Conditional generative surrogates in high-energy physics, such as models that predict reconstructed jets from partons, are often evaluated on $1\text{D}$ marginal divergences among other metrics. Taken alone these metrics can reward conditional collapse. On a CMS simulation benchmark, a sampler that ignores the conditioner beats a trained Mixture Density Network (MDN) on all four target marginals under both KL and Wasserstein-1, and cannot be stably separated from a Conditional Flow Matching (CFM) model on two of the four. We instead score the models with the Continuous Ranked Probability Skill Score (CRPSS) from forecast verification, taking the exact marginal as the reference. We show how global skill depends on the evaluation spectrum, and we also report it within bins of a conditioning variable, where that dependence largely goes away. We then introduce a data-driven $k$-Nearest-Neighbor ($k$-NN) extrapolation that estimates the best CRPS the conditioning information allows. Both models agree with this estimate on all four targets, which suggests that current architectures have reached the information available in the conditioner, at least as far as these per-target scores can tell.
Henning Bahl, Victor Bresó-Pla, Anja Butter, Joaquín Iturriza Ramirez
Scaling laws describing the dependence of neural network performance on the amount of training data, the spent compute, and the network size have emerged across a huge variety of machine learning task and datasets. In this work, we systematically investigate these scaling laws in the context of amplitude surrogates for particle physics. We show that the scaling coefficients are connected to the number of external particles of the process. Our results demonstrate that scaling laws are a useful tool to achieve desired precision targets.
Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach
Emre Gurkanli, Michael Spannowsky
AI 速览：作者提出并检验一种受MERA启发的多尺度张量网络自编码器，用于对撞机喷注的基于重建的异常检测，并在其基准设定下与稠密自编码器及树张量网络等基线比较。
We investigate whether a multiscale tensor-network architecture provides a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is naturally organised across angular and momentum scales. This motivates an autoencoder that compresses information hierarchically and can reorganise short-range correlations before coarse-graining. Guided by this picture, we formulate a Multiscale Entanglement Renormalization Ansatz (MERA)-inspired autoencoder acting on ordered jet constituents. To our knowledge, a MERA-inspired autoencoder has not previously been proposed, and this architecture has not been explored in collider anomaly detection. We compare this architecture to a dense autoencoder, the corresponding tree-tensor-network limit, and classical baselines within a background-only reconstruction framework. The paper is organised around two main questions: whether locality-aware hierarchical compression is genuinely supported by the data, and whether the disentangling layers of MERA contribute beyond a simpler tree hierarchy. To address these questions, we combine benchmark comparisons with a training-free local-compressibility diagnostic and a direct identity-disentangler ablation. In the nominal benchmark, the MERA-inspired model attains a higher mean AUC than the dense autoencoder at all three latent dimensions while using roughly one-third of its trainable parameters. The locality-preserving multiscale structure is well matched to jet data, and, at the strongest compression bottleneck, the trained disentanglers move substantially away from the identity and are accompanied by a positive mean performance shift. Overall, the study supports locality-aware hierarchical compression as a useful and parameter-efficient inductive bias for reconstruction-based jet anomaly detection in this benchmark setting.
Farouk Mokhtar, Joosep Pata, Michael Kagan, Javier Duarte
The workflow from particle collision to physics analysis passes through a series of reconstruction steps that are traditionally modular and disconnected, with no shared representation linking low-level detector data to high-level analysis tasks. We show that casting event reconstruction as a machine learning problem naturally produces such a shared representation. We repurpose a machine learning model trained for particle-flow reconstruction (MLPF) to perform three distinct analysis tasks: jet flavor identification, jet energy regression, and missing momentum regression. By appending the per-particle latent representations learned during reconstruction as additional input features, we substantially improve over baselines that use conventional particle-level features alone. We further demonstrate that a single linear layer trained using only the latent representations achieves competitive performance against state-of-the-art baseline architectures, and outperforms the baseline for missing momentum regression with approximately 35 times fewer parameters. These results demonstrate that the latent representations learned during reconstruction encode essential physics information needed for downstream analysis, establishing MLPF as a foundation model and offering a concrete step toward an end-to-end pipeline from detector data to physics analysis.
