Vision Calorimeter (ViC) Overview

• Vision Calorimeter (ViC) is an end-to-end framework that reinterprets calorimeter readouts as images for particle reconstruction.
• It reformulates anti-neutron detection by using pseudo bounding boxes and a detector-style network, significantly reducing angular bias and improving momentum metrics.
• Leveraging imaging calorimetry, ViC integrates techniques like unwrap mapping and energy encoding, with broader implications for particle flow and fast simulation.

Vision Calorimeter (ViC) is, in its primary contemporary usage, an end-to-end framework that treats calorimeter responses as images and applies modern computer-vision machinery to particle reconstruction. In the formulation introduced for BESIII electromagnetic calorimeter (EMC) data, ViC reconstructs anti-neutron incident position and momentum by recasting EMC readouts as a two-dimensional image and training a detector-style network in which incident position is represented by the center of a pseudo bounding box and momentum is regressed in a unified head (Yu et al., 2024). In a broader sense, the term also sits within the larger development of imaging calorimetry, computer-vision particle flow, calorimeter-image classification, and vision-based fast simulation, all of which exploit the fact that highly segmented calorimeters encode physically meaningful spatial patterns rather than only aggregate energy sums (Bilki et al., 2013).

1. Conceptual setting and relation to imaging calorimetry

Imaging calorimetry is the underlying detector and reconstruction paradigm from which ViC draws much of its logic. A high-granularity imaging calorimeter is a sampling calorimeter with fine lateral and longitudinal segmentation that produces detailed two- and three-dimensional images of particle showers. Such granularity supports topology-based reconstruction, separation of nearby showers, identification of electromagnetic subshowers inside hadronic cascades, software compensation in non-compensating calorimeters, and integration with Particle Flow Algorithms (PFAs) (Bilki et al., 2013).

Within that broader landscape, ViC is part of a shift from handcrafted clustering toward learned image-based inference. Related work has learned per-cell neutral fractions from multi-layer calorimeter images and tracking inputs for particle flow (Bello et al., 2020), benchmarked Vision Transformers and hybrid ViT-CNN models on ECAL/HCAL/track jet-view images for quark-gluon jet classification (Jahin et al., 17 Jun 2025), and used universal ViTs for fast calorimeter simulation across regular and irregular geometries (Favaro et al., 7 Jan 2026). This suggests that ViC is best understood not as an isolated model family, but as one instance of a broader research program in which calorimeter data are treated as structured visual or tokenized fields.

The anti-neutron ViC baseline is distinctive because it migrates the object-detection paradigm itself to particle images. Rather than segmenting showers or classifying a jet crop, it aligns point localization with box-based detection and exploits the detector-style combination of classification, localization, and confidence scoring (Yu et al., 2024).

2. BESIII anti-neutron reconstruction problem

At BESIII, the EMC is optimized for photons, whereas neutrons and anti-neutrons interact dominantly via the strong interaction and are comparatively “transparent” to an EMC. Their showers are sparse and diffuse and deposit less energy than photons, which makes position and momentum reconstruction intrinsically difficult for conventional clustering algorithms (Yu et al., 2024).

Classical EMC clustering computes energy-weighted centroids within contiguous above-threshold cells and sums energies for clusters. In this setting, it struggles to sift neutrons from photon-like backgrounds and yields large uncertainties in both position and momentum. The ViC formulation starts from the observation that the spatial distribution of deposited energy across the EMC’s segmented cell array contains contextual cues, including spread and anisotropy, that correlate with incidence direction and energy (Yu et al., 2024).

The BESIII EMC comprises 6,240 segmented cells across a barrel and two end-caps. The barrel has $44$ rings with $120$ cells each; the end-caps have $6$ layers with $\{96,96,80,80,64,64\}$ cells. The ViC dataset comprises 986,343 BESIII $e^+e^-$ collision events with a single particle per EMC observation, annotated with incident $(\phi,\theta)$ and momentum derived from energy–momentum conservation; 100,000 samples are reserved for testing and the remainder for training (Yu et al., 2024).

