Transformer based Reconstruction for LHCb PicoCal Calorimeter

Current LHCb calorimeter reconstruction uses rule-based clustering without exploiting timing or learned representations. The PicoCal upgrade will provide picosecond timing and longitudinal segmentation, creating an opportunity for ML-based reconstruction. I propose a space-time kernel transformer that embeds timing as a physics-informed spatial coordinate for energy reconstruction, benchmarked against the Cellular Automaton and Graph Clustering baselines across four incremental dataset stages. Deliverables include a complete end-to-end pipeline, trained models with timing ablation study, benchmark tables with physics and latency metrics, and a documented open-source PyTorch Geometric codebase for the LHCb group.