NuGraph2: GNN for LArTPC Neutrino Reconstruction

• NuGraph2 is a graph neural network designed for low-level neutrino event reconstruction in LArTPCs, processing native hit data with a 3D-context-aware mechanism.
• It replaces conventional grid-based methods by modeling detector hits as graph nodes in heterogeneous planar and nexus subgraphs to achieve cross-view semantic consistency.
• Empirical results demonstrate high precision and recall in hit filtering and semantic labeling, underscoring its potential for physics-informed improvements in neutrino reconstruction.

Searching arXiv for NuGraph2 and closely related papers. NuGraph2 is a graph neural network (GNN) reconstruction engine for low-level neutrino event reconstruction in liquid-argon time projection chambers (LArTPCs), introduced as a response to the mismatch between regular-grid deep-learning architectures and sparse detector data represented natively as wire-plane hits in $wire \times time$ coordinates (Hewes et al., 2024). In its baseline form, NuGraph2 performs two hit-level tasks on simulated neutrino interactions in the MicroBooNE detector geometry: binary background filtering and semantic labeling, operating directly on detector observables across multiple 2D representations while using a 3D-context-aware mechanism to encourage consistency between these representations (Hewes et al., 2024). Subsequent work has treated NuGraph2 both as a platform for physics-informed improvements in semantic segmentation and as a case study for post-hoc explainability in scientific geometric deep learning (Grizzi et al., 12 Sep 2025, Voetberg et al., 12 Sep 2025).

1. Historical position and reconstruction setting

NuGraph2 is situated within a line of neutrino-reconstruction methods that seek alternatives to dense and sparse convolutional networks for LArTPC data. The central objection to dense CNNs is that they waste computation on empty space and require fixed-size images, while sparse CNNs, although more efficient, still require regular Euclidean gridding and then a return to the detector’s native representation (Hewes et al., 2024). NuGraph2 instead operates directly on detector hits as graph nodes, so the reconstruction is performed in the native domain of the observables (Hewes et al., 2024).

The detector context in the baseline study is MicroBooNE, a LArTPC with three wire planes, $U$, $V$, and $Y$, oriented at $+60^\circ$, $-60^\circ$, and $0^\circ$ relative to vertical (Hewes et al., 2024). Charged particles ionize the argon; electrons drift under an electric field and induce or deposit signals on the wire planes, with each plane providing a different 2D projection of the same 3D interaction in wire-time coordinates (Hewes et al., 2024). If the interaction time $t_0$ is known, the drift time gives the distance to the wire planes, and combining all three views enables 3D reconstruction (Hewes et al., 2024).

The baseline paper uses the MicroBooNE public simulated dataset, consisting of simulated $\nu_e$ and $\nu_\mu$ interactions in realistic detector geometry with real cosmic data overlaid, and considers only hits passing Pandora neutrino slice selection (Hewes et al., 2024). In the later semantic-segmentation study, the task is described specifically on the MicroBooNE public datasets, including the MicroBooNE BNB Inclusive Overlay Sample (No Wire Info) and the MicroBooNE BNB Electron Neutrino Overlay Sample (No Wire Info), again with simulated neutrino interactions overlaid on off-beam data collected with the MicroBooNE detector (Grizzi et al., 12 Sep 2025).

A core conceptual shift relative to earlier graph-based approaches is the move from link prediction to node classification. The baseline paper contrasts NuGraph2 with HEPTrkX-style link prediction, which exploits the layered, approximately radial structure of collider trackers, and with the authors’ earlier “NuGraph1,” which inherited more of that link-prediction mindset (Hewes et al., 2024). In LArTPC neutrino detectors there is no analogous geometric prior connecting detector structure to particle direction, so NuGraph2 instead performs node classification on detector-plane hits and introduces a dedicated mechanism to exchange context across the three 2D wire-plane projections through “nexus” nodes (Hewes et al., 2024). This shift from predicting edges to learning rich node embeddings with cross-view consistency is the baseline paper’s essential conceptual advance (Hewes et al., 2024).

