Cluster Reconstruction in Electromagnetic Calorimeters Using Machine Learning Methods

Kalina Dimitrova; Peicho Petkov; Ruslan Nastaev; Venelin Kozhuharov

REVIEW 5 major objections 5 minor 1 cited by

Cluster Reconstruction in Electromagnetic Calorimeters Using Machine Learning Methods

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A modified convolutional autoencoder trained on simulated energy matrices reconstructs photon impact points in a segmented BGO calorimeter to within 1 cm and yields a near-zero mean energy bias.

desk verdict A credible simulation-only proof-of-concept for CNN calorimeter clustering, but the reported metrics are conditional on a generous matching window and there is no baseline. read the letter →

arxiv 2505.24740 v1 pith:K223YEPJ submitted 2025-05-30 physics.ins-det

Kalina Dimitrova , Venelin Kozhuharov , Ruslan Nastaev , Peicho Petkov This is my paper

classification physics.ins-det PACS 29.40.Vj

keywords convolutionalneuralnetworkautoencoderelectromagneticcalorimeterclusterreconstructionBGOcrystalimpactpointenergyMonteCarlosimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to show that a convolutional autoencoder, trained on labeled Monte Carlo events, can reconstruct individual photon hits in a segmented electromagnetic calorimeter directly from the pattern of energy deposited in its crystals. Unlike a standard autoencoder, the network is not asked to reproduce its input; it is trained to output an upsampled grid in which only the bin at each true photon impact point carries that photon's energy. On a held-out simulated dataset, most predicted impact points fall within 1 cm of the true positions, and the deeper of the two models reconstructs energies with a mean bias of 3.15 MeV and a spread of 75.46 MeV. The authors see this as a step toward reliable automatic separation of overlapping showers, which is the main obstacle to accurate event reconstruction in high-rate calorimeter data.

What carries the argument

The carrying object is a convolutional autoencoder: an encoder that compresses the 29-by-29 energy map through successive 2D convolution layers, and a decoder of transposed convolution layers that expands it back. The modification that makes reconstruction work is the use of labels as the training target rather than the input, together with two upsampling layers that produce a 116-by-116 output. This upsampling is what gives sub-crystal spatial resolution. A final post-processing step scans the output with a 5-by-5 window, merges neighboring non-zero values into the local maximum, and reads off one position and one energy per recognized cluster. The optimization minimizes the chi-squared difference between the label array and the predicted array.

What would settle it

A beam test that sends photons of known energy at known positions into a 29-by-29 BGO crystal matrix would settle it: if the network's predicted impact points are systematically off by more than 1 cm, or if the mean energy residual moves far from 3 MeV, the simulation-to-experiment transfer fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that a modified CNN autoencoder can map the 29-by-29 matrix of accumulated crystal energies directly to the positions and energies of all photons that hit the detector during an event. The training target is a 116-by-116 array obtained by dividing each 2 cm by 2 cm crystal into 0.5 cm by 0.5 cm bins and placing each photon's energy in the bin that contains its true impact point. At inference, the position of the maximum value in each predicted cluster is read as the impact point, and a 5-by-5 summation window around that maximum gives the cluster energy. On independent simulated events with up to 50 photons per event, the method places most reconstructed clusters within 1 cm of the true hit point, and the deeper model achieves an energy residual with mean 3.15 MeV and standard deviation 75.46 MeV, close to zero bias.

Load-bearing premise

The load-bearing premise is that the simulated detector behaves like the real BGO calorimeter, so the sub-centimeter positions and near-zero energy bias learned from simulated showers will survive contact with experimental data.

Editorial extensions

If this is right

A single trained network could replace hand-written clustering and position-fitting code for calorimeters of this type.
The near-zero mean energy bias of the deeper model means reconstructed energies need little or no additional offset correction after the network output.
Because each crystal is divided into 0.5 cm bins in the labels, position precision is tied to the label bin size rather than to the physical crystal size.
The method targets high-occupancy events with many overlapping showers, where conventional cluster separation is most likely to fail.
Deeper architectures with dropout improve energy reconstruction without changing position reconstruction, so the two tasks can be tuned separately.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: a stress test with showers arriving closer together than one crystal width would reveal the actual two-photon separation limit, which the paper leaves for future work.
Editorial inference: the same label-up-sampling idea could be applied to other segmented detectors whose readout is a 2D grid, such as hadron calorimeters or imaging time-projection chambers.
Editorial inference: the small systematic x-coordinate bias of about 2 mm suggests a shift in the encoder's feature maps; training with mirrored or rotated events could show whether it is a simulation artifact or a model bias.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

I've read the paper and the stress-test note. I think the note is right: the reported accuracy is conditional on a 5x5-bin matching window, and the missing match efficiency and fake rate are the biggest holes.

