Oliver Atkinson, Akanksha Bhardwaj, Christoph Englert et al.
Anomaly detection through employing machine learning techniques has emerged as a novel powerful tool in the search for new physics beyond the Standard Model. Historically similar to the development of jet observables, theoretical consistency has not always assumed a central role in the fast development of algorithms and neural network architectures. In this work, we construct an infrared and collinear safe autoencoder based on graph neural networks by employing energy-weighted message passing. We demonstrate that whilst this approach has theoretically favourable properties, it also exhibits formidable sensitivity to non-QCD structures.
We present a general method, called Qade, for solving differential equations using a quantum annealer. The solution is obtained as a linear combination of a set of basis functions. On current devices, Qade can solve systems of coupled partial differential equations that depend linearly on the solution and its derivatives, with non-linear variable coefficients and arbitrary inhomogeneous terms. We test the method with several examples and find that state-of-the-art quantum annealers can find the solution accurately for problems requiring a small enough function basis. We provide a Python package implementing the method at gitlab.com/jccriado/qade.
Steve Abel, Juan Carlos Criado, Michael Spannowsky
The training of neural networks (NNs) is a computationally intensive task requiring significant time and resources. This paper presents a novel approach to NN training using Adiabatic Quantum Computing (AQC), a paradigm that leverages the principles of adiabatic evolution to solve optimisation problems. We propose a universal AQC method that can be implemented on gate quantum computers, allowing for a broad range of Hamiltonians and thus enabling the training of expressive neural networks. We apply this approach to various neural networks with continuous, discrete, and binary weights. Our results indicate that AQC can very efficiently find the global minimum of the loss function, offering a promising alternative to classical training methods.
Jack Y. Araz, Juan Carlos Criado, Michael Spannowsky
Chiral magnets have attracted a large amount of research interest in recent years because they support a variety of topological defects, such as skyrmions and bimerons, and allow for their observation and manipulation through several techniques. They also have a wide range of applications in the field of spintronics, particularly in developing new technologies for memory storage devices. However, the vast amount of data generated in these experimental and theoretical studies requires adequate tools, among which machine learning is crucial. We use a Convolutional Neural Network (CNN) to identify the relevant features in the thermodynamical phases of chiral magnets, including (anti-)skyrmions, bimerons, and helical and ferromagnetic states. We use a flexible multi-label classification framework that can correctly classify states in which different features and phases are mixed. We then train the CNN to predict the features of the final state from snapshots of intermediate states of a lattice Monte Carlo simulation. The trained model allows identifying the different phases reliably and early in the formation process. Thus, the CNN can significantly speed up the large-scale simulations for 3D materials that have been the bottleneck for quantitative studies so far. Moreover, this approach can be applied to the identification of mixed states and emerging features in real-world images of chiral magnets.
We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved classification performance, our findings show that selecting the appropriate group symmetries is crucial for optimising generalisation and sample efficiency. We develop a theoretical foundation for designing group equivariant neural networks that align the choice of symmetries with the underlying probability distributions of the data. Our approach provides a unified methodology for improving classification accuracy across a broad range of applications by carefully tailoring the symmetry group to the specific characteristics of the problem. Theoretical analysis and experimental results demonstrate that optimal classification performance is not always associated with the largest equivariant groups possible in the domain, even when the likelihood ratio is invariant under one of its proper subgroups, but rather with those subgroups themselves. This work offers insights and practical guidelines for constructing more effective group equivariant architectures in diverse machine-learning contexts.
The performance of Quantum Autoencoders (QAEs) in anomaly detection tasks is critically dependent on the choice of data embedding and ansatz design. This study explores the effects of three data embedding techniques, data re-uploading, parallel embedding, and alternate embedding, on the representability and effectiveness of QAEs in detecting anomalies. Our findings reveal that even with relatively simple variational circuits, enhanced data embedding strategies can substantially improve anomaly detection accuracy and the representability of underlying data across different datasets. Starting with toy examples featuring low-dimensional data, we visually demonstrate the effect of different embedding techniques on the representability of the model. We then extend our analysis to complex, higher-dimensional datasets, highlighting the significant impact of embedding methods on QAE performance.
