Integer Quantization of Graph Neural Networks for Real-Time FPGA Track Finding
Real-time track finding for displaced-muon signatures in the CMS Level-1 trigger must operate under strict fixed-latency constraints of 12.5 $μ$s while processing high-throughput detector data. Because muon hits map naturally onto sparse, irregular graphs, graph neural networks (GNNs) are attractive candidates; however, mapping message-passing models to field-programmable gate arrays (FPGAs) requires careful co-design of numerical precision, microarchitecture, and high-level synthesis (HLS) implementation. This work presents a reproducible, bit-exact workflow bridging GNN design and FPGA prototyping for fixed-latency inference. The methodology is demonstrated by implementing a two-layer GraphSAGE network onto an XCVU13P FPGA, using the Cora citation network as a fixed-size benchmark for firmware evaluation that decouples deployment feasibility from the physics task. Starting from a 32-bit floating-point reference that exceeds the available FPGA resource budget, we derive an integer-only datapath through post-training quantization (INT8 weights and activations, INT32 biases), a power-of-two scale approximation that replaces rescaling multipliers with arithmetic shifts, and data-driven bit-width narrowing. Every stage is validated bit-exactly against a Python integer emulator in Vitis HLS C-simulation. The optimized INT8 power-of-two design achieves an inference latency of 19 clock cycles (52.8 ns at the nominal 360 MHz clock) at 20\% DSP, 6\% FF, and 27\% LUT utilization, with 75.0$\pm$1.1\% accuracy compared to the 78.0$\pm$0.8\% for FP32. Accuracy is reported as the average across multiple training seeds. The resulting workflow establishes a concrete, transferable path toward fixed-latency GNN-based track reconstruction in the CMS Level-1 trigger.