for achieving actionable insights into com- plex, high-dimensional systems by leveraging graph-based representations of accelerator beamline configura- tions. The beamline is modeled as a heterogeneous graph where nodes represent different elements, divided into sctting nodes (which can be actively adjusted by human operators) and reading nodes (which are observ- able but not lunable). Directed edges caplure the beamline's lopology, where influence flows from ream to downstream nodes. Each node associated with a unique feature vector representing state. However, two key challenges arise in this setting. First, only the setting nodes can be adjusted, while the reading nodes only passively reflect system outcomes. This imposes constraint: it is infeasible to freely vary setting node features, as the resulting changes in the reading nodes are not directly known. Second, adjusting multiple setting nodes simultaneously can lead to complex, nonlinear interactions, making it difficult to disentangle their individual contributions and interpret the resulting changes in reading node features. As a result, explaining the effects of specific adjustments remains a significant challenge. Understanding these effects is essential for effective beamline tuning.
To address these challenges, our method identifies and ranks influential nodes based on their contribution to beamline changes. To isolate the impact of setting nodes, train representation learner that predicts reading node features based solely on scttings, thus enabling clean comparison between predicted and actual outcomes. Second, to model the joint influence of multiple setting nodes, we introduce trainable node masks with regularization that help isolate the most. influential adjustments. These masks are optimized to highlight setting nodes that siguificantly impact downstream behavior, providing interpretable node importance scores that can guide beam tuning. Moreover, evaluating our framework is challenging due the absence of ground truth for node importance. To address this, we estimate setting node influence by measuring how individual adjustments affect the prediction error reading nodes. This provides principled proxy for assessing explanation accuracy. The main contributions of this work are follows:
1. Novel Representation: We model particle accelerator beamlines as heterogencous, directed graphs, where nodes represent beamline elements and edges capture their interactions. This enables effective application of graph-based machine learning techniques for beamline analysis.
2. Explanation Mechanism:
We propose an explanation-driven framework that identifies the most influ- ential sctting nodes responsible for observed beamline changes. This is achieved by training a node-mask mechanism with regularization based on predicted versus actual reading node changes.
3. Practical Evaluation:
Our approach is validated on real-world beamline datasets. To achieve ground truth for evaluation, we design an efficient method to independently measure the impact of each node. The results demonstrate its ability to identify important changed nodes and provide interpretable insights.
By focusing on explanations, our framework provides a practical tool for improving particle accelerator operations while empowering operators with a greater understanding of a high-dimensional, complex system.
2
Preliminaries
2.1 Data Preparation
The Contimuuss Electron Beam Accelerator Facility (CEBAF), located at the Thomas Jefferson National Accelerator Facility (Jaab), a powerful recirculating linear accelerator capable of simultancously delivering electron beams to four nuclear physics experimental stations (Reece, 2016 Adderley et al., 2024). A schematic of CEBAF is shown in Figure [a] For this study, focus specifically the injector beamline. The injector serves as excellent testbed due to its relatively compact scale, diversity of beamline components, and extensive archived tuning data. This region is critical to beam performance and serves as focal point of operational adjustments, providing abundant data for the development of data-driven models. To show how a beamline can be represented as a graph, consider the example illustrated in Fig, [b] The beamline compriscs various element types, including beam current monitors (BCMs), beam position monitors (BPMs), quadrupoles (Q), solenoids (SOL), and correctors (CORR), all represented as nodes in the graph. Each mode type is characterized by unique features: quadrupoles, correctors, and solenoids have single value
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CORRI
8PM
SOLI
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GRAPH
strength
2.6 2e++0z
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44688+00
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strength
1.321e+02
moth inac
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A
O
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reading
strength 3. 3.086e+04
current
1 1.032-006
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Figure 1: (a) Schematic of the CEBAF accelerator. Electrons are generated in the injoctor. Multiple passes through the north and south linacs accelerate the beam to multi-GeV energies. The beam is then sent to the four muclear physics experimental halls (A, B, C, and D). (b) Illustrations that showcase an arbitrary accelerator beamline (top) and our approach for constructing a corresponding graph (bottom). Here, each node represents an individual clement, while the node features correspond to the relevant paramcters of the respective element. The edges between nodes are determined by user-defined window size of 2. These edges are directed to reflect the fact that an element cannot impact upstream elements in the beamline.
corresponding to their field strength, BCMs provide beam current measurements, and BPMs include the horizontal and vertical beam positions as well as the sum signal, which is proportional to the beam current in the beamline. The resulting graph is heterogeneous and directed, where heterogeneity arises from the diverse node types, and directionality reflects the causal flow along the beamline.