We present a machine-learning-based workflow to model an unbinned likelihood from its samples. A key advancement over existing approaches is the validation of the learned likelihood using rigorous statistical tests of the joint distribution, such as the Kolmogorov-Smirnov test of the joint distribution. Our method enables the reliable communication of experimental and phenomenological likelihoods for subsequent analyses. We demonstrate its effectiveness through three case studies in high-energy physics. To support broader adoption, we provide an open-source reference implementation, nabu.
Daniel Maître, Vishal S. Ngairangbam, Michael Spannowsky
The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the advent of geometric deep learning has enabled neural network architectures that incorporate known symmetries directly into their design, leading to more efficient learning. This paper presents a novel approach that combines MEM-inspired symmetry considerations with equivariant neural network design for particle physics analysis. Even though Lorentz invariance and permutation invariance overall reconstructed objects are the largest and most natural symmetry in the input domain, we find that they are sub-optimal in most practical search scenarios. We propose a longitudinal boost-equivariant message-passing neural network architecture that preserves relevant discrete symmetries. We present numerical studies demonstrating MEM-inspired architectures achieve new state-of-the-art performance in distinguishing di-Higgs decays to four bottom quarks from the QCD background, with enhanced sample and parameter efficiencies. This synergy between MEM and equivariant deep learning opens new directions for physics-informed architecture design, promising more powerful tools for probing physics beyond the Standard Model.
Classical deep neural networks can learn rich multi-particle correlations in collider data, but their inductive biases are rarely anchored in physics structure. We propose quantum-informed neural networks (QINNs), a general framework that brings quantum information concepts and quantum observables into purely classical models. While the framework is broad, in this paper, we study one concrete realisation that encodes each particle as a qubit and uses the Quantum Fisher Information Matrix (QFIM) as a compact, basis-independent summary of particle correlations. Using jet tagging as a case study, QFIMs act as lightweight embeddings in graph neural networks, increasing model expressivity and plasticity. The QFIM reveals distinct patterns for QCD and hadronic top jets that align with physical expectations. Thus, QINNs offer a practical, interpretable, and scalable route to quantum-informed analyses, that is, tomography, of particle collisions, particularly by enhancing well-established deep learning approaches.
Artificial neural networks are at the heart of modern deep learning algorithms. We describe how to embed and train a general neural network in a quantum annealer without introducing any classical element in training. To implement the network on a state-of-the-art quantum annealer, we develop three crucial ingredients: binary encoding the free parameters of the network, polynomial approximation of the activation function, and reduction of binary higher-order polynomials into quadratic ones. Together, these ideas allow encoding the loss function as an Ising model Hamiltonian. The quantum annealer then trains the network by finding the ground state. We implement this for an elementary network and illustrate the advantages of quantum training: its consistency in finding the global minimum of the loss function and the fact that the network training converges in a single annealing step, which leads to short training times while maintaining a high classification performance. Our approach opens a novel avenue for the quantum training of general machine learning models.
We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for synergies between these systems, to understand and explain neural network dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of neural networks, we analytically match the dynamics of the mean background and the dynamics of small perturbations around the mean field, highlighting potential differences in separate limits. We perform empirical tests of this analytic description and quantitatively show the dependence of the effective field theory parameters on hyperparameters of the neural network. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update.
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of Machine Learning on highly complex, simulated LHC data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase-space from the data. We offer our results using three main TN ansatz: Tree Tensor Networks, Matrix Product States, and Multi-scale Entanglement Renormalisation Ansatz.
We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in 'quantum-ness' of the theory, or by a scaling the Ising couplings up or down. This behaviour is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimising several increasingly hard two dimensional potentials. For all the potentials we find the general behaviour that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimisation very markedly better than any of these classical techniques. A quantum anneal can be designed so that the system almost never gets trapped in a false minimum, and rapidly and successfully minimises the potentials.
Jack Y. Araz, Juan Carlos Criado, Michael Spannowsky
We present Elvet, a Python package for solving differential equations and variational problems using machine learning methods. Elvet can deal with any system of coupled ordinary or partial differential equations with arbitrary initial and boundary conditions. It can also minimize any functional that depends on a collection of functions of several variables while imposing constraints on them. The solution to any of these problems is represented as a neural network trained to produce the desired function.