What's actually new: the group applied their labeled-autoencoder approach, previously used for 1D pulse traces, to 2D shower clusters in a BGO calorimeter. The idea is simple and legitimate: upsample the labels to 0.5 cm bins, train a CNN to map crystal energies to a sparse position-energy map, then post-process with a moving 5x5 sum. The main results—sub-centimeter position residuals and a near-zero mean energy bias for one of the two architectures—are believable as far as the simulation goes. The comparison between a 4-layer and a 5-layer encoder is a concrete check, and the paper is honestly written: it doesn't pretend cluster separation is solved, and it flags mismatched events as a possible cause of large energy tails.

That said, the soft spots are real but not fatal. First, the matching criterion is generous: any non-zero prediction inside a 2.5x2.5 cm window counts as a match, and all position/energy distributions are built only from matched clusters. Without the match efficiency and fake rate, you can't tell how often the method actually finds a photon versus hallucinating or merging nearby showers. This is internal to the analysis, so it matters even assuming perfect simulation. Second, there is no baseline—no energy-weighted centroid, no nearest-neighbor clustering, no classical algorithm. For a reconstruction paper that is a big gap, because the reader can't judge whether the CNN has any real advantage. Third, there are no error bars from repeated training runs and no code or data release, so the stability of the sigma values is unknown. Fourth, simulation-to-real transfer is untested, which is a standard caveat for this kind of study but still worth stating. Also, the abstract claims the method can be applied where separation of overlapping signals is key, but the paper itself says that is future work; that overreach should be fixed.

Net: this is a modest, honest contribution that could be made solid with a moderately sized revision. It deserves peer review—a referee would give the authors a clear checklist—and I'd expect it to be acceptable after adding the missing efficiency numbers and at least one classical comparison. I don't think it's important enough to cite in my own work unless I happen to work on calorimeter clustering, but I'd bring it to a reading group as an example of how evaluation choices can shape ML reconstruction claims.

Referee Report

5 major / 5 minor

Summary. The paper applies convolutional autoencoders to the reconstruction of photon clusters in a simulated 29×29 BGO electromagnetic calorimeter. The network is trained on GEANT4-simulated events with upsampled sparse labels (116×116 bins) that encode photon impact positions and energies, and the output is post-processed by summing 5×5 windows around local maxima. Two model architectures are compared on an independent simulated test set, and the paper reports position residuals (sub-centimeter for most matched clusters) and energy residuals (σ ≈ 75 MeV; mean bias 3.15 MeV for Model 2). The authors claim that the method can reconstruct impact points within the same segment as the true position and suggest applicability to separating overlapping signals.

Significance. If the claims were fully established, the method would be a useful ML-based alternative to classical clustering for segmented calorimeters, particularly at high occupancy where overlapping showers are an issue. The paper has clear strengths: it uses a well-defined supervised training setup with sparse labels, provides architectural details sufficient for reproduction, and reports residuals on a held-out simulated sample. However, the reported metrics are conditioned on a permissive 5×5-bin matching window, and the paper does not report cluster-level efficiency, fake rate, or any baseline comparison. The significance as currently demonstrated is therefore limited to a proof-of-principle on simulated data, and the abstract overstates the demonstrated capability on overlapping signals.

major comments (5)

