Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.

Nature Machine Intelligence Dear Editors, We are hereby submitting the paper'AXXX' to Nature Machine Intelligence as we believe that the content fits the target audience of this Journal and the novelty criteria you require. To our knowledge the present study is the first demonstration of the application of graph neural networks for jet tagging on FPGAs for inference time within O(100) ns. Using the HLS4ML library combined with quantization-aware training and efficient FPGA implementations, we show that O(100) ns inference of complex architectures like graph convolutional neural networks, garnet and interaction networks is feasible at low resource-cost. Our target application is the real-time processing of Large Hadron Collider (LHC) data. However, we believe that the proposed solution could fit other problems related to low latency data selection beyond the LHC. The conditions at the LHC are unique and at the extreme end of the inference-on-the-edge spectrum.

This work presents a novel reconfigurable architecture for Low Latency Graph Neural Network (LL-GNN) designs for particle detectors, delivering unprecedented low latency performance. Incorporating FPGA-based GNNs into particle detectors presents a unique challenge since it requires sub-microsecond latency to deploy the networks for online event selection with a data rate of hundreds of terabytes per second in the Level-1 triggers at the CERN Large Hadron Collider experiments. This paper proposes a novel outer-product based matrix multiplication approach, which is enhanced by exploiting the structured adjacency matrix and a column-major data layout. Moreover, a fusion step is introduced to further reduce the end-to-end design latency by eliminating unnecessary boundaries. Furthermore, a GNN-specific algorithm-hardware co-design approach is presented which not only finds a design with a much better latency but also finds a high accuracy design under given latency constraints. To facilitate this, a customizable template for this low latency GNN hardware architecture has been designed and open-sourced, which enables the generation of low-latency FPGA designs with efficient resource utilization using a high-level synthesis tool. Evaluation results show that our FPGA implementation is up to 9.0 times faster and achieves up to 13.1 times higher power efficiency than a GPU implementation. Compared to the previous FPGA implementations, this work achieves 6.51 to 16.7 times lower latency. Moreover, the latency of our FPGA design is sufficiently low to enable deployment of GNNs in a sub-microsecond, real-time collider trigger system, enabling it to benefit from improved accuracy. The proposed LL-GNN design advances the next generation of trigger systems by enabling sophisticated algorithms to process experimental data efficiently.

The Earth mover's distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent. In this paper, we train a convolutional neural network (CNN) to learn a differentiable, fast approximation of the EMD and demonstrate that it can be used as a substitute for computing-intensive EMD implementations. We apply this differentiable approximation in the training of an autoencoder-inspired neural network (encoder NN) for data compression at the high-luminosity LHC at CERN. The goal of this encoder NN is to compress the data while preserving the information related to the distribution of energy deposits in particle detectors. We demonstrate that the performance of our encoder NN trained using the differentiable EMD CNN surpasses that of training with loss functions based on mean squared error.

Unsupervised deep learning techniques are widely used to identify anomalous behaviour. The performance of such methods is a product of the amount of training data and the model size. However, the size is often a limiting factor for the deployment on resource-constrained devices. We present a novel procedure based on knowledge distillation for compressing an unsupervised anomaly detection model into a supervised deployable one and we suggest a set of techniques to improve the detection sensitivity. Compressed models perform comparably to their larger counterparts while significantly reducing the size and memory footprint.

Auto-encoders (AEs) have the potential to be effective and generic tools for new physics searches at colliders, requiring little to no model-dependent assumptions. New hypothetical physics signals can be considered anomalies that deviate from the well-known background processes generally expected to describe the whole dataset. We present a search formulated as an anomaly detection (AD) problem, using an AE to define a criterion to decide about the physics nature of an event. In this work, we perform an AD search for manifestations of a dark version of strong force using raw detector images, which are large and very sparse, without leveraging any physics-based pre-processing or assumption on the signals. We propose a dual-encoder design which can learn a compact latent space through conditioning. In the context of multiple AD metrics, we present a clear improvement over competitive baselines and prior approaches. It is the first time that an AE is shown to exhibit excellent discrimination against multiple dark shower models, illustrating the suitability of this method as a performant, model-independent algorithm to deploy, e.g., in the trigger stage of LHC experiments such as ATLAS and CMS.

