Nanosecond anomaly detection with decision trees and real-time application to exotic Higgs decays

The Large Hadron Collider (LHC) at CERN is a high-energy particle collider designed to discover and study the Higgs boson and search for physics beyond the Standard Model (BSM). Despite extensive searches, there's a lack of direct evidence for BSM physics. This motivates the search for rare BSM events, often obscured by a vast number of SM processes. Unsupervised machine learning (ML) algorithms, particularly autoencoders, offer a promising approach for signal-agnostic searches for these rare events. While many studies use autoencoders for offline analysis of LHC data, enabling real-time anomaly detection on the trigger path is crucial for more efficient data selection. The LHC's 40 MHz collision rate, with 25 ns between collisions, demands exceptionally fast anomaly detection algorithms. The trigger system, composed of FPGAs and a computing farm, must quickly filter the vast data stream, selecting only a fraction for detailed offline analysis. Previous work demonstrated FPGA-based anomaly detection using neural networks, achieving latencies ranging from 80 to 1480 ns. This research aims to develop an interpretable autoencoder using deep decision trees, achieving significantly lower latency while minimizing resource consumption on FPGA.

Significant research focuses on applying autoencoders, primarily neural network-based, for detecting BSM physics in pre-collected LHC data. However, real-time anomaly detection within the FPGA-based trigger system remains a significant challenge. This paper builds upon previous work demonstrating the feasibility of deploying ML algorithms, specifically deep decision trees, on FPGAs for high-speed inference in high-energy physics. The use of decision trees offers advantages in terms of interpretability and efficient FPGA implementation compared to neural networks. Prior studies have shown the effectiveness of decision-tree based methods for event classification and regression tasks in high-energy physics. This work extends these efforts to anomaly detection in a real-time trigger environment.

This study introduces a novel interpretable autoencoder built using a forest of deep decision trees, leveraging the fwXmachina framework for efficient FPGA implementation. The autoencoder takes an input vector *x*, encodes it to a latent space *w*, and decodes it back to an output vector *x*. The anomaly score is calculated as the distance between the input and output vectors. The core of the method is a novel machine learning training algorithm that builds a deep decision tree grid (DTG) by recursively splitting the input space based on the probability density function (PDF) of the input variables. This process creates a forest of deep decision trees (DDT). The median is used as the estimator for each bin, minimizing the L1 norm. Unlike traditional autoencoders, this design performs encoding and decoding simultaneously, bypassing the explicit latent space. The anomaly score is the sum of L1 distances for each tree. The training focuses on known SM processes, aiming to generate a low anomaly score for SM events and a high score for BSM events. The training process involves recursive importance sampling of the input variables to build the DTG. The algorithm recursively splits the sample based on thresholds obtained from sampling the PDF, stopping when the maximum depth is reached or the sample size falls below a predefined threshold. Weighted randomness in variable and threshold selection ensures non-identical trees in the forest, improving overall accuracy. The framework’s implementation uses 8-bit integers for input variables. Monte Carlo simulations generate training and testing samples, including SM background and simulated Higgs boson decays to BSM pseudoscalars (Haa → γγjj). Offline quantities approximate trigger-level inputs. Invariant masses, transverse momenta (pT), and ΔR (η-φ distance) of photons and jets are used as input variables. The autoencoder's performance is evaluated by comparing its acceptance of signal events against that of a conventional cut-based diphoton trigger. FPGA implementation uses a Xilinx Virtex UltraScale+ VU9P FPGA. The system's performance is then evaluated on two datasets: a simulated dataset for the benchmark exotic Higgs decay scenario and a public LHC physics dataset containing various BSM signal models.

The decision-tree-based autoencoder achieves a latency of 30 ns (10 clock cycles at 200 MHz) on an FPGA. Resource utilization is low: approximately 7% of look-up tables (LUTs) and 1% of flip-flops (FFs), with negligible DSP usage. The benchmark exotic Higgs decay (H125 → aa → γγjj) scenario shows a significant improvement in signal acceptance compared to a conventional diphoton trigger. At a 3 kHz SM background rate, the autoencoder achieved 6.1% acceptance for the H125 signal, almost three times higher than the 2.2% acceptance of the diphoton trigger. For a cross-check scenario (H70 → aa → γγjj), the autoencoder showed a substantial increase in acceptance (1.4%) compared to the negligible acceptance (0.01%) of the diphoton trigger. The autoencoder's performance was also compared against a previously published neural-network-based autoencoder on a public LHC physics dataset featuring various BSM signals. The decision-tree-based autoencoder shows comparable Area Under the Curve (AUC) values, demonstrating similar discrimination power. The FPGA resource usage is comparable or better than the neural network implementation while having lower latency (30 ns versus 80 ns). A robustness study demonstrates that the autoencoder maintains performance even with signal contamination up to 33% in the training data. With 33% signal contamination, the H125 acceptance was still roughly twice that of the conventional trigger.

This work successfully demonstrates the feasibility of real-time anomaly detection at the LHC using an interpretable decision-tree-based autoencoder implemented on an FPGA. The low latency (30 ns) and minimal resource utilization make this approach suitable for integration into the LHC's real-time trigger systems. The superior performance compared to a conventional cut-based trigger and comparable performance to existing neural-network based solutions underscores the advantages of this approach. The interpretability of the decision-tree model is a significant advantage for understanding the trigger behavior and identifying potential systematic effects. The robustness study indicates that the autoencoder is relatively insensitive to signal contamination in the training data, making it practical for training directly with real LHC data.

This paper presents a novel, interpretable, and efficient FPGA-based autoencoder for real-time anomaly detection in high energy physics. The method significantly improves the detection efficiency for rare BSM events compared to conventional triggers. The low latency and low resource consumption of this approach are promising for future upgrades and for other applications requiring low latency anomaly detection. Future research should focus on extending this work to handle more complex input data from raw detector channels and exploring other advanced decision tree architectures.

The study primarily relies on simulated data. While efforts were made to mimic real-world conditions, differences between simulated and real data could influence the results. The current implementation assumes the availability of pre-processed physics objects as input. Adapting the algorithm to handle raw detector data will require substantial modifications. The robustness study, while demonstrating some tolerance to signal contamination, suggests that performance degrades with high levels of contamination. The generalizability of the findings might be limited by the specific BSM models and physics scenarios considered in the study.