2. Graph representation, node types, and detector observables

Each event in NuGraph2 is converted into a heterogeneous graph with three planar subgraphs, one for each wire plane, and an additional nexus subgraph (Hewes et al., 2024). On the detector planes, nodes correspond to Gaussian hit objects reconstructed from wire pulses (Hewes et al., 2024). The standard planar-node input feature vector has four components: wire index, time coordinate, Gaussian pulse integral, and Gaussian pulse RMS width (Hewes et al., 2024). In the semantic-segmentation extension paper, these same four features are denoted as $U$0, $U$1, $U$2, and $U$3, and are described as the original input feature vector for planar nodes in standard NuGraph2 (Grizzi et al., 12 Sep 2025).

Within each wire plane, edges are defined using Delaunay triangulation on the $U$4 coordinates (Hewes et al., 2024). The baseline paper reports that $U$5-nearest-neighbor and radius graphs were also tested, but Delaunay triangulation was both more efficient and more performant (Hewes et al., 2024). The practical consequence is that Delaunay produces a graph with both local and some longer-range edges, helping preserve connectivity when detector effects create apparent gaps, such as dead wires, or when physics creates disconnected but related structures such as sparse shower fragments (Hewes et al., 2024).

Cross-view information is introduced through nexus nodes generated from “spacepoints” produced by the upstream SpacePointSolver algorithm, which groups corresponding 2D hits across planes (Hewes et al., 2024). These nexus nodes are virtual: they do not carry their own input features and they have no edges among themselves (Hewes et al., 2024). Their only role is to connect corresponding hits from different planes, and by construction a nexus node is connected to at most one planar hit from each plane (Hewes et al., 2024). The result is a genuinely heterogeneous graph in which planar hit nodes live in three separate 2D subgraphs and nexus nodes act as cross-plane anchors encoding tentative 3D correspondence (Hewes et al., 2024).

The semantic-segmentation paper restates this representation in closely related terms: each hit in one of the wire planes is a planar node, and information is exchanged both within a plane and across planes (Grizzi et al., 12 Sep 2025). It also describes the graph as having two node types, planar nodes and nexus nodes, with the three planes coupled through nexus nodes that provide inter-plane communication (Grizzi et al., 12 Sep 2025). This paper further emphasizes that node connectivity is constructed in the $U$6 plane for the three different planes $U$7, $U$8, and $U$9 (Grizzi et al., 12 Sep 2025).

Two prediction tasks define the baseline output space. The filter decoder performs binary classification of hits into signal or background, identifying whether a hit belongs to the primary neutrino interaction rather than cosmic or other overlaid activity (Hewes et al., 2024). The semantic decoder assigns each signal hit to one of five physics-motivated categories: MIP, HIP, shower, Michel electron, and diffuse (Hewes et al., 2024). The same five semantic classes are used in the later segmentation and explainability studies (Grizzi et al., 12 Sep 2025, Voetberg et al., 12 Sep 2025).

3. Core architecture and message-passing mechanism

NuGraph2 has three stages: an encoder, an iterative message-passing engine, and task-specific decoders (Hewes et al., 2024). A key design feature is the use of a categorical embedding indexed by semantic class. If there are $V$0 nodes, $V$1 semantic categories, and $V$2 latent features per category, then hidden tensors have shape

$V$3

This means that each node carries a separate latent feature vector for each semantic class, allowing the network to maintain class-specific hypotheses internally rather than collapsing everything into a single shared embedding too early (Hewes et al., 2024).

The encoder begins with the raw node feature tensor $V$4 and repeats it across the category dimension to produce

$V$5

followed by a categorical linear MLP: $V$6 The baseline paper characterizes the categorical-linear mechanism as using separate linear maps per category, equivalent to grouped linear convolutions, thereby reducing parameter count by a factor of $V$7 relative to a comparable dense mixing and enforcing a form of conditional independence among category channels (Hewes et al., 2024).