Edges between nodes are established based on user-defined "window". In the example in Fig. 1b window size of 2 is applied, meaning each setting node is connected to the two immediate downstream setting nodes, with any intermediate reading nodes also included. Setting nodes represent elements that operators actively adjust during beam tuning, such as Q1 (the first quadrupole), SOL1 (the first solenoid), and CORR1 (the first corrector), whereas reading nodes passively provide diagnostic feedback (e.g., BPMs and BCMs). The directed edges reflect the unidirectional nature of the beamline, as upstream nodes cannot be influenced by downstream elements. Notably, the window size is adjustable, allowing graph representations for specific downstream tasks and beamline characteristics. In previous work (Wang et al. 2024 the results shows that window size of 2 achieves the best performance in the classification of beamline configurations, compared to window sizes of 1, 3, and 5. This setting achieves balance between capturing local interactions and avoiding spurious long-range links. Thus, we follow this work and choose the optimal window size of 2. To facilitate the integration of global beamline parameters, we create a master node connecting to all other nodes, enabling the inclusion of global fcatures such as beam current, environmental conditions (e.g., temperature and humidity), and temporal information. This design allows for more comprehensive representation of the beamline. For this study, each beamline graph consists of 12 distinct node types, 207 nodes in total, 393 features, and 530 edges (based on a window size of 2), with a master node connecting to all others. Each node type has specific features that can vary significantly in magnitude due to the nature of the physical quantities they represent. To address this, we perform element-wise normalization. For each dataset, we calculate the mean and standard deviation for each node feature and standardize them.
be tailored
2.2 Problem Formulation
In this section, we present formal definition of the beamling explanation task. Consider datasct D. which is composed of multiple graphs: D = {G1, G2...., GDD|). Each individual graph G is characterized by the triplet = EV, Specifically, V and denote the collection of nodes and edges, respectively. An alternative representation of graph G through its adjacency matrix E Ra*a, where n corresponds to the number of nodes in the graph. The element At, the intersection of the i-th row and j-th column is set to 1 if an edge exists between node i and node j; otherwise, Aij 0. Given that beamline graphs
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Prediction Model Training
Overall Explaining Framework
Graph
Prodicted Reading Attribatte
Difference in
Predicted Reading Attributes
Prediction Model
Setting Atrrlmites
Prediction Model
Embedding Model
Compare
Node Dift.
Input Gruph
Compane
Reading
Ground Truth Attributes
Node Diff.
Learied Embbedinng
Graph
Reading Attributes
Difference between the Lwo Graphs
Setting
Large Mask
Small Mask
Graph
The overall framework. On the left-hand side, we illustrate the training process of the prediction model, which prodicts the reading attributes, given the setting attributes of an input beamline graph. On the right-hand side, the explanation framework takes two beamline graphs as input and computes the difference in setting node features between them. Then the framework optimizes the node mask to learn the importance.
Figure 2:
are inherently heterogeneous, we introduce node type mapping function T T, where T denotes the set of all node types. With this mapping function, the type of node vú is given by r(i). Furthermore, node features are encoded as X' = (x1, X,,,, where x; E R4 represents the feature vector of node U, and (s))) corresponds to the dimensionality of features specific to the node type r()).
The primary goal is to develop an explanation-driven framework that identifies and ranks the most influential nodes responsible for differences between two beamline graphs. Formally, given a pair of graphs Giuit EV, (()) and Gend (V, E, (()),, where both share the same topology but differ in node features due to changes in subset of setting nodes V. V, the objective is to compute ranking over Ve that reflects the importance of each node in contributing to the observed difference between Ginit. and Gend- This task enables interpretable analysis of how changes of specific elements can propagate through the beamline graph, offering practical guidance for operators during beam tuning.
3 Methodology
The primary motivation is to improve accelerator operators' physical intuition about how specific setting adjustments impact broader beamline configurations, thus improving operational efficiency. Accelcrator tuning, the process converging to a desired operational point, is inherently iterative and often time- consuming. By providing insights into the relationship between setting changes and embedding movements, we not only explain the behavior of the system, but also offer practical guidance recover desired operational states. We seck to determine the most significant setting nodes that account for embedding movement between two points in the learned represental ion space. This formulation of explainability serves a practical purpose in accelerator operations.
Consider a common scenario: beamline operating at optimal performance gradually degrades over several days as different. operators make adjustments response to beam variations or environmental changes. While general guidelines cxist for injector tuning, the specific implementation varies among operators. In such cases, identifying the primary setting changes relative to known stable operating point can provide valuable guidance for state recovery.
Determining these important nodes presents significant challenges. The heterogencous nature of the acceler- alor system means that the magnitude of setting changes alone is insufficient to determine node importance. For instance, an equivalent normalized change in a quadrupole settinng versus an accelerating cavity phase will have substantially different effects on the beam. Morcover, the spatial location of the modified node within the beamline critically influences its downstream effects. This complexity requires a more sophisticated approach to ranking the significance of setting changes.
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Workflow. Our framework follows structured workflow consisting of three main components: an embedding model, a prediction model, and an explanation model, as illustrated in Fig. 2 Utilizing the representations learned by the embedding model and the predicted reading attributes from the prediction model, the expla- nation model identifies the most influential setting nodes contributing to changes between any two beamline graphs. By inlegrating these components into a comprehensive framework, we aim to enable the explanation for the scientific domain of particle accelerators with unique constraints. Unlike generic contrastive learning, our aligmment loss preserves operational geometry between setting nodes, which is crucial for interpretable state transitions in accelerators.
3.1 Embedding Model
This section presents our approach to learning graph embeddings for CEBAF injector beamline graphs while accounting for node type diversity. The heterogencous nature of the acoelerator system presents a significant challenge for learning the embeddings, as the magnitude of setting changes alone is insufficient determine node importance. Therefore, for the embedding model, introduce heterogeneous graph convolution method to encode beamline graphs (Hu et al. 2019 Yang al. 2023 Zhao et al. 2021 This approach addresses variations in feature distributions across different node types by transforming them into unified latent space through linear layers.
