Efficient Graph Coloring with Neural Networks: A Physics-Inspired Approach for Large Graphs

The graph coloring problem is an optimization problem involving the assignment of one of q colors to each vertex of a graph such that no two adjacent vertices share the same color. This problem is NP-hard and arises in various practical applications. In this work, we present a novel algorithm that leverages graph neural networks to tackle the problem efficiently, particularly for large graphs. We propose a physics-inspired approach that leverages tools used in statistical mechanics to improve the training and performance of the algorithm. The scaling of our method is evaluated for different connectivities and graph sizes. Finally, we demonstrate the effectiveness of our method on a dataset of Erdos-Renyi graphs, showing its applicability also in hard-to-solve connectivity regions where traditional methods struggle.

Fast Neural Network Inference on FPGAs for Triggering on Long-Lived Particles at Colliders

Experimental particle physics demands a sophisticated trigger and acquisition system capable to efficiently retain the collisions of interest for further investigation. Heterogeneous computing with the employment of FPGA cards may emerge as a trending technology for the triggering strategy of the upcoming high-luminosity program of the Large Hadron Collider at CERN. In this context, we present two machine-learning algorithms for selecting events where neutral long-lived particles decay within the detector volume studying their accuracy and inference time when accelerated on commercially available Xilinx FPGA accelerator cards. The inference time is also confronted with a CPU- and GPU-based hardware setup. The proposed new algorithms are proven efficient for the considered benchmark physics scenario and their accuracy is found to not degrade when accelerated on the FPGA cards. The results indicate that all tested architectures fit within the latency requirements of a second-level trigger farm and that exploiting accelerator technologies for real-time processing of particle-physics collisions is a promising research field that deserves additional investigations, in particular with machine-learning models with a large number of trainable parameters.