The message-passing engine is iterative, with each iteration composed of a planar block and a nexus block (Hewes et al., 2024). At iteration $V$8, the current hidden state $V$9 is concatenated with the replicated original input $Y$0 to form $Y$1, preserving an explicit shortcut from the original detector observables into each iteration (Hewes et al., 2024). Within each detector plane, the planar block computes categorical cross-attention scores on every planar edge,

$Y$2

forms messages

$Y$3

aggregates them by sum pooling,

$Y$4

and updates the planar state through

$Y$5

The paper describes $Y$6 as a categorical cross-attention block in which an MLP reduces the categorywise hidden representation to one scalar per category and applies a softmax across the category dimension (Hewes et al., 2024).

The nexus block is the 3D-context-aware mechanism. Its function is to break degeneracies inherent in any individual 2D projection, such as the ambiguity between a long minimum-ionizing track at shallow angle to one wire plane and a shorter, apparently more highly ionizing object in that single view (Hewes et al., 2024). Planar features are first lifted into nexus space,

$Y$7

then aggregated by concatenation across planes, with missing views set to zero, and processed via

$Y$8

The fused nexus features are then sent back to planar nodes by computing cross-attention coefficients

$Y$9

forming nexus-to-plane messages

$+60^\circ$0

aggregating them with mean pooling,

$+60^\circ$1

and updating the node state through

$+60^\circ$2

The baseline paper explicitly notes that mean pooling in the nexus-to-planar phase outperforms the sum pooling used in the planar phase (Hewes et al., 2024).

The decoders are task-specific. For background filtering, the final categorical tensor is flattened from $+60^\circ$3 to $+60^\circ$4, passed through a linear layer, and then through a sigmoid to obtain a binary probability per node (Hewes et al., 2024). For semantic labeling, the categorical structure is retained: each category’s hidden features are reduced to a single logit and a softmax over categories yields class probabilities per node (Hewes et al., 2024). At inference, the filter task uses a threshold of $+60^\circ$5 in the main reported results, and the semantic task uses the argmax class (Hewes et al., 2024).

The baseline study describes the architecture as using a “multi-head attention message-passing mechanism,” but does not report an explicit transformer-style head count (Hewes et al., 2024). It does state that every linear convolution layer is followed immediately by an activation function; softmax and sigmoid are used for categorical and binary outputs, and all other convolutions use $+60^\circ$6, which outperformed ReLU and Mish in both stability and performance (Hewes et al., 2024).

4. Optimization, empirical performance, and deployment characteristics

Training uses PyTorch, PyTorch Geometric, and PyTorch Lightning (Hewes et al., 2024). Optimization uses AdamW with learning rate $+60^\circ$7 and a OneCycleLR schedule for 80 epochs (Hewes et al., 2024). The filter loss is binary cross-entropy, while the semantic loss is Recall Loss, chosen because the dataset is class-imbalanced and because inverse-frequency weighted categorical cross-entropy over-optimized minority recall at the expense of precision, while focal loss failed to learn minority classes adequately (Hewes et al., 2024). The two task losses are combined using the uncertainty-based multitask weighting scheme of Kendall et al. (Hewes et al., 2024).

The main reported results are hit-level recall and precision. For filtering, using a threshold of $+60^\circ$8, the model achieves recall $+60^\circ$9 and precision $-60^\circ$0, corresponding to identifying hits associated with the primary interaction with $-60^\circ$1 efficiency (Hewes et al., 2024). For semantic labeling, assigning the maximum-probability class to each hit, the model achieves overall recall and precision $-60^\circ$2, described as $-60^\circ$3 efficiency/purity (Hewes et al., 2024). The equality of precision and recall is attributed to the chosen loss-weighting scheme (Hewes et al., 2024).