Formally, given a beamline graph G = (V,E, we define the adjacency matrix with self-connections as A' = A I, where is the identity matrix of size n, with n = [/]. The degree matrix M is then given by M Σ A.j. Generally, the propagation rule at each layer in the standard graph convolution operation Kiipf & Welling 2017 Xu ct al. 2019 Hamilton et al. 2017a b) for homogencous graphs can be formulated as:
h(+1 MP (hh) I [uEE(()),,))))
(1)
where MP(+) denotes the message-passing function that can aggregate representations from a set of nodes and output a representation for a specific node. Moreover, h(--1) denotes the representation of node v at layer ++1. 1. (0) corresponds to the initial node features of v. N, denotes the set of neighboring nodes of v.
To take into account the heterogeneity of node types and varying feature dimensions, we employ a hetero- gencous graph convolution strategy (Hu et al., 2019; Liu et al. 2020 Chang et al., 2015 Hu ct al., 2020). allowing integration of multi-lype node information. We lirst project the node features of different node types into a common latent space:
h =x, Wr(w) + by(w), where T(U) ET.
(2)
Here W E Re ( and Br(e) E R are projection parameters for node type r(v) of node v. Here. dr(e) denotes the input feature dimension for nodes of type 7()), and (() is the dimension of layer 0. T is the set of node types. Given this transformation, heterogencous graph convolution is performed as:
H w + +b49))
H = ReLU
EA, reT
(3)
where À = A'M-' is the normalized adjacency matrix, and ( and (()) are the trainable parameters for layer !! and b. are layer-specific parameters for node type r. Unlike standard GCN, we assign distinct parameters different node lypes, ensuring feature transformations into shared latent space. Additionally, A, represents submatrix of A, encoding connections between nodes and their neighbors of type т.
Self-Supervised Optimization for Representation Learning. We propose self-supervised optimiza- tion strategy that encourages aligument between node features and their learned embeddings for more comprehensive representation learning. Specifically, we introduce an alignment loss, which aims to preserve the pairwise distances between nodes in the original feature space within the embedding space. This encour- ages the embodding space maintain the structural geometry of the input features and mitigates potential distortions introduced by heterogeneous transformations. Given pair of node feature vectors x1, X2 and
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their corresponding learned embeddings h1, h2, define the self-supervised alignment loss as:
L = D(x1.x)) - D(,, b2)), where x2) =
(i1, 22,)).
(4)
Here -(.,)) represents the Euclidean distance between standardized feature vectors, with standardization given by: T1, = (x1,- (xxx))/ This ensures distances in the input feature space appropriately aligned with distances in the embodding space, promoting consistency in graph representations. This loss aims to explicitly align distances in feature space with those in the latent embedding space, ensuring that operationally meaningful differences (e.g., in quadrupole strengths or cavity phases) are preserved. The em- bedding space, therefore, maintains a geometry consistent with the input features while also leveraging graph connectivity to capture causal dependencies. This alignment guarantees that minimizing latent distance cor- responds to recovering a physically plausible state. An example of nearly 52,000 learned representations after optimization are illustrated in Fig. 3 which reflects the CEBAF operational run in 2022.
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Figure 3: Embeddings representing CEBAF injector operations in 2022. Markers are color-coded by month. Note that there was a scheduled accelerator down during March, April, and May.
3.2 Prediction Model
This subsection presents the training details of our prediction model (as shown in the left- side of Fig. 2) The purpose of this model is to estimate the features of reading nodes based on the features of setting nodes. This design aligns with the physical constraints of roal-world accelerator systems: operators directly manipulate the values of setting nodes (e.g., magnet strengths, RF phases), but not the values of reading nodes, which passively reflect system diagnostics and feedback.
To capture the relationship between these two types of nodes, we train a dedicated prediction model that learns to approximate the effect of setting adjustments on the readings. The prediction task involves learning mapping from setting node features to reading node features, which can be formalized as:
Proad (Veet Exet, Kaet), where Exet = (v,, U;) u;)lu;, 0y E Vseth, Xatt = (xx|V E Vset)
(5)
where fo is a graph neural network parameterized by 0, Vset denotes the set of setting nodes, Eset = ((v,, v,) Ug by E V the set of edges among setting nodes, and X = fx, V represents the corresponding node features. The model is trained to minimize the mean squared error (MSE) between the predicted and actual reading node features:
i argmin
Proad xnead
(6)
jev
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This objective ensures that the model learns an accurate functional approximation of how beamline readings respond to configuration changes.
3.3 Explanation Model
Our explanation model interprets the relationships between setting attributes and reading attributes in a self-supervised manner (as shown in the right-hand side of Fig. 2). We first train a prediction model that learns to infer reading attributes based on setting attributes.
Given a trained GNN model Φ we aim to identify the most important setting nodes whose features and connectivity explain the change between two beamline graphs. To achieve this, we seek to learn a continuous node mask that highlights which nodes contribute most the observed shift in representation between two beamline graphs.