The task is therefore not a generic calorimeter regression problem. It is a specific EMC-only anti-neutron reconstruction problem in which sparse hadronic signatures must be inferred from a detector designed primarily for electromagnetic showers.

3. Image formation and pseudo-box targets

ViC unwraps the cylindrical EMC surface into a two-dimensional image with width $w_{\mathrm{img}}=960$ and height $h_{\mathrm{img}}=480$. The image coordinates $(x,y)$ are put in bijection with spherical angles $(\phi,\theta)$ by

$120$0

with $120$1 and $120$2 (Yu et al., 2024).

The deposited energy $120$3 is encoded into RGB channels through a log-transformed, piecewise mapping adapted to the heavily imbalanced EMC energy distribution. The three bands are low energy in blue, medium energy in green, and high energy in red:

$120$4

for low energy,

$120$5

for medium energy, and

$120$6

for high energy. To mitigate overfitting from sparse foregrounds, zero-mean Gaussian background noise is injected with standard deviation $120$7, corresponding to a 30 dB SNR (Yu et al., 2024).

A direct formulation would regress the incident pixel or the corresponding spherical angles:

$120$8

ViC instead reformulates incident position prediction as box localization by generating a pseudo ground-truth bounding box centered at the annotated incident position and sized as a multiple of the local cell size (Yu et al., 2024).

This target construction encodes a trade-off already visible in the calorimeter geometry. Smaller boxes sharpen center accuracy but starve the detector of contextual energy, whereas larger boxes provide richer context but relax center constraints. Ablations show that an adaptive $120$9 cell-size pseudo box is a robust default, and that adaptive sizing outperforms fixed-size boxes by preserving spatial cues tied to EMC geometry, including flatter boxes near edges (Yu et al., 2024).

4. Architecture, objectives, and inference

The baseline ViC instantiates a standard one-stage detector with a pre-trained backbone, specifically Swin-T pre-trained on ImageNet, together with an FPN. The detector head branches into a position head for pseudo-box regression, a momentum head for incident momentum magnitude regression, and a classification head for foreground/background prediction and confidence scoring (Yu et al., 2024).

Training follows standard object-detection practice, including focal loss on classification and either dense anchors or anchor-free assignment, with a single pseudo ground-truth bounding box per image. During inference, ViC retains the highest-confidence detection, converts its center to $6$0 through the inverse unwrap mapping, and decodes momentum from a normalized regressor output by

$6$1

with $6$2 and $6$3 by default (Yu et al., 2024).

The key position metric is the angular bias on the sphere. For angles $6$4, define

$6$5

and

$6$6

ViC reports mean Angular Bias (mAB) over the test set and at various relative-efficiency operating points (Yu et al., 2024).

To improve center accuracy, box regression is augmented with the center-oriented loss

$6$7

where $6$8 is the center angular bias, $6$9 is the angular bias associated with the minimum enclosing rectangle’s diagonal points, and $\{96,96,80,80,64,64\}$0 in the reported setting. For momentum, performance is assessed using

$\{96,96,80,80,64,64\}$1

$\{96,96,80,80,64,64\}$2

together with the Pearson correlation coefficient $\{96,96,80,80,64,64\}$3 (Yu et al., 2024).

The reported training setup uses batch size $\{96,96,80,80,64,64\}$4, learning rate $\{96,96,80,80,64,64\}$5, and $\{96,96,80,80,64,64\}$6 epochs on $\{96,96,80,80,64,64\}$7 RTX 4090, with $\{96,96,80,80,64,64\}$8 inputs and $\{96,96,80,80,64,64\}$9 pseudo boxes unless otherwise stated. The implementation is compatible with standard detector infrastructure such as MMDetection-like pipelines, and the public repository includes data conversion, detector configuration files, training scripts, and evaluation code (Yu et al., 2024).

5. Reported performance and empirical behavior

For incident position prediction, ViC substantially improves over the conventional clustering algorithm. At 100% relative efficiency, the mean Angular Bias drops from $e^+e^-$0 to $e^+e^-$1, a reduction of 42.81%, and also outperforms direct point regression, reported as S.F.S. with Swin-T at $e^+e^-$2 (Yu et al., 2024).