The semantic confusion structure is physically interpretable rather than random. The best-performing class is MIP, the most abundant category in the dataset, while the weakest is Michel, the rarest class and one with low hit multiplicity (Hewes et al., 2024). HIP and MIP are often confused because both are track-like and differ mainly in stopping power and length; the baseline paper reports that $-60^\circ$4 of true HIP hits are predicted as MIP (Hewes et al., 2024). It also reports that $-60^\circ$5 and $-60^\circ$6 of true Michel hits are misclassified as shower-like and diffuse, respectively, and that $-60^\circ$7 and $-60^\circ$8 of true diffuse hits are misclassified as shower-like and Michel-like (Hewes et al., 2024). A further asymmetry arises from class balancing: only $-60^\circ$9 of true MIP hits are misclassified as Michel, but because MIP dominates the dataset, those errors make up $0^\circ$0 of all Michel predictions; by contrast, $0^\circ$1 of Michel hits are misclassified as MIP, but they account for only $0^\circ$2 of predicted MIP hits (Hewes et al., 2024).

A central empirical result concerns cross-view consistency, which directly tests the nexus mechanism. The baseline paper defines semantic consistency as the fraction of nexus nodes for which all connected planar nodes share the same semantic label (Hewes et al., 2024). Ground-truth labels have a consistency of $0^\circ$3, NuGraph2 predictions achieve $0^\circ$4, and a planar-only ablation in which the nexus phase is removed reaches only $0^\circ$5 (Hewes et al., 2024). This is the clearest direct evidence that the 3D-context-aware nexus mechanism materially improves agreement among the three 2D views (Hewes et al., 2024).

The paper also provides a width study. The nominal model uses 64 planar features and 16 nexus features, yielding filter recall $0^\circ$6, semantic recall $0^\circ$7, and training GPU memory $0^\circ$8 GB (Hewes et al., 2024). Reducing planar width to 4 drops filter recall to $0^\circ$9 and semantic recall to $t_0$0 while reducing memory to $t_0$1 GB; increasing planar width to 128 gives only marginal gain, with filter recall $t_0$2, semantic recall $t_0$3, and memory $t_0$4 GB (Hewes et al., 2024). Varying nexus width from 4 to 32 changes semantic recall only from $t_0$5 to $t_0$6, supporting the view that most representational burden sits in the per-plane message passing (Hewes et al., 2024).

Inference characteristics are also reported explicitly. Raw model inference takes $t_0$7 on CPU and $t_0$8 on GPU for sufficiently large batch sizes (Hewes et al., 2024). A TorchScript-compiled CPU implementation integrated into the LArSoft framework achieves $t_0$9, including both graph construction and inference, with peak CPU memory $\nu_e$0 (Hewes et al., 2024). These timings place NuGraph2 in a regime practical for offline reconstruction pipelines; a plausible implication is that the architecture was designed with deployment constraints in mind, although the paper does not explicitly claim trigger-level use (Hewes et al., 2024).

5. Physics-informed modifications and diagnostic studies

A later study examines NuGraph2 specifically as a hit-level semantic-segmentation architecture and focuses on the hardest and most underrepresented class in the benchmark, Michel electrons (Grizzi et al., 12 Sep 2025). This paper identifies three limitations of vanilla NuGraph2: weak Michel performance, latent-space overlap especially between Michel and MIP, and the expressivity constraints of standard message-passing GNNs, described as limited to the expressive power of the 1-Weisfeiler-Leman test (Grizzi et al., 12 Sep 2025). It also emphasizes a structural limitation: NuGraph2 predicts only hit labels and does not explicitly represent particles or whole events internally, which makes particle-level or event-level constraints awkward to impose (Grizzi et al., 12 Sep 2025).

The principal successful intervention is a context-aware feature extension for planar nodes. The baseline four input features $\nu_e$1 are augmented with four physics-motivated features: node degree, shortest edge length or nearest-neighbor distance in the $\nu_e$2 plane, $\nu_e$3, and $\nu_e$4 (Grizzi et al., 12 Sep 2025). The double-difference continuity features are defined by

$\nu_e$5

where $\nu_e$6 is either the wire coordinate or the time coordinate and $\nu_e$7 are the two nearest neighbors in the $\nu_e$8 plane (Grizzi et al., 12 Sep 2025). The paper argues that these quantities are approximately zero along straight tracks or segments of fixed direction, encoding local track continuity directly in the input representation (Grizzi et al., 12 Sep 2025).