Let G = (V) be a beamline graph with node features X, and let H = g(V, E Rd denote the dense representation produced by the GNN. Given a pair of graphs Giait and Gend where certain setting nodes have changed, we denote their respective representations as H and H²2) Our goal is to explain the transition between these two states by identifying the explanation graph Gs. defined by the node mask m {m,, m2,....... ] E [0, 1J", where n is the number of changed setling nodes. With the explanation graph Gg, we aim to provide insights of nodes whose features and connectivity are most informative about the latent transition from (1)) to H(2)
Optimization via Mutual Information. To effectively learn the masks to constitute Gs, propose to utilize the concept of mutual information for optimization. Particularly, we aim to maximize the mutual information between the explanation graph Gs and the target representation shift:
max MI(H, Gs) = H(H) H(H -(( G = =Gs, = =xs), Gs
where X's denotes the masked input features corresponding to Gs, and H(-) denotes differential entropy. Notably, H(H) is fixed for trained representation model. Thus, maximizing the mutual information is equivalent to minimizing conditional entropy:
min H(H G Gs, -Eris [l Xs)] G3
(8)
In practice, we model this process through reconstruction: we seck a masked input of the beamline graph that produces a representation as close as possible to the true representation H(2), The explanation is thus formulated the mask that minimizes the distance between the masked-output representation and (2)
Variational Mask Optimization. To enable gradient- gradient-based optimization, we use continuous relaxation of the binary node mask m E [0, 1]". This mask is applied individually to each setting node (on its features), such that the node features of the masked graph becomes ('). The masked representation is then computed as:
1 = X(m)), where X(m) = Xeet (m) U Fread (m).
Here (m) denotes the new node features. Particularly, we calculate X(m) separately for setting nodes and reading nodes as follows. For setting nodes, consider the difference between the two beamline graphs Ginit and Gend- If a specific setting node changes between these two graphs, we will learn a node mask for it. In this way, the features of Ginit added with the node mask multiplied by the change will become the new features. For setting nodes that are not changed, their features remain unchanged. The calculation is as follows:
U; E Vant, where 5, = m if 02 Vehange> X (m)= (xx") + 6, (x(%) - x(")
(10)
if Us & Vehange
Here Vehange denotes the set of setting nodes changed between the two graphs. For the reading node features, it is inappropriate to use the same adding strategy, the changes of reading node features are dependent
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the collective impact of multiple setting nodes. Therefore, we leverage the trained prediction model fo to obtain the predicted reading node feat
Xread (m) = So Exet; Aset (m))-
(11)
The predicted reading node leatures, together with the new setting node features, will constitate the features for Gg. To optimize the node masks, i.e, m, we propose the following objective to obtain the optimal node masks mn as follows:
argmin || H 11 / + Al|m|||
(12)
where À is a regularization hyperparameter that encourages sparsity in the learned mask, thereby improving the interpretability of the explanation. The optimization objective is to minimize || - H[*)|, ensuring that the modified graph remains as similar as possible the target graph in the latent space. This enables the model to effectively capture the underlying structure and reasoning behind the transformations in the dataset.
By optimizing this loss, we obtain soft mask m that highlights the most influential nodes driving the repre- sentation shift between two graphs The result is an interpretable explanation in terms of node importance, revealing which setting changes contributed the most significantly to the transition. This explanation sup- ports human operators understanding beamline behavior and facilitates more effective control in real-world accelerator settings.
3.4 Establishing the Ground Truth
Particle accelerator data lacks ground truth annotations for identifying impor- tant nodes in explanations, making it dif- ficult to evaluate our explanation frame- work's 's performance and compare it fairly with existing baselines. To address this challenge, we propose a statistical analy- sis approach to approximate the ground truth by quantifying node importance based on their individual contributions to changes between two beamline graphs. This serves principled way lo con- struct a proxy for ground truth, enabling more meaningful ovaluation. The core idea to iterate over all possible permu- tations of the changed setting nodes, as the order in which node changes are applied can also influence the resulting graph difference. This is illus- trated in Fig. The blue trace represents the actual trajectory in the low-dimensional space while moving between an initial (green) and end (red) injector configuration ion during a bean study at CEBAF. The black traces represent the 719 other possible trajectories if we consider all permutations of the six setting node changes. By evaluating every permutation, we can mitigate the effect of ordering bias and assess each node's impact more fairly. For each permutation, we compute the marginal contribution each node by measuring how much reduces the MAE (Mean Absolute Error) between the readings of two beamline graphs. The nodes are then ranked based on their average contribution across all permutations.
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Figure Visualizing 720 possible trajectories between the initial (green) and end (red) configuration. The blue line represents the actual path taken in the experiment.
This exhaustive approach becomes computationally infeasible when the number of changed nodes is large (e.g., 24! x 6 x 20 permutations). To make this process tractable, we adopt a more efficient strategy: first, we identify the top-k most influential nodes based on a heuristic ranking, and then we enunerate all k! permutations of this reduced subset. In the experiments, we set. = 4. This significantly reduces the computational burden while preserving the fidelity of the importance estimates.
Important Node Identification. We analyze the impact of individual node modifications within a graph, considering two distinct cases, each represented graph with specifie number of nodes. We define
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of these graphs the starting case and systematically apply individual node modifications to observe their effects. The key objective is to determine which nodes contribute most significantly to changes in the overall graph behavior.
Formally, given an initial graph Giit = (V,E,)) and a set of changed nodes Vehange, we iteratively apply each modification is Vehange to generate a modified graph Gmod The difference between the original and modified graphs is quantified using the change in prediction error, defined as:
AD(e.) (fo(Gmma((s)) fG
(13)
where (D; denotes the prediction error of the model when modification e2 is applied.
