hep-exSep 24, 2024
SaveDenoising Graph Super-Resolution towards Improved Collider Event Reconstruction
Organizations: Weizmann Institute of Science, Israel
Abstract
In preparation for Higgs factories and energy-frontier facilities, future colliders are moving toward high-granularity calorimeters to improve reconstruction quality. However, the cost and construction complexity of such detectors is substantial, making software-based approaches like superresolution an attractive complementary tool. This study explores integrating superresolution techniques into an LHC-like reconstruction pipeline to effectively enhance calorimeter granularity and suppress noise. We find that this software preprocessing step significantly improves reconstruction quality at fixed detector granularity, narrowing the performance gap to a finer calorimeter without closing it. To demonstrate its impact, we propose a novel transformer-based particle-flow model that offers improved particle reconstruction quality and interpretability. Our results serve as a proof of concept, demonstrating the potential of superresolution to enhance reconstruction in collider environments.
Figures & tables
| Layer | ECAL1 | ECAL2 | ECAL3 | |
|---|---|---|---|---|
| [MeV] | (Low) | 13 | 34 | 41 |
| segmentation | (Low) | 128 | 128 | 64 |
| single electron | (High) | 256 | 256 | 128 |
| segmentation | (Low) | 64 | 64 | 32 |
| multiparticle | (High) | 256 | 256 | 128 |
Table 1: Noise levels and granularity of the three electromagnetic calorimeter layers in both low and high resolution. The noise is only included for the low-granularity cells.
Figure 1: Phoenix event display [ 28 ] of one electron and two photons in cocoa , demonstrating the dataset creation procedure. Here we see (a) the truth high-resolution configuration, (b) the truth low-resolution configuration, and (c) the measured low-resolution configuration which also contains noise.
Figure 2: Creation of high-resolution cell in our approach. Each low-resolution cell is split in and by the superresolution factor and , respectively. They get their new angular coordinates and the parent low-resolution energy is copied to serve as the conditional inputs. Here, we see the procedure for and . Each cell is a node in the graph, but, for illustrative purpose, we are denoting them as images.
Figure 3: The superresolution architecture. indicates concatenation.
| Hyperparameter | |
| Batch size | 25 |
| Optimizer | AdamW [ 33 ] |
| Learning rate | 0.001 |
| Number of epochs | 100 |
| Number of time steps | 25 |
| Number of transformer layers | 4 |
Table 2: Hyperparameters used in the superresolution model.
Figure 4: The PFlow – architecture. The core concept is similar to [ 23 ] , but instead of learning the incidence matrix through iterative refinements, we predict it as a standard cross attention.
| Hyperparameter | |
| Batch size | 30 |
| Optimizer | AdamW [ 33 ] |
| Learning rate | 0.001 |
| Number of epochs | 100 |
| Number of transformer encoder layers | 3 |
| Number of transformer decoder layers | 4 |
Table 3: Hyperparameters used in the particle-flow model.
Figure 5: Superresolution applied to a single-electron event from the test set. The three rows depict the superresolution process for the three ECAL layers. For each layer, the measured LR cell energy distribution, the target HR cell energy distribution, and the predicted HR are shown. The predicted HR cells closely match the truth HR ones. Additionally, the time evolution of the cell energy distribution is also illustrated.
Figure 6: Comparison of flow and regression model outputs for superresolution on a single-electron event from the test set.
Figure 7: (a) The event-level relative energy residual for the LR measured cell energy and the HR predicted cell energies with an ensemble size of 10. (b) The one- width of the event-level residual distributions for the predicted cell energies as a function of the ensemble size.
Figure 8: Substructure distributions for the truth high-resolution, measured low-resolution and predicted high-resolution cell energies (upper row), and the corresponding per-event residuals with respect to the truth high-resolution value (lower row). All sets of cells are computed on the same events. Here and denote the median and the interquartile range divided by .
| Accuracy | ||
| Truth cardinality | LR (measured) (%) | HR (predicted) (%) |
| 1 | 99.38 | 99.41 |
| 2 | 88.52 | 91.02 |
| 3 | 77.62 | 81.97 |
| 4 | 81.32 | 81.42 |
Table 4: Cardinality prediction with the network trained on the LR cells with measured energy, compared with the network trained on the HR cells with predicted energy.
Figure 9: Particle-flow performance. (a) The relative energy residuals, (b) the relative transverse momentum residuals, (c) the pseudorapidity residuals, and (d) the azimuthal angle residuals between the truth particles and the reconstructed particles with PFlow model trained on measured low-resolution cells and the predicted high-resolution cells. The dashed line indicates the performance of an additional PFlow model trained on the low-resolution cells but with over 10 more parameters.
Figure 10: Particle-flow performance with the correction network . (a) The relative energy residuals, (b) the relative transverse momentum residuals, (c) the pseudorapidity residuals, and (d) the azimuthal angle residuals between the truth particles and the reconstructed particles, for the PFlow models trained on measured low-resolution cells and on predicted high-resolution cells. The energy and transverse momentum residuals are computed with respect to the deposited energy, which is the quantity the models are trained to predict, and the corresponding transverse momentum. Both models are identical to those in Fig. 9 apart from the correction network applied to the proxy kinematics.
Figure 11: Event display illustrating the application of superresolution on particle flow, as well as the interpretability of the particle reconstruction model. Each cell is assigned a fractional weight based on the predicted attention or incidence values, which determine the cell colors. The legend shows the truth and predicted particles with their energies. The true deposited energy for the truth particles is shown in parentheses. The particle-flow model trained on the predicted high-resolution cells correctly identifies all three particles with very accurate energy estimations, while the model trained on low-resolution measured cells fails to disentangle the event into three particles and predicts only two particles.
Figure 12: Predicted against true pseudorapidity (left) and azimuthal angle (right) for the particle-flow model trained on the measured low-resolution cells, without the correction network. The predictions are quantized in steps of one low-resolution cell. The dashed line indicates equality.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure 13: Particle-flow performance with the correction network for three sets of input cells: (top left) the relative energy residuals, (top right) the relative transverse momentum residuals, (bottom left) the pseudorapidity residuals, and (bottom right) the azimuthal angle residuals. The three models are identical apart from their inputs. The denoised low-resolution cells are obtained by summing the predicted high-resolution cells within each parent low-resolution cell, so they carry the noise suppression of the superresolution model at the original granularity, and the difference between them and the predicted high-resolution cells reflects the granularity of the representation alone.
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