This extension changes the pre-message-passing representation only from 132 to 136 dimensions, since in standard NuGraph2 the four raw features are encoded to a hidden vector of size 128 and concatenated back with the original four features to form 132 dimensions (Grizzi et al., 12 Sep 2025). The gains are therefore attributed to improved inductive bias rather than substantial capacity increase (Grizzi et al., 12 Sep 2025). In the reported results, feature extension is the only tested modification that improves all semantic classes and gives the best Michel performance: Michel precision increases from $\nu_e$9 to $\nu_\mu$0, and Michel recall from $\nu_\mu$1 to $\nu_\mu$2 (Grizzi et al., 12 Sep 2025).

Two other intervention families are reported as unsuccessful. The first adds auxiliary decoders intended to exploit class-level correlations, including a binary Michel decoder at node level, a graph-level Michel counter, and a full class-distribution decoder (Grizzi et al., 12 Sep 2025). Although the class-distribution decoder performs best among these variants, none surpasses the baseline semantic segmentation; the “Count Decoder” condition lowers Michel precision from $\nu_\mu$3 to $\nu_\mu$4 and Michel recall from $\nu_\mu$5 to $\nu_\mu$6 (Grizzi et al., 12 Sep 2025). The authors attribute this chiefly to optimization conflict, stating that “the gradient directions from the count and semantic loss components did not align very well” (Grizzi et al., 12 Sep 2025).

The second unsuccessful intervention introduces Michel-energy regularization motivated by the fact that Michel electrons arise from muon decay at rest (Grizzi et al., 12 Sep 2025). Since deposited energy is not directly available at hit level, the hit waveform integral is used as a proxy (Grizzi et al., 12 Sep 2025). One explicit regularization form is

$\nu_\mu$7

with $\nu_\mu$8 tested in the range 90 to 160 MeV (Grizzi et al., 12 Sep 2025). The paper also considers a Langauss-distribution penalty and a simulation-derived distribution penalty, with the Langauss fit applied only for

$\nu_\mu$9

because the peak near $U$00 MeV is treated as a simulation artifact (Grizzi et al., 12 Sep 2025). These regularizers do not improve Michel labeling; in the “Michel Reg.” condition, Michel precision changes from $U$01 to $U$02 and recall from $U$03 to $U$04 (Grizzi et al., 12 Sep 2025). The paper attributes this to excessive conservatism, the noisy relation between integral and true deposited energy, and the mismatch between a particle-level prior and a hit-level architecture (Grizzi et al., 12 Sep 2025).

The overall conclusion of this extension study is that, for NuGraph2, representation-level physics context is more effective than auxiliary higher-level tasks or Michel-specific regularization (Grizzi et al., 12 Sep 2025). A plausible implication is that NuGraph2’s strongest mode of improvement lies in better hit-level inductive bias rather than in losses defined at particle or event granularity.

6. Explainability, limitations, and research outlook

A separate explainability study treats NuGraph2 as a scientific ML system requiring post-hoc analysis beyond predictive accuracy (Voetberg et al., 12 Sep 2025). It adapts GNNExplainer to the heterogeneous NuGraph2 graph by jointly optimizing six masks, one for each planar graph and one for each planar-to-nexus connection set, with the entropy-based objective

$U$05

The paper also evaluates explanations using

$U$06

and

$U$07

interpreting lower Fidelity$U$08 and higher Fidelity$U$09 as preferable (Voetberg et al., 12 Sep 2025).