We rank all changed based on (D( and identify the top & nodes that induce the most significant changes in graph behavior. The selected nodes, Veop,k; are as follows:
Viop,k argmax
Σ AD(u), where V C Vehange:
[V = k.
(14)
V WEV!
Ground Truth Establishment via All Permutations. To evaluate the impact of these nodes, we compute all possible permutations of these k nodes and analyze their contributions by running the prediction model across all k! possible orderings. In this way, the specific node that causes the largest MAE reduction in readings from Ginit to Gend is considered the most important node in this permutation. Ultimately, the nodes that have the largest. proportion of being the most important nodes across all permulations will be considered the most influential nodes. This allows us systematically assess the influence of node interactions. Notably, the established ground truth is based marginal contribution to prediction error, not directly the masks learned by the explanation model. Thus, while both use the prediction model, the explanation model optimizes in the embedding space, whereas the established ground truth evaluates marginal error reduction. Although the real ground truth is not available at the current stage, future directions will include collaborating with CEBAF operators for validation and integrating expert feedback.
Notably, our establishment of ground truth naturally incorporates the order- dependence effect, which is explicitly considered among the most influential k nodes. Rather than simply averaging over all permutations, our method applies principled filter that balances computational feasibil- ity with fairness in evaluating node importance. Importantly, this design also reflects the practical reality of accelerator operations, where operators often make iterative adjustments, making it difficult to define a strict sequential ground truth.
Order-Dependence.
Case Study, In Fig. ! six setting nodes change between the two graphs. In this case, we exhaustively evaluated all 720 possible permutations of the six node changes and compared them with the results producod by our framework. Our framework ranked the nodes in descending order of importance as 6, 1, 2, 4, 5, 3. Notably, both approaches consistently identified the same most influential node: the setting node associated with the last change, which shifted the value of PCA component 1 from 10 to -12. This agreement between the exhaustive permutation analysis and our framework highlights the validity of our explanation method.
4 Experiments
To evaluate our proposed framework, we perform experiments on real-world datasets by analyzing heteroge- neous graph-based settings and their influence on prediction performance.
4.1 Experimental Setup
Our framework is implemented using PyTorch (Paszke et al.) 2017), scikit-learn (Pedregosa et al. 2011 p, and Torch Geometric (Fey & Lenssen 2019). We run the model on single NVIDIA A6000 GPU with 48GB of memory. The batch size is set to 16 for self-supervised training and 32 for supervised fine-tuning. The model is trained for total of 200 epochs with a learning rate of 0.001. The hidden size of the GNN models in our framework is set to 16, and we use a 3-layer architecture. The model is optimized using Adam (Kingma & Ba 2015). We conduct largo-scale experiments on the 2022 datasct. Each graph represents a unique case, and we analyze the impact of node modifications across a wide variety of graph structures. For the 2022
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dataset, consider two splits: (1) Jan-Feb and (2)
Table 1: Statistics of two beamline datasets.
Jun-Jul-Aug. The detailed statistics are provided in
Dataset
# Graphs
# Edges
# Nodes
# Types
Table ! We choose these two splits because they are closer together in time. We randomly select 250 samples from each the two splits constitule the final test set. The empirical results using various evaluation metrics are provided in Table Code is https://github.com//Seen W-SW W-SW/CEBAW-WWBCCC CEBAFFExx
Jan-Feb
25,916
530
207
Jun-Jul-Aug
25,801
4.2 Baselines and Evaluation Metrics
We compare our framework with several statc-of-tho-art explanation methods for graph-based learning:
GNNExplainer (Ying et al. 2019 A model-agnostic approach that learns node importance by
optimizing a mutual information based objective to explain GNN predictions.
PGExplainer (Luo et al. 2020 A parameterized explainer that learns probabilistic mask for graph structures to highlight important nodes and edges.
Gradient Integration: An explanation approach that utilizes backpropagated gradients to measure the importance of features in node embeddings, identifying their influence on final predictions.
Feature: A feature-based approach that evaluates the impact of individual node features by analyzing the magnitude of node embeddings in trained graph models.
4.3 Evaluation Metrics
For each experiment, we randomly select two graphs G1 and G2 and identify the most important node differences between them. Using our framework, we rank nodes in Vehange with our explanation results. To quantitatively assess the effectiveness of the results, we compute two metrics: (1) Precision@k measures the overlap between the identified important nodes and the ground-truth. (2) Hits@k is recall-based metric that measures whether at least one of the top-k predicted nodes appears in the ground-truth set. These two metrics can be formulated as above:
[pred, Viop.kl
f1. if pred, 0 Veop.k k # 0, 0. otherwisc.
Precision@k
Hits@k
(15)
k
Here Upred,t represents the top-k nodes predicted as influential, and Viop.k is the ground-truth set of the top-k influential nodes, established in Eq. (14.. Notably, unlike Precision@k; which quantifies the proportion of correctly identified nodes, Hits@k provides a binary measure of whether at least one correct node was retrieved within the top-k predictions. This metric is particularly useful for evaluating whether a method can successfully identify critical nodes in nige-dimensiooal settings. By considering both Precision@k and Hits@k, aim to provide more comprehensive understanding of how well different methods identify important nodes in beamline graphs.
