Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty. Learning a separate flow for every parameter configuration quickly becomes intractable, since the number of joint settings grows exponentially with the number of parameters. We introduce Factorizable Normalizing Flows (FNFs), which represent the parameter-dependent density as a fixed, high-fidelity flow for a reference configuration composed with a learnable transformation that is polynomial in the parameters and factorized over them. This structure has a practical consequence: each parameter's effect is learned in isolation, from samples in which that parameter alone is varied. The combined response of many parameters is then recovered by summation at inference, without ever sampling their combinatorially large joint space. On a controlled problem with two interpretable deformations applied jointly to the data, the learned transformation reproduces the true deformations and matches the optimal likelihood, while optional interaction terms capture residual correlations when several parameters vary strongly at once. The resulting model is interpretable, scales linearly with the number of parameters, and keeps the likelihood tractable. This provides a general tool for any inference workflow requiring continuous density morphing, and directly enables the next generation of unbinned likelihood fits in high energy physics.

Neural Information Processing Systems http://nips.cc/

Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo simulations. In this work, we introduce HI-SIGMA, a method to perform unbinned high-dimensional statistical inference with data-driven background distributions. In contradistinction to many applications of Simulation Based Inference in High Energy Physics, HI-SIGMA relies on generative ML models, rather than classifiers, to learn the signal and background distributions in the high-dimensional space. These ML models allow for efficient, interpretable inference while also incorporating model errors and other sources of systematic uncertainties. We showcase this methodology on a simplified version of a di-Higgs measurement in the $bbγγ$ final state, where the di-photon resonance allows for efficient background interpolation from sidebands into the signal region. We demonstrate that HI-SIGMA provides improved sensitivity as compared to standard classifier-based methods, and that systematic uncertainties can be straightforwardly incorporated by extending methods which have been used for histogram based analyses.

The FAIR Universe -- HiggsML Uncertainty Challenge focuses on measuring the physics properties of elementary particles with imperfect simulators due to differences in modelling systematic errors. Additionally, the challenge is leveraging a large-compute-scale AI platform for sharing datasets, training models, and hosting machine learning competitions. Our challenge brings together the physics and machine learning communities to advance our understanding and methodologies in handling systematic (epistemic) uncertainties within AI techniques.

Weak supervision combines the advantages of training on real data with the ability to exploit signal properties. However, training a neural network using weak supervision often requires an excessive amount of signal data, which severely limits its practical applicability. In this study, we propose addressing this limitation through data augmentation, increasing the training data's size and diversity. Specifically, we focus on physics-inspired data augmentation methods, such as $p_{\text{T}}$ smearing and jet rotation. Our results demonstrate that data augmentation can significantly enhance the performance of weak supervision, enabling neural networks to learn efficiently from substantially less data.

Several techniques for domain adaptation have been proposed to account for differences in the distribution of the data used for training and testing. The majority of this work focuses on a binary domain label. Similar problems occur in a scientific context where there may be a continuous family of plausible data generation processes associated to the presence of systematic uncertainties. Robust inference is possible if it is based on a pivot - a quantity whose distribution does not depend on the unknown values of the nuisance parameters that parametrize this family of data generation processes. In this work, we introduce and derive theoretical results for a training procedure based on adversarial networks for enforcing the pivotal property (or, equivalently, fairness with respect to continuous attributes) on a predictive model. The method includes a hyperparameter to control the tradeoff between accuracy and robustness. We demonstrate the effectiveness of this approach with a toy example and examples from particle physics.

In the field of high-energy physics, deep learning algorithms continue to gain in relevance and provide performance improvements over traditional methods, for example when identifying rare signals or finding complex patterns. From an analyst's perspective, obtaining highest possible performance is desirable, but recently, some attention has been shifted towards studying robustness of models to investigate how well these perform under slight distortions of input features. Especially for tasks that involve many (low-level) inputs, the application of deep neural networks brings new challenges. In the context of jet flavor tagging, adversarial attacks are used to probe a typical classifier's vulnerability and can be understood as a model for systematic uncertainties. A corresponding defense strategy, adversarial training, improves robustness, while maintaining high performance. Investigating the loss surface corresponding to the inputs and models in question reveals geometric interpretations of robustness, taking correlations into account.

Estimating uncertainty is at the core of performing scientific measurements in HEP: a measurement is not useful without an estimate of its uncertainty. The goal of uncertainty quantification (UQ) is inextricably linked to the question, "how do we physically and statistically interpret these uncertainties?" The answer to this question depends not only on the computational task we aim to undertake, but also on the methods we use for that task. For artificial intelligence (AI) applications in HEP, there are several areas where interpretable methods for UQ are essential, including inference, simulation, and control/decision-making. There exist some methods for each of these areas, but they have not yet been demonstrated to be as trustworthy as more traditional approaches currently employed in physics (e.g., non-AI frequentist and Bayesian methods). Shedding light on the questions above requires additional understanding of the interplay of AI systems and uncertainty quantification. We briefly discuss the existing methods in each area and relate them to tasks across HEP. We then discuss recommendations for avenues to pursue to develop the necessary techniques for reliable widespread usage of AI with UQ over the next decade.

The advent of deep learning has yielded powerful tools to automatically compute gradients of computations. This is because training a neural network equates to iteratively updating its parameters using gradient descent to find the minimum of a loss function. Deep learning is then a subset of a broader paradigm; a workflow with free parameters that is end-to-end optimisable, provided one can keep track of the gradients all the way through. This work introduces neos: an example implementation following this paradigm of a fully differentiable high-energy physics workflow, capable of optimising a learnable summary statistic with respect to the expected sensitivity of an analysis. Doing this results in an optimisation process that is aware of the modelling and treatment of systematic uncertainties.

Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the dimensionality using feature engineering and histograms, whereby the latter technique allows to build the likelihood using Poisson statistics. However, in the presence of systematic uncertainties represented by nuisance parameters in the likelihood, the optimal dimensionality reduction with a minimal loss of information about the parameters of interest is not known. This work presents a novel strategy to construct the dimensionality reduction with neural networks for feature engineering and a differential formulation of histograms so that the full workflow can be optimized with the result of the statistical inference, e.g., the variance of a parameter of interest, as objective. We discuss how this approach results in an estimate of the parameters of interest that is close to optimal and the applicability of the technique is demonstrated with a simple example based on pseudo-experiments and a more complex example from high-energy particle physics.