On selected failure cases, however, adapted GNNExplainer produces poor explanation-quality results. For a showcased event, the reported average metrics over the three planes are $U$10 and $U$11 for the base GNNExplainer, with similarly uninformative values for class-targeted and correctness-targeted variants (Voetberg et al., 12 Sep 2025). The authors interpret this to mean that the method effectively deems almost everything important, so mask-based local subgraph extraction fails to produce concise explanations for NuGraph2 (Voetberg et al., 12 Sep 2025).

The explainability paper connects this failure to edge redundancy and investigates the issue through graph rewiring and pruning. Several manipulations are tested, but only degree-capping preserves performance well enough to analyze in detail (Voetberg et al., 12 Sep 2025). Limiting maximum degree to 20 produces no significant difference relative to baseline confusion matrices, and limiting it to 12 causes only a very small degradation (Voetberg et al., 12 Sep 2025). For $U$12, the paper reports that in some graphs as many as 800 edges are pruned, roughly 30% of nodes had degree greater than 12, in many graphs the prune fraction is below 5%, and for most graphs about 13% of edges were removed (Voetberg et al., 12 Sep 2025). The paper’s principal finding here is that NuGraph2’s edge structure contains significant redundancy, which in turn helps explain why edge-mask explanation methods are diffuse and uninformative (Voetberg et al., 12 Sep 2025).

The same study probes the latent space through PCA and silhouette analysis at different network stages, specifically after the encoder and after message-passing steps 1, 3, and 5 (Voetberg et al., 12 Sep 2025). The mean silhouette scores show that clustering quality often drops immediately after the first message-passing step but improves by later steps, especially by step 5, for HIP, MIP, shower, diffuse, and background (Voetberg et al., 12 Sep 2025). Michel is the exception: its silhouette score declines monotonically from 0.0098 at encoder to 0.0034 at step 5 (Voetberg et al., 12 Sep 2025). The paper interprets this as support for five message-passing iterations while also reinforcing the conclusion that Michel electrons remain poorly encoded in latent space, likely due to class imbalance (Voetberg et al., 12 Sep 2025).

The most novel explainability tool in that paper is a family of post-hoc decoder probes that attach single-layer fully connected classifiers to intermediate embeddings and test whether specific concepts are linearly accessible (Voetberg et al., 12 Sep 2025). The concepts include track-like particle detection, track-like particle separation, and Michel-only accuracy, using probe losses such as

$U$13

and

$U$14

These probes suggest that coarse track recognition is learned quickly, finer HIP–MIP separation is harder but improves with depth, and Michel remains difficult throughout (Voetberg et al., 12 Sep 2025).

Across the baseline, improvement, and explainability studies, several limitations recur. NuGraph2 is evaluated on simulation with real cosmic overlays rather than fully on detector data, so simulation-to-data transfer remains open (Hewes et al., 2024). The quality of cross-plane reasoning depends on upstream SpacePointSolver correspondences (Hewes et al., 2024). High-multiplicity topologies remain difficult, particularly when projections overlap or sparse electromagnetic fragments resemble diffuse activity (Hewes et al., 2024). The hit-level architecture also limits the natural incorporation of particle-level or event-level priors, which the semantic-segmentation paper identifies as a main reason why auxiliary decoders and Michel-energy regularization underperform (Grizzi et al., 12 Sep 2025).

The literature therefore presents NuGraph2 as both a successful reconstruction engine and an architectural waypoint. The baseline paper describes it as a general-purpose solution for particle reconstruction in neutrino physics with a core convolution engine that can support tasks beyond filtering and semantic labeling (Hewes et al., 2024). Later work suggests that future hierarchical architectures such as NuGraph3, with explicit particle- and event-level reasoning, would provide a more natural setting for advanced decoders and physics-based regularization (Grizzi et al., 12 Sep 2025). This suggests that NuGraph2’s lasting significance lies not only in its reported performance, but also in establishing a graph-native, multi-view, 3D-context-aware formulation for LArTPC reconstruction against which subsequent hierarchical and interpretable neutrino GNN systems can be defined.