4.4 Empirical Results on Large Datasets
The results demonstrate the effectiveness of our proposed method compared to various baselines. The key observations are summarized as follows:
Superior Performance: Our approach achieves the highest performance across multiple metrics, par- ticularly in Hits@5 (42.25%) and Hits@10 (44.26%), demonstrating its effectiveness in identifying key nodes within graph structures.
Incremental Gains from PGExplainer over GNNExplainer: PGExplainer slightly outperforms GNNExplainer across all metrics, suggesting that incorporating additional probabilistic explanations en- hances interpretability and accuracy.
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Table 2: Performance comparison across different methods.
Method
Hits@1
Hits@3
Hits@5
Hits@10
Precision
Precision
Feature
6.35%
14.20%
34.05%
36 82%
25.49%
28.21%
Gradient Integration 5.39%
12.69%
31.52%
35.73%
27.02%
29.35%
GNNExplainer
8.52%
16.39%
37.43%
41.90%
27.48%
32.50%
PGExplainer
9.07%
16.49%
38.34%
42.58%
28.25%
32.77%
Ours
8.76%
17.84%
42.25%
44.26%
28.55%
33.13%
Table 3: Performance comparison under different initialization values.
Method
Hits@1
Hits@3
Hits@5
Hits@10
Precision
Precision@5
Ours (Init=0.5)
8.76%
17.84%
42.25%
44.26%
28.55%
33.13%
Ours (Init=0.75)
7.51%
16.94%
41.99%
43.05%
27.98%
32.97%
Ours (Init=1.0)
7.13%
16.27%
39.82%
40.85%
27.91%
32.87%
Ours (Init=0)
6.56%
15.62%
38.92%
39.66%
27.47%
31.70%
Limited Performance of Gradient Integration: Gradient Integration lags behind other mothods, particularly in Hits@1 (5.39%) and Hits@3 (12.69%), indicating that it struggles to accurately highlight the most influential nodes.
Feature Approach as Weak Bascline: The Feature method consistently shows the lowest results, with Hits@I at only 6.35%, realfirming the necessity of advanced explainability methods in graph-based tasks.
Our method also achieves the highest precision scores, with 28.55% Precision and 33.13% at Precision@55, highlighting its ability to prioritize correct nodes more effectively.
Precision Trends:
Trade-off in Hits vs. Precision: While PGExplainer slightly improves over our method in the Hits@1 metric, its Precision@k value is lower than our method, indicating that PGExplainer enhances the ranking of the top several nodes but does not drastically improve the correctness of top selections.
Notably, all values are below 50% under the challenging setting in our experiments, as multiple nodes may plausibly contribute to observed outcomes. Importantly, our method consistently outperforms baseline approaches and demonstrates clear relative offectiveness. In sum, these results validate the effectiveness of our proposed approach, demonstrating superior generalizability and robustness identilying critical nodes within large-scale graph datasets.
4.5 Parameter Sensitivity
We explore the effects of various hyperparameters, specifically analyzing how different initialization val- ues impact model performance. We experiment with three initialization values of weight masks: Init=0, Init=0.5, and Init=1. 0, and compare them against the baseline methods. The results in Table 3 iillustrate the scnsitivity of our method to differont initialization values. Key observations include:
Optimal Performance at Init=0.5: Our method achieves the highest results al Init=0.5, outper- forming all other initialization settings in Hits@k and Precision@k metrics.
Decreasing Performance with Init=00 or Init=1.0: Setting the initialization or 1.0 results drop performance across all metrics, indicating that an intermediate initialization provides better balance between model stability and adaptability.
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Published in Transactions on Machine Learning Research (01/2026)
Table 4: Ablation study results showing the impact of different components on performance.
Method
Hits@1
Hits@3
Hits@5
Hits@
Precision@3
Precision@5
Ours
8.76%
17.84%
42.25%
44.26%
28.55%
33.13%
Ours w/o Graph 6.68%
14.91%
39.06%
41.58%
26.80%
29.79%
Ours w/o Emb.
7.28%
15.88%
40.26%
41.76%
27.32%
28.64%
Comparison with Baselines: Even under suboptimal initialization settings (Init=0 or Init=1.0), our method still surpasses the Feature Value baseline in all metrics, demonstrating robustness.
Hits vs. Precision Trade-off: Although the overall Hits@k performance is the highest for Init=0.5, the Precision@k scores show smaller variance across different scttings, suggesting that precision is loss sensitive to initialization values.
These findings highlight the importance of careful hyperparameter selection, particularly in choosing initial- ization values that optimize both model convergence and prediction accuracy.
4.6 Ablation Study
We conduct an ablation study by systematically removing key components and evaluating their impact on performance. Specifically, we consider the following variations:
Ours: The full version of method incorporating all three models, including the embodding model, the prediction model, and the explanation model.
Ours w/o Graph: A variant where the graph-based embedding model is removed, assessing the impact of graph structures, In this variant, the GNN embedding model is replaced with multiple linear layers.
Ours w/o Emb.: A variant where the optimization loss for the node masks is calculated based reading attributes instead of learned embeddings. As a result, the embedding model is not used in the computation and optimization of the node masks.
The results in Table 4 highlight the importance of each component in our framework:
Impact of Graph-Based Reasoning: Removing the graph-based based embedding model (Ours w/o Graph) leads to a noticeable decline in performance across all metrics, particularly in Hits@k scores, demonstrating the crucial role of structured graph information in enhancing predictions.