[Section 3, matching criterion] The paper defines a match as any non-zero predicted value inside a 5×5-bin window around the true hit, and all reported Δr_i and ΔE_i distributions are computed only for these matched clusters. The paper never states the fraction of true clusters that are matched, the number of predicted clusters with no true match, or the number of true clusters that compete for one predicted peak. Since the 5×5 window (2.5×2.5 cm) is much larger than the claimed sub-centimeter precision, the headline accuracy is conditional on a permissive association criterion and may not hold for all input photons. Please report cluster-level efficiency, fake rate, and a multiplicity confusion matrix, and use an assignment procedure that enforces one-to-one matching.
[Abstract and Section 4] The abstract states that the method 'can be applied' in cases where separation of overlapping signals is key, but Section 4 explicitly defers cluster-separation studies to future work. This is an internal inconsistency: the central advertised application is not demonstrated. Either add quantitative two-photon separation metrics (e.g., resolution as a function of separation distance) or soften the abstract's claim to match the presented evidence.
[Section 3, energy results] The comparison between Model 1 (ΔE mean 42.39 MeV) and Model 2 (ΔE mean 3.15 MeV) is made from single test-set evaluations without error bars, bootstrap intervals, or repeated training runs. Neural network training is stochastic, and architecture comparisons based on one run can be misleading. The claim that Model 2 shows much better energy reconstruction needs run-to-run variation or confidence intervals on the reported means and widths.
[Section 3, no baseline comparison] No comparison is made to a classical clustering algorithm, such as a local-maximum finder with a fixed energy-sum window, which would be the natural baseline for this task. Without such a baseline, the reader cannot judge whether the reported sub-centimeter position accuracy and 75 MeV energy width represent an improvement over existing methods or simply a re-implementation of a standard approach. Please add a comparison to a non-ML reference algorithm using the same matching and evaluation protocol.
[Section 2, simulation-only validation] The entire method is developed and evaluated on GEANT4-simulated data, and the paper does not discuss how simulation-to-detector differences (shower shape, noise, thresholds, calibration) would affect the reported residuals. This is a limitation for a detector-reconstruction paper, though not a fatal one if framed correctly. Please add an explicit statement that the results are simulation-only proof-of-principle and discuss the main sources of systematic uncertainty that would need to be addressed before application to real data.

minor comments (5)

[Section 2, Eq. (4)] The post-processing algorithm is not fully specified when two predicted local maxima fall within the same 5×5 window or when windows overlap; please state the order in which maxima are processed and how energy assigned to one cluster is removed from consideration for subsequent clusters.
[Section 3] The paper does not state the size of the independent test set, the number of photons per event in that set, or how the test set was generated relative to the training set; please provide these details for reproducibility.
[Section 3] The notation Δ1x, Δ2x, and σ2(Δy) is introduced without explicit definition, and the units are missing for σ2(Δy) = 0.518; please standardize the notation and include units throughout.
[Section 2, simulation setup] The GEANT4 simulation is described only as producing electromagnetic showers; please specify the physics list, the energy threshold per crystal, and any noise or digitization effects, since these directly affect the realism of the training data.
[General] There are several typographical and formatting issues, including the author name 'V enelin' with an unwanted space and the figure caption 'Right:. ' in Figure 3; a careful proofread is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: supervised ML training and held-out simulated evaluation are self-contained, and the cited prior work is not load-bearing.

full rationale

The paper's central derivation is a standard supervised machine-learning pipeline: a GEANT4 simulation generates labeled training data (input crystal energies epsilon_{k,l}; target one-hot-like labels with particle energies placed at true hit bins), a CNN autoencoder is trained by minimizing chi^2 over (E_{k,l} - E^pred_{k,l})^2, and performance is evaluated on an independent simulated test set by comparing predicted and true positions/energies. There is no step in which a fitted parameter is renamed as a prediction, no equation in which the output is defined in terms of the input by construction, and no uniqueness theorem or ansatz smuggled in via citation. The only self-citation is reference [8], mentioned as 'A similar approach [8] is already developed for the case of time series data reconstruction,' which is descriptive and not load-bearing for the reported cluster reconstruction results. The caveats noted by the reader and skeptic (simulation-only validation, conditional metrics after a permissive 5x5 matching window, and unstated match/fake rates) are legitimate correctness and robustness concerns about generalizability and interpretation, but they do not make the derivation circular: the network is evaluated against held-out labels that are independent of the training fit, and the reported errors are measured quantities rather than quantities forced by the loss function. The absence of reported cluster identification efficiency and fake rates weakens the strength of the headline claims but does not reduce any claimed prediction to an input by definition. Therefore the appropriate circularity score is 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method's performance rests on several hand-chosen parameters (upsampling factor, post-processing window, architecture depth, simulation distributions) and on the unvalidated assumption that the GEANT4 simulation and the point-like label representation capture the real detector physics. No new physical entities are introduced; the only invented artifact is the post-processing window, which is a heuristic rather than an entity.

free parameters (5)

Post-processing window size = 5 by 5 bins (2.5 x 2.5 cm)
Chosen by hand to sum predicted cluster energy; no optimization or robustness check is reported.
Upsampling factor = 4x per axis (0.5 cm bins)
Chosen to improve spatial resolution; no study of alternative resolutions is given.
Model architecture hyperparameters = Model 1: 4+4 conv layers, no dropout; Model 2: 5+5 layers, dropout 0.2
Only two architectures are tested; filter counts, kernel sizes, and training hyperparameters are not specified.
Simulated particle multiplicity distribution = Uniform between 0 and 50
Defines the test conditions; performance may depend on occupancy, but only this one distribution is used.
Simulated photon energy distribution = Gaussian, mean 200 MeV, sigma 200 MeV
Defines the energy range of the evaluation; the quoted 75 MeV energy spread is specific to this distribution.

