Jet tagging is a central task in collider physics. Over the past decade, machine learning has driven major advances in jet tagging, with increasingly sophisticated architectures achieving very high classification performance on simulated datasets [1-11]. This success naturally raises a key question: have current jet taggers already reached the fundamental limit of jet tagging, or does a gap remain between practical performance and the true statistical optimum? The Neyman-Pearson (NP) limit, defined by the likelihood ratio, is the best possible discriminant between two different underlying physics processes - such as top and QCD jets - that any classifier could achieve if it had access to the exact data likelihoods [12]. In practice, however, this limit cannot be evaluated directly because the true likelihood of the data-generating process is unknown. It therefore remains unclear how close existing classifiers are to this ultimate bound. Recently, Ref. [13] proposed using autoregressive GPT-style generative models to probe this limit for top vs. QCD jets from the JetClass dataset [14]. These models operate on discretized, tokenized representations of jet constituents and yield explicit log-likelihoods, enabling the computation of likelihood ratios between jet classes.

Figure 7: Jet images averaged over 10000 jet samples.

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.

Figure 7: Jet images averaged over 10000 jet samples.

Foundation models are deep learning models pre-trained on large amounts of data which are capable of generalizing to multiple datasets and/or downstream tasks. This work demonstrates how data collected by the CMS experiment at the Large Hadron Collider can be useful in pre-training foundation models for HEP. Specifically, we introduce the AspenOpenJets dataset, consisting of approximately 180M high $p_T$ jets derived from CMS 2016 Open Data. We show how pre-training the OmniJet-$\alpha$ foundation model on AspenOpenJets improves performance on generative tasks with significant domain shift: generating boosted top and QCD jets from the simulated JetClass dataset. In addition to demonstrating the power of pre-training of a jet-based foundation model on actual proton-proton collision data, we provide the ML-ready derived AspenOpenJets dataset for further public use.

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a function of training set size, with distinct power law indices. This result highlights the importance of comparing classifiers as a function of dataset size rather than for a fixed training set, as the optimal classifier may change considerably as the dataset is scaled up. We speculate on the interpretation of our results in terms of previous models of scaling laws observed in natural language and image datasets.

At the CERN LHC, the task of jet tagging, whose goal is to infer the origin of a jet given a set of final-state particles, is dominated by machine learning methods. Graph neural networks have been used to address this task by treating jets as point clouds with underlying, learnable, edge connections between the particles inside. We explore the decision-making process for one such state-of-the-art network, ParticleNet, by looking for relevant edge connections identified using the layerwise-relevance propagation technique. As the model is trained, we observe changes in the distribution of relevant edges connecting different intermediate clusters of particles, known as subjets. The resulting distribution of subjet connections is different for signal jets originating from top quarks, whose subjets typically correspond to its three decay products, and background jets originating from lighter quarks and gluons. This behavior indicates that the model is using traditional jet substructure observables, such as the number of prongs -- energetic particle clusters -- within a jet, when identifying jets.

Autoencoders are widely used in machine learning applications, in particular for anomaly detection. Hence, they have been introduced in high energy physics as a promising tool for model-independent new physics searches. We scrutinize the usage of autoencoders for unsupervised anomaly detection based on reconstruction loss to show their capabilities, but also their limitations. As a particle physics benchmark scenario, we study the tagging of top jet images in a background of QCD jet images. Although we reproduce the positive results from the literature, we show that the standard autoencoder setup cannot be considered as a model-independent anomaly tagger by inverting the task: due to the sparsity and the specific structure of the jet images, the autoencoder fails to tag QCD jets if it is trained on top jets even in a semi-supervised setup.

We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which quantifies the "work" required to rearrange one event into another, while significantly reducing the computational cost. It also furnishes a Euclidean embedding amenable to simple machine learning algorithms and visualization techniques, which we demonstrate in a variety of jet tagging examples. The LOT approximation lowers the threshold for diverse applications of the theory of optimal transport to collider physics.