Effect of Removing Embedding Model in Explanation Computation: Excluding the embedding model (Ours w/o Emb.) also results in a performance drop, though it is less pronounced than the removal of graph-based reasoning. This suggests that embeddings contribute significantly to refining node importance but are more effective when combined with graph structures.
Overall Contribution of Components: The full model consistently outperforms both ablated versions, confirming that both graph-based reasoning and embedding- based enhancements are complementary and necessary for optimal performance.
This ablation study underscores the necessity of integrating structured graph reasoning and embedding- based feature refinement to achieve superior reasoning performance in our framework.
5 Conclusion
In this work, we presented an explanation-driven framework for optimizing particle accelerator beamline operations through graph-based machine learning. By representing beamline configurations as heteroge- neous graphs and applying a novel node-masking approach, method successfully identifies and ranks the
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Published in Transactions on Machine Learning Research (01/2026)
most infiuential setting nodes responsible for observed changes in beam behavior. Experimental results real-world CEBAF injector data demonstrate that our approach outperforms existing explainability meth- ods across multiple metrics, with particular improvements in Hits@5 (42.25%) and Precision@5 (33.13%). Ablation studies further confirm the importance of both graph-based reasoning and embedding- en- hancements in achieving these results. This framework offers a practical tool for accelerator operators, providing interpretable insights that can significantly reduce tuning time and improve operational efficiency. This successful proof-of-concept demonstration motivates its use on more recent data and deployment operational tool in the control system. By bridging the gap between complex physical systems and interpretable AI, our work represents an important step toward more explainable and efficient. accelera- tor operations, with potential applications extending to other scientific instruments and industrial systems, where understanding cause-effect relationships in high-dimensional set settings is crucial.
Acknowledgements
This material is based work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Contract No. DE-AC05-060R23177.
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14


Reviews:
[{"review_id": "CpKAp0kJt9", "reviewer": "Reviewer_B3WP", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Pros.\n1. The work tackles a complex, real-world problem where improvements can lead to significant savings in time and resources. Applying advanced explainability techniques to a physical system like a particle accelerator is both novel and highly practical.\n\n2. The proposed three-model architecture is logical and well-designed. The separation of the prediction and explanation tasks is particularly clever, as it correctly models the physical constraint that operators can only adjust settings, while readings are outcomes. The use of an L1-regularized mask to encourage sparse, interpretable explanations is a well-suited choice for the problem.\n\n3. The approach for establishing a proxy ground truth is a standout feature. This method addresses a critical challenge in XAI and allows for a quantitative and fair comparison against other methods. The experimental setup is thorough, including comparisons to multiple SOTA GNN explanation baselines, ablation studies, and parameter sensitivity analysis.\n\n4. The proposed framework consistently outperforms baseline methods across multiple metrics, achieving the highest performance in Hits@5 (42.25%) and Precision@5 (33.13%). The ablation study further validates the design, confirming that both the graph-based structure and the embedding model are crucial for achieving optimal performance.\n\nCons:\n\nThe permutation-based method for generating ground truth is innovative but rests on the assumption that a node's contribution can be averaged across all possible ordering of changes. However, in a physical system, the order of adjustments can matter. The paper shows the \"actual path\" taken during an experiment (the blue trajectories in Fig. 4) but then creates the ground truth by averaging over all 720 possible paths. This might obscure order-dependent effects and should be discussed as a potential limitation of the proxy.\n\nThe explanation model's objective is to minimize the distance between two graph states in the learned embedding space. While technically sound, the paper does not fully motivate why this is a good proxy for physical similarity. A deeper justification for how the self-supervised learning objective (Eq. 4) ensures that the embedding space captures meaningful operational states would strengthen the argument of this paper.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a novel, explanation-driven framework using graph-based machine learning to improve the operational efficiency of particle accelerators. Focusing on the injector beamline at the Continuous Electron Beam Accelerator Facility (CEBAF), the authors model the system as a heterogeneous graph to identify the most influential machine settings that cause changes in the electron beam's behavior.\n\nThe primary contribution of this work is a three-part framework designed to provide actionable insights for human operators during beam tuning. The contributions are:\n\n1. The authors model the accelerator beamline as a heterogeneous, directed graph. Nodes are categorized as setting nodes (e.g., magnets, correctors), which operators can adjust, and reading nodes (e.g., beam position monitors), which provide diagnostic feedback. This structure effectively captures the physical components and the directional flow of the beamline.\n\n2. The core of the work is an explanation model that identifies which setting adjustments are most responsible for a change between two different beamline states (e.g., from an optimal state to a drifted state). This is achieved through a workflow that includes: (a) An embedding model that learns to represent the entire beamline graph in a low-dimensional space using heterogeneous graph convolutions. (b) A prediction model that is trained to estimate the values of reading nodes based solely on the values of setting nodes, mimicking the real-world cause-and-effect relationship. (c) An explanation model that optimizes a \"node mask\" to identify the smallest set of setting nodes that can explain the transition between the two beamline states in the learned embedding space.\n\n3. Lacking explicit ground truth for node importance in accelerator data, the authors devise a principled statistical method to create a reliable proxy. They assess a node's importance by measuring its marginal contribution to reducing prediction error across all possible permutations of changes, providing a robust method for evaluation. The framework's effectiveness is validated on a large, real-world dataset from CEBAF operations.