SPADE: Split-and-Delay Embeddings for Autoregressive High-Granularity Calorimeter Simulation

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

OmniJet-${α_{ C}}$: Learning point cloud calorimeter simulations using generative transformers

We show the first use of generative transformers for generating calorimeter showers as point clouds in a high-granularity calorimeter. Using the tokenizer and generative part of the OmniJet-${\alpha}$ model, we represent the hits in the detector as sequences of integers. This model allows variable-length sequences, which means that it supports realistic shower development and does not need to be conditioned on the number of hits. Since the tokenization represents the showers as point clouds, the model learns the geometry of the showers without being restricted to any particular voxel grid.