Ting-Hsiang Hsu, Bai-Hong Zhou, Qibin Liu, Yue Xu, Shu Li, George Wei-Shu Hou, Benjamin Nachman, Shih-Chieh Hsu 等 11 位作者
Data-intensive collider experiments increasingly require models that transfer across high-dimensional, partially observed measurements, yet most analyses still optimize separate models for each task. Here, to address this bottleneck, we introduce EVENET, an event-level foundation model pretrained on 500 million simulated collision events using self-supervised learning and physics-informed supervision. The model constructs a shared particle-cloud representation from the variable-length set of physics objects in each event. Across searches for heavy resonances and exotic Higgs decays, EVENET outperforms both established and state-of-the-art baselines, particularly in low-statistics regimes. We validate transfer to experimental data by rediscovering the $Υ$ meson in CMS Open Data. The pretrained model also supports precise extraction of quantum-correlation observables that remain stable under the tested systematic variations. Together, these results establish a reusable backbone for diverse collider analyses, improving downstream adaptation after a substantial one-time pretraining investment.
Reinforcement learning (RL) is a machine learning paradigm in which an agent learns a decision-making policy by interacting with an environment, guided by a scalar reward rather than explicit supervision. Supervised and unsupervised learning have become indispensable tools in high-energy physics (HEP), but they learn from fixed datasets, whereas many HEP tasks are closed-loop decisions: the data an algorithm observes depend on its choices, the feedback is sparse or delayed, and the objective is often measured on a real machine or in a stochastic simulation, not by a differentiable model. This survey reviews the application of RL to such tasks: accelerator control and feedback, data quality monitoring, jet grooming, clustering, and representation, charged particle tracking, beyond-the-Standard-Model (BSM) and string model building, detector design, trigger control, analysis, and formal quantum field theory computation. It provides a self-contained introduction to the underlying RL methods, from model-free and model-based to multi-agent, offline, inverse, and bandit approaches, reviews each domain against its traditional methods, and summarizes the head-to-head comparisons. The applications range from policies deployed on real accelerators and evaluated on recorded collision data to exploratory studies in formal theory. RL is most advantageous for repeated tasks with a fast simulator, decisions inside fast control loops, operation under faults and corrupted measurements, physics-based rewards in place of labels, and sequential discrete constructions with a reusable policy, while Bayesian optimization, genetic algorithms, and differentiable methods remain competitive elsewhere. We conclude with the open challenges that recur across domains, including reward design, sim-to-real transfer, safety, the lack of shared benchmarks, and the statistical validity of policy-driven decisions.
Pratik Jawahar, Riccardo Maggioni, Jonas Petersen, Matteo Cozzi, Gian-Alessandro Lombardi, Marek Gajewski, Camilla Mazzoleni, Federico Martelli
Test-time compute mechanisms, such as retries, confidence-based escalation and non-local routing, are conventionally deployed as black-box additions to trained models. They typically add forward passes or halting heads, but give no structural account of what the extra compute buys or what it costs against the model's stability guarantees. We therefore propose a theoretical and empirical framework for test-time compute on a Latent Dynamics Model used as the memory. When an encoder's latent state $(q,p)$ is advanced by a damped symplectic (velocity-Verlet) step of a learned Hamiltonian, every mechanism that expands access has an exact phase-volume Jacobian, a bounded energy change and an exact latch-transport law. We split reachability failures into escape failures and reach failures. A Lorentz squeeze resolves escape failures by injecting bounded, re-absorbable energy. A gated canonical translation (a one-step channel across $C_T$) resolves reach failures at $\detJ=1$ exactly. We verify this certificate stack on a designed analytic testbed. Reaching just beyond $C_T$ with the squeeze requires energy that grows quadratically in the excess distance. The gated channel's energy cost equals the potential difference between its endpoints, which is zero on the matched channel measured here, and so does not grow with distance in this testbed. An untrained state-replacing map annihilates phase volume and erases stored charge, while the gated channel transports it. On a learned physics-structured memory, we show calibrated compute rationing and evaluate the scaling limits of non-local routing against a physics-free baseline. The main contribution is the formalization and verification of the certificate stack, not benchmark performance.
