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SPADE introduces a novel autoregressive transformer architecture that decouples multi-feature token embeddings to leverage standard self-attention for learning intra-token correlations. This approach achieves state-of-the-art performance in high-granularity calorimeter simulation while offering a generalizable framework for LLM-style pretraining on higher-dimensional data. The method effectively bridges generative modeling techniques with specialized physics instrumentation tasks, demonstrating significant improvements over existing VQ-VAE baselines.
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SPADE: Split-and-Delay Embeddings for Autoregressive High-Granularity Calorimeter Simulation

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arXiv:2606.11304v1 Announce Type: cross 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-$\alpha_C$. The mechanism is applicable to any generative task with multi-feature tokens, enabling LLM-style pretraining workflows for higher-dimensional data.

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-$\alpha_C$. The mechanism is applicable to any generative task with multi-feature tokens, enabling LLM-style pretraining workflows for higher-dimensional data.

Instrumentation and Detectors (physics.ins-det); Machine Learning (cs.LG); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph)

arXiv:2606.11304 [physics.ins-det]

(or arXiv:2606.11304v1 [physics.ins-det] for this version)

https://doi.org/10.48550/arXiv.2606.11304 arXiv-issued DOI via DataCite (pending registration)

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