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please consider to include a brief discussion in the methodology or conclusion about the potential limitations of the permutation-based ground truth would add transparency. Acknowledging that this proxy averages out order-dependent effects and explaining why it is still a reasonable approach would strengthen the paper's integrity. In addition, the paper would be significantly more impactful if it included a short, concrete example of the framework in action.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "l6l2kPmN39", "reviewer": "Reviewer_GpC3", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strength:**\n1. Clearly distinguishes adjustable (setting) and observable (reading) nodes, reflecting practical constraints.\n1. Combines heterogeneous GNNs with interpretability, addressing a practical, real-world operational optimization problem.\n1. Real-world applicability that could significantly improve operator efficiency and reduce downtime.\n\n**Weakness:**\n1. Absence of true ground truth explained via permutation-based statistical analysis, needing further validation or theoretical justification.\n1. High computational load of exhaustive permutation evaluation could limit practical applicability.\n1. Lack of Explicit Discussion of Figures 2, 3, and 4.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces an explanation-driven framework aimed at facilitating interpretability and efficient operational control of particle accelerator beamlines. Specifically, the authors model particle accelerators as heterogeneous graphs, distinguishing between actively adjustable nodes (setting nodes) and passive diagnostic nodes (reading nodes). The proposed approach employs a GNN-based embedding model to encode graph structures and an explanation model that learns node-level importance via trainable node masks. This enables the identification of critical nodes responsible for beamline configuration changes. Experiments conducted on real-world data demonstrate that the method successfully identifies influential setting adjustments, significantly improving interpretability and potentially reducing operational overhead.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "***Critical:*\n1. Clarify Figure 1 (b): Figure 1(b) has two instances labeled \"BPM1.\" Authors should clarify this potential typo; one likely should be \"BPM2.\"\n1. Define \"Q1\" Node in Figure 1 (b): Explicitly describe the \"Q1\" node to clarify its specific role or type within the beamline configuration.\n1. Justify Window Size Selection: Explicitly justify the choice of the window size of 2 by reporting empirical results from experiments with alternative window sizes or clearly referencing and summarizing findings from Wang et al., 2024.\n1. Explicit Discussion of Figures 2, 3, and 4: Clearly connect these figures to corresponding manuscript sections:\n    - Figure 2: Clearly map figure elements to methodological steps described.\n    - Figure 3: Explain the embeddings’ implications explicitly—what does this visualization reveal about model performance?\n    - Figure 4: Clearly explain the visualization of possible trajectories and its importance in understanding or validating the explanation methodology.\n1. Clarify Ground Truth Approximation Method: Provide additional justification or theoretical backing for the validity and potential biases or limitations of the permutation-based ground-truth approximation.\n\n**Non-critical**\n1. Scalability Analysis: Briefly discuss computational complexity and scalability, particularly for real-time scenarios.\n1. Visualization Enhancements: Include additional visual examples, such as node importance heatmaps, to further enhance interpretability and reader understanding.", "broader_impact_concerns": "Currently, the paper does not explicitly discuss broader ethical or societal impacts. While direct ethical concerns may be minimal, the authors should briefly address implications regarding operator trust and reliance on automated explanations in safety-critical decisions, potentially adding a concise Broader Impact Statement.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "wTFvMmSxXT", "reviewer": "Reviewer_L9ir", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strengths\n\n- The problem is well motivated with a concrete application domain in mind\n- I am not an expert in beam tuning and what has been done, but it seems interesting that the authors tried to use modern machine learning tools such as GNNs to tackle this problem\n\n# Weaknesses\n\n- The proposed framework is largely a combination of well-known methods applied to a new domain and the methodological contributions appear incremental at best. For instance, the section on \"self-supervised optimization for representation\" can be viewed as a variation/instance of the \"self-supervised contrastive learning\", which is well-studied but not referenced/compared against in the paper.\n- The approach proposed by the paper seems to have limited generalizability beyond the specific problem studied here. Furthermore, despite having explainability as a goal, there was no demonstration that the outputs are truly understandable or usable by real operators.\n- I am concerned with the evaluation process. From equation (13) in Section 3.4, we see that the pseudo ground truth is generated using the same $f_\\theta$ that is being used by the method. How is this a fair evaluation? I also suspect that the proposed approach for generating pseudo ground truth based on combinatorial simulations will be prone by spurious correlations and does not offer a strong validation signal. Lastly, there is no human or domain-expert validation to confirm whether the identified nodes are truly important.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Motivated by the time-consuming and challenging task of beam tuning at the Continuous Electron Beam Accelerator Facility (CEBAF), this paper aims to devlop an explanation-driven framework to identify and rank influential \"setting nodes\" responsible for feature differences between two beamline graphs. Experiments were conducted to evaluate the proposed methods.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "No", "audience_explanation": "", "requested_changes": "- Please address my concerns in the weaknesses section\n- Question: Why is it reasonable to treat node features across the heterogenous types in the same latent space? For example, if one node controls temperature and another controls pressure, why should \"high temperature\" and \"high pressure\" features should have the same latent representation? Are setting nodes \"exchangeable\" in some sense?\n- Question: How should I interpret the numbers in the evaluation? Everything is below 50%. Is that supposed to be good?\n- Typo: Missing space between \"graphG\" in the second paragraph of Section 3.1", "broader_impact_concerns": "Nil", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)