Giada Badaracco, Sean Benevedes, Christina Reissel, Philip Harris, Gaia Grosso
Density estimation with generative models is a common task in the physical sciences, for example in background estimation in particle physics. Existing machine learning techniques, however, lack methods to quantify uncertainties that can be propagated into a statistical test. That limits the validation of generative models to standard goodness-of-fit tests, in which the generative model is treated as exact (point-null hypothesis). But a model fitted to a finite training set is never exact, so if its uncertainties are neglected, any sufficiently powerful goodness-of-fit test will eventually reject it once the test set is large enough to resolve this estimation error. We propose SIGMA, an end-to-end framework combining density estimation with principled uncertainty quantification. We use Gaussian mixture models, for which uncertainties are tractable, and further construct a new goodness-of-fit test in which these uncertainties are profiled as nuisance parameters to account for the statistical error of the fit, promoting the conventional point-null test to a composite one. A rejection then signals genuine mismodeling rather than a test set large enough to resolve the error of the fit, provided the propagated uncertainties faithfully cover that error. We demonstrate the framework on a controlled two-dimensional toy model and on a collider physics benchmark modeling the QCD background process. With uncertainties included, the same model can be trusted on test sets up to an order of magnitude larger than the standard test allows. Our work thus provides a statistically grounded basis for a robust use of generative models in the physical sciences.
Lund-plane and Particle Transformer (ParT) jet taggers can differ in performance because one representation is weaker, or because a weaker downstream computation reads an adequate one. Standalone performance cannot separate these. Model stitching can: it links the frozen early layers of one network to the frozen late layers of another through a single trained linear map. As a positive control we use an incomplete Lund representation, the primary declustering branch, whose deficit is known independently. Stitched into ParT's downstream, it reaches a background rejection at least as much as its own downstream recovers, yet far below ParT's background rejection: the deficit is representational, not computational. A hypergraph reader over splitting triplets does no better, ruling out higher-order correlations as the cause. The gap is invisible in AUC, which stays within 1\% of its target value, and appears only in background rejection at low signal efficiency. It localizes to 0.6\% of background jets, at and above the top mass, with more constituents but fewer primary splittings than typical background. Rebuilding the representation on the full Cambridge/Aachen declustering tree repairs the deficit as predicted: standalone rejection rises, closing 72\% of the gap. Masking nodes at inference shows the repaired network still relies almost entirely on the primary branch; the secondary splittings make the representation learnable rather than supplying information it reads. Along the primary branch, the widest-angle splitting, near the top and $W$ opening angles, is worth nearly twice a random one. For quark/gluon tagging the primary branch is far less deficient, retaining 77.6\% of ParT's rejection (46.9\% for top), and the full tree closes only 33\% of the gap (72\% for top).
We study the training dynamics of a feed-forward neural network (NN) through the analysis of the neural tangent kernel (NTK) in a phenomenologically relevant fit of parton distribution functions (PDFs) from deep inelastic scattering (DIS) data. The exact integration of the gradient flow derived in a previous single-flavour analysis is generalised to the multi-flavour case, yielding an analytical perspective on the relationship between data and methodology during training. The Shapley value recently used in the context of PDFs is derived within our statistical framework for observables that depend linearly on the PDFs, and we outline a geometric interpretation of training. We expose the role of gradient-based optimisation algorithms and of the parametrisation in the regularisation of the ill-posed inverse problem that affects the determination of PDFs from experimental data, demonstrating that the regularisation amounts to the incremental inclusion of NTK modes, each learned at the timescale set by the corresponding eigenvalue. We find that only a few leading modes of the NTK are necessary to reconstruct the target PDFs, while the noise of the data is carried by the sub-leading ones learned at later stages of training. Finally, we consider the impact of the initialisation on the training dynamics, and recover a transient behaviour observed in the previous analysis and in the machine learning (ML) literature. Beyond sharpening our understanding of the training dynamics, our framework can be applied to other parametrisations (such as fixed functional forms) and ML applications in physics, as well as to stress tests in the presence of inconsistent data.