physics.ins-det · 2606.11304 Copy arXiv ID · Jun 9, 2026 Save SPADE: Split-and-Delay Embeddings for Autoregressive High-Granularity Calorimeter Simulation Authors: Joschka Birk , Frank Gaede , Anna Hallin , Gregor Kasieczka , Martina Mozzanica , Henning Rose
Organizations: Institute for Experimental Physics, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany · Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
Abstract We introduce SPADE (SPlit And Delay Embeddings), an autoregressive transformer for sequences whose tokens carry multiple features. Rather than embedding these features jointly, SPADE embeds them independently. Delaying each feature stream relative to the previous one allows intra-token correlations to be learned by the standard self-attention mechanism. Applied to point-cloud calorimeter shower generation in the highly granular ILD detector, SPADE is competitive with the state of the art AllShowers model on photon showers, and substantially outperforms its VQ-VAE-based predecessor OmniJet-α C α_C α C
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Thorsten Buss, Henry Day-Hall, Frank Gaede, Gregor Kasieczka +1
Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany · Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
Accurate and efficient detector simulation is essential for modern collider experiments. To reduce the high computational cost, various fast machine learning surrogate models have been proposed. Traditional surrogate models for calorimeter shower modeling train separate networks for each particle species, limiting scalability and reuse. We introduce AllShowers, a unified generative model that simulates calorimeter showers across multiple particle types using a single generative model. AllShowers is a continuous normalizing flow model with a Transformer architecture, enabling it to generate complex spatial and energy correlations in variable-length point cloud representations of showers. Trained on a diverse dataset of simulated showers in the highly granular ILD detector, the model demonstrates the ability to generate realistic showers for electrons, photons, and charged and neutral hadrons across a wide range of incident energies and angles without retraining. In addition to unifying shower generation for multiple particle types, AllShowers surpasses the fidelity of previous single-particle-type models for hadronic showers. Key innovations include the use of a layer embedding, allowing the model to learn all relevant calorimeter layer properties; a custom attention masking scheme to reduce computational demands and introduce a helpful inductive bias; and a shower- and layer-wise optimal transport mapping to improve training convergence and sample quality. AllShowers marks a significant step towards a universal model for calorimeter shower simulations in collider experiments.