For momentum, ViC improves the Pearson correlation coefficient from $e^+e^-$3 to $e^+e^-$4, reduces mAE from $e^+e^-$5 to $e^+e^-$6 GeV/$e^+e^-$7, and lowers mRE from $e^+e^-$8 to $e^+e^-$9 relative to S.F.S. The work emphasizes that this occurs in a challenging sub-GeV regime where hadronic calorimeters typically exceed 50% relative error (Yu et al., 2024).

Method or baseline	Position metric	Momentum metric
Conventional clustering	mAB $(\phi,\theta)$0	—
S.F.S. with Swin-T	mAB $(\phi,\theta)$1	Corr $(\phi,\theta)$2, mAE $(\phi,\theta)$3 GeV/$(\phi,\theta)$4, mRE $(\phi,\theta)$5
ViC	mAB $(\phi,\theta)$6	Corr $(\phi,\theta)$7, mAE $(\phi,\theta)$8 GeV/$(\phi,\theta)$9, mRE $w_{\mathrm{img}}=960$0

Ablations characterize the principal design choices. Adaptive $w_{\mathrm{img}}=960$1 cell-size pseudo boxes attain the best overall mAB; $w_{\mathrm{img}}=960$2 excels at low efficiency but loses context; fixed-size boxes underperform. CO Loss yields the best mAB relative to L1, GIoU, and DIoU. One-stage and anchor-free designs generally outperform two-stage detectors under single pseudo-box supervision, and stronger backbones pre-trained on natural images, including VMamba, vHeat, and Swin-T, correlate with better mAB (Yu et al., 2024).

The framework also extends beyond the single-species baseline. With 400k training samples each for anti-neutron and anti-lambda and 50k test samples per species, ViC attains classification accuracies of 93.14% for anti-neutron and 73.82% for anti-lambda, while maintaining competitive mAB and momentum errors for both; anti-lambda is explicitly harder because of decays to anti-neutron plus two photons (Yu et al., 2024).

6. Clarifications, later variants, and limitations

A central clarification in the ViC literature concerns the status of heat-conduction and frequency-domain operators. The 2024 ViC baseline explicitly states that it does not introduce or use a Heat-Conduction Operator (HCO) nor a DCT-based implementation; rather, radial priors aligned with expected shower diffusion and frequency-domain features via DCT are presented there as promising future extensions, not as components of the current baseline (Yu et al., 2024).

A later paper, "Vision Calorimeter for High-Energy Particle Detection," introduces precisely such an extension. In that formulation, HCO and the adaptive variant HCO-K are implemented through DCT/IDCT diffusion operators, the backbone is vHeatK, the position head remains local, the momentum head is made global, and the reported performance reaches $w_{\mathrm{img}}=960$3 mAB and $w_{\mathrm{img}}=960$4 mRE on the anti-neutron task (Yu et al., 29 Jan 2026). This later result is therefore best read as a follow-on development rather than as the architecture of the 2024 baseline.

The baseline ViC also has explicit operating assumptions. It assumes single-particle EMC observations and a fixed unwrap mapping; complex multi-shower overlap, edge effects in the unwrap, and nonuniformities in EMC cell responses may degrade accuracy. Ground-truth momenta are derived via conservation laws rather than direct hadronic calorimeter measurements, which can introduce systematic biases. Uncertainty quantification is not yet integrated, although Bayesian heads or ensemble variance are identified as plausible additions for downstream physics analyses (Yu et al., 2024).

Across the broader literature, the same vision-based perspective has been applied to neutral–charged disentanglement in particle flow (Bello et al., 2020), jet substructure classification from calorimeter images (Jahin et al., 17 Jun 2025), and universal fast simulation across detector geometries (Favaro et al., 7 Jan 2026). This suggests that ViC is evolving from a single anti-neutron reconstruction baseline into a more general methodological direction: calorimeter analysis as computer vision, with detector geometry, shower topology, and physics-aware inductive bias encoded directly in the model class.