Model compression is instrumental in optimizing deep neural network inference on resource-constrained hardware. The prevailing methods for network compression, namely quantization and pruning, have been shown to enhance efficiency at the cost of performance. Determining the most effective quantization and pruning strategies for individual layers and parameters remains a challenging problem, often requiring computationally expensive and ad hoc numerical optimization techniques. This paper introduces FITCompress, a novel method integrating layer-wise mixed-precision quantization and unstructured pruning using a unified heuristic approach. By leveraging the Fisher Information Metric and path planning through compression space, FITCompress optimally selects a combination of pruning mask and mixed-precision quantization configuration for a given pre-trained model and compression constraint. Experiments on computer vision and natural language processing benchmarks demonstrate that our proposed approach achieves a superior compression-performance trade-off compared to existing state-of-the-art methods. FITCompress stands out for its principled derivation, making it versatile across tasks and network architectures, and represents a step towards achieving optimal compression for neural networks.

The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis $\rm H_1$ is generic enough not to introduce a significant bias while at the same time avoiding overfitting. A practical implementation of this idea (dubbed NPLM) has been developed in the context of high energy physics, targeting the detection in collider data of new physical effects not foreseen by the Standard Model. In this paper we initiate a comparison of this methodology with other approaches to goodness of fit, and in particular with classifier-based strategies that share strong similarities with NPLM. NPLM emerges from our comparison as more sensitive to small departures of the data from the expected distribution and not biased towards detecting specific types of anomalies while being blind to others. These features make it more suited for agnostic searches for new physics at collider experiments. Its deployment in other contexts should be investigated.

The high-energy physics community is investigating the feasibility of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to improve physics sensitivity while meeting data processing latency limitations. In this contribution, we introduce a novel end-to-end procedure that utilizes a machine learning technique called symbolic regression (SR). It searches equation space to discover algebraic relations approximating a dataset. We use PySR (software for uncovering these expressions based on evolutionary algorithm) and extend the functionality of hls4ml (a package for machine learning inference in FPGAs) to support PySR -generated expressions for resource-constrained production environments. Deep learning models often optimise the top metric by pinning the network size because vast hyperparameter space prevents extensive neural architecture search. Conversely, SR selects a set of models on the Pareto front, which allows for optimising the performanceresource tradeoff directly. By embedding symbolic forms, our implementation can dramatically reduce the computational resources needed to perform critical tasks. We validate our procedure on a physics benchmark: multiclass classification of jets produced in simulated proton-proton collisions at the CERN Large Hadron Collider, and show that we approximate a 3-layer neural network with an inference model that has as low as 5 ns execution time (a reduction by a factor of 13) and over 90% approximation accuracy.

There has been a recent explosion in research into machine-learning-based generative modeling to tackle computational challenges for simulations in high energy physics (HEP). In order to use such alternative simulators in practice, we need well-defined metrics to compare different generative models and evaluate their discrepancy from the true distributions. We present the first systematic review and investigation into evaluation metrics and their sensitivity to failure modes of generative models, using the framework of two-sample goodness-of-fit testing, and their relevance and viability for HEP. Inspired by previous work in both physics and computer vision, we propose two new metrics, the Fr\'echet and kernel physics distances (FPD and KPD, respectively), and perform a variety of experiments measuring their performance on simple Gaussian-distributed, and simulated high energy jet datasets. We find FPD, in particular, to be the most sensitive metric to all alternative jet distributions tested and recommend its adoption, along with the KPD and Wasserstein distances between individual feature distributions, for evaluating generative models in HEP. We finally demonstrate the efficacy of these proposed metrics in evaluating and comparing a novel attention-based generative adversarial particle transformer to the state-of-the-art message-passing generative adversarial network jet simulation model. The code for our proposed metrics is provided in the open source JetNet Python library.