Nanosecond machine learning regression with deep boosted decision trees in FPGA for high energy physics

We present a novel application of the machine learning / artificial intelligence method called boosted decision trees to estimate physical quantities on field programmable gate arrays (FPGA). The software package fwXmachina features a new architecture called parallel decision paths that allows for deep decision trees with arbitrary number of input variables. It also features a new optimization scheme to use different numbers of bits for each input variable, which produces optimal physics results and ultraefficient FPGA resource utilization. Problems in high energy physics of proton collisions at the Large Hadron Collider (LHC) are considered. Estimation of missing transverse momentum (E_T ^miss) at the first level trigger system at the High Luminosity LHC (HL-LHC) experiments, with a simplified detector modeled by Delphes, is used to benchmark and characterize the firmware performance. The firmware implementation with a maximum depth of up to 10 using eight input variables of 16-bit precision gives a latency value of 𝒪(10) ns, independent of the clock speed, and 𝒪(0.1)% of the available FPGA resources without using digital signal processors.