assumptions (4)

domain assumption GEANT4 simulation faithfully models the BGO calorimeter response
Section 2 states all training and validation use simulated data; if the simulation is unfaithful, the reported precision does not transfer to real detectors.
domain assumption The label representation, placing the full photon energy in a single upsampled bin, is a valid ground truth
Section 2 defines labels this way; it assumes the incident energy can be attributed to a point rather than being spread over the shower.
ad hoc to paper The 5x5 moving-window sum in Eq. (4) correctly aggregates all energy belonging to one photon and separates adjacent clusters
No validation is given that the window matches the lateral shower size or that the greedy merging avoids split or merged clusters.
domain assumption A convolutional autoencoder with labeled outputs can disentangle overlapping showers
This is the paper's central working hypothesis; no prior or theoretical argument beyond the reported test-set performance supports it.

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Cite this review

Pith. "Pith review of Cluster Reconstruction in Electromagnetic Calorimeters Using Machine Learning Methods." pith.science (2026). https://pith.science/paper/K223YEPJ

@misc{pith2026250524740,
  author       = {Pith},
  title        = {Pith review of: Cluster Reconstruction in Electromagnetic Calorimeters Using Machine Learning Methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K223YEPJ}},
  note         = {Machine review of arXiv:2505.24740}
}

read the original abstract

Machine-learning-based methods can be developed for the reconstruction of clusters in segmented detectors for high energy physics experiments. Convolutional neural networks with autoencoder architecture trained on labeled data from a simulated dataset reconstruct events by providing information about the hit point and energy of each particle that has entered the detector. The correct reconstruction of the positionand the energy of the incident particles is crucial for the accurate events reconstruction. The presented method shows the ability to reconstruct the impact point within the same segment as the true position and determines the particle energy with good precision. It can be applied in a wide range of cases of event reconstruction where the good separation of overlapping signals plays a key role in the data analysis.

Figures

Figures reproduced from arXiv: 2505.24740 by the authors.

**Figure 1.** To perform event reconstruction and evaluate its precision we developed several CNNs with autoencoder architecture. All models have similar architectures, consisting of an encoder and a decoder part. The encoder consists of several 2D convolution layers with a decreasing number of filters with a decreasing kernel size. Dropout layers are used between the convolution layers. The decoder features a mirrored structur… view at source ↗

**Figure 1.** Up, left: A simulated event in a 29×29 crystal calorimeter containing several clusters created by photons entering the detector. The value for each crystal represents the energy accumulated in the corresponding channel for the whole duration of the event. Up, right: The label, assigned to the event. Each crystal is divided in 16 smaller bins. The ones where a photon has hit the detector have the value of the photon’… view at source ↗

**Figure 2.** Structure of the hidden layers in the two tested models. Both models consist of an encoder and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: Difference between the true and the predicted position for all found clusters in the test dataset. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 4.** Figure 4: Difference between the true and the predicted values for the energy of the particles the identified [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Antineutron reconstruction in electromagnetic calorimeters with mixed-representation learning
hep-ex 2026-07 accept novelty 7.0 of 10

MrCAL jointly reconstructs antineutron identity, direction and momentum from ECAL readouts alone, improving direction precision by up to 96% and achieving ~17% momentum resolution at 1 GeV/c.

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages · cited by 1 Pith paper

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

and Raspereza, A

Morgunov, V. and Raspereza, A. (2004) Novel 3-D clustering algorithm and two particle separation with tile HCAL. Contribution to: International Conference on Linear Colliders (LCWS 04) 431-436

work page 2004

[2] [2]

(2017) A better autoencoder for image: Convolutional autoencoder In Proceedings of the ICONIP17-DCEC, Guangzhou, China, 14--18 October 2017

Zhang, Y. (2017) A better autoencoder for image: Convolutional autoencoder In Proceedings of the ICONIP17-DCEC, Guangzhou, China, 14--18 October 2017

work page 2017

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(2015) TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems

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(2015) Keras

Chollet, F. (2015) Keras. Available online: https://keras.io

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(1997) ROOT — An object oriented data analysis framework

Brun, R.; Rademakers, F. (1997) ROOT — An object oriented data analysis framework. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 389 81--86

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(2003) GEANT4--a simulation toolkit Nucl

Agostinelli, S., et al. (2003) GEANT4--a simulation toolkit Nucl. Instrum. Meth. A 506 250--303

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