Ultrafast jet classification on FPGAs for the HL-LHC

TL;DR

The paper tackles real-time jet-origin classification for HL-LHC Level-1 Triggers under tight latency and hardware constraints. It compares three neural-network families—MLP, permutation-invariant Deep Sets, and permutation-invariant Interaction Networks—on unordered jet constituent data and implements them on an FPGA via the hls4ml flow with quantization-aware training. Key findings show that permutation-invariant architectures (DS and IN) scale better with increasing constituent count (up to $N=32$), at the cost of higher resource usage, while 8-bit quantization preserves accuracy and pruning enables fitting larger models; the target latency aligns with $O(100)$ ns, illustrating feasibility for L1T deployment. The work demonstrates the practical viability of FPGA-based jet classifiers in HL-LHC triggers, guiding design choices and paving the way for a full FPGA implementation and further optimization.

Abstract

Three machine learning models are used to perform jet origin classification. These models are optimized for deployment on a field-programmable gate array device. In this context, we demonstrate how latency and resource consumption scale with the input size and choice of algorithm. Moreover, the models proposed here are designed to work on the type of data and under the foreseen conditions at the CERN LHC during its high-luminosity phase. Through quantization-aware training and efficient synthetization for a specific field programmable gate array, we show that $O(100)$ ns inference of complex architectures such as Deep Sets and Interaction Networks is feasible at a relatively low computational resource cost.

Figures (3)

• Figure 1: Schematic of all the considered models. (a) A simple multilayer perceptron. The 2D input is flattened to one dimension before it is passed through the MLP. (b) A permutation-invariant deep set network ds. The initial MLP acts on the features of each input constituent. The aggregation layer $S$ performs a permutation invariant operation at the constituent level and hence brings the input to a 1D vector. (c) A permutation-invariant interaction network battaglia as implemented before in Ref. jedi. The input is transformed by the marshaling function $m$ into a fully-connected graph. The exact mechanics of the IN are described in Section \ref{['sec:models']}. For each network type, all hyperparameters, such as the number of layers and number of nodes per layer, are optimized depending on the number of constituents. The hyperparameters of each network are presented in Section \ref{['sec:models']} and their respective performance is shown in Table \ref{['table:modelvsNcontituents']}.
• Figure 2: The inverse of the Average False Positive Rate ($\overline{\mathrm{FPR}}$) at a fixed true positive rate (TPR) of 80% over $k=5$ folds of data for $N\in\{8, 16, 32\}$ constituents per jet. This TPR is chosen since it is a conventional working point in related literature. The size of the MLP is constrained by requiring it to be synthesizable in hls4ml. Therefore, the number of parameters per consecutive layer is limited and the MLP performance decreases from 16 to 32 constituents. This is not a factor for the other networks that use a 2D representation of the data. The models are quantized to 8 bits.
• Figure 3: The inverted average FPR across the five jet classes, $1/\overline{\mathrm{FPR}}$, as a function of the bit width for the IN, DS, and MLP. For each model, the threshold on the classifier score corresponds to a TPR of 80%. The model performance shown here is determined on the $N=8$ data set. A bit width of 8 maintains good classification accuracy.