Artificial Intelligence and Symmetries: Learning, Encoding, and Discovering Structure in Physical Data

Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a remarkable ability to extract low-dimensional structure from high-dimensional data through representation learning. This review examines the interplay between these two perspectives, focusing on the extent to which symmetry-induced constraints can be identified, encoded, or diagnosed using machine learning techniques. Rather than emphasizing architectures that enforce known symmetries by construction, we concentrate on data-driven approaches and latent representation learning, with particular attention to variational autoencoders. We discuss how symmetries and conservation laws reduce the intrinsic dimensionality of physical datasets, and how this reduction may manifest itself through self-organization of latent spaces in generative models trained to balance reconstruction and compression. We review recent results, including case studies from simple geometric systems and particle physics processes, and analyze the theoretical and practical limitations of inferring symmetry structure without explicit inductive bias.

Strengthening Anomaly Awareness

We present a refined version of the Anomaly Awareness framework for enhancing unsupervised anomaly detection. Our approach introduces minimal supervision into Variational Autoencoders (VAEs) through a two-stage training strategy: the model is first trained in an unsupervised manner on background data, and then fine-tuned using a small sample of labeled anomalies to encourage larger reconstruction errors for anomalous samples. We validate the method across diverse domains, including the MNIST dataset with synthetic anomalies, network intrusion data from the CICIDS benchmark, collider physics data from the LHCO2020 dataset, and simulated events from the Standard Model Effective Field Theory (SMEFT). The latter provides a realistic example of subtle kinematic deviations in Higgs boson production. In all cases, the model demonstrates improved sensitivity to unseen anomalies, achieving better separation between normal and anomalous samples. These results indicate that even limited anomaly information, when incorporated through targeted fine-tuning, can substantially improve the generalization and performance of unsupervised models for anomaly detection.

Learning symmetries in datasets

We investigate how symmetries present in datasets affect the structure of the latent space learned by Variational Autoencoders (VAEs). By training VAEs on data originating from simple mechanical systems and particle collisions, we analyze the organization of the latent space through a relevance measure that identifies the most meaningful latent directions. We show that when symmetries or approximate symmetries are present, the VAE self-organizes its latent space, effectively compressing the data along a reduced number of latent variables. This behavior captures the intrinsic dimensionality determined by the symmetry constraints and reveals hidden relations among the features. Furthermore, we provide a theoretical analysis of a simple toy model, demonstrating how, under idealized conditions, the latent space aligns with the symmetry directions of the data manifold. We illustrate these findings with examples ranging from two-dimensional datasets with $O(2)$ symmetry to realistic datasets from electron-positron and proton-proton collisions. Our results highlight the potential of unsupervised generative models to expose underlying structures in data and offer a novel approach to symmetry discovery without explicit supervision.

Establishing a real-time traffic alarm in the city of Valencia with Deep Learning

Urban traffic emissions represent a significant concern due to their detrimental impacts on both public health and the environment. Consequently, decision-makers have flagged their reduction as a crucial goal. In this study, we first analyze the correlation between traffic flux and pollution in the city of Valencia, Spain. Our results demonstrate that traffic has a significant impact on the levels of certain pollutants (especially $\text{NO}_\text{x}$). Secondly, we develop an alarm system to predict if a street is likely to experience unusually high traffic in the next 30 minutes, using an independent three-tier level for each street. To make the predictions, we use traffic data updated every 10 minutes and Long Short-Term Memory (LSTM) neural networks. We trained the LSTM using traffic data from 2018, and tested it using traffic data from 2019.

Exploring how a Generative AI interprets music

We use Google's MusicVAE, a Variational Auto-Encoder with a 512-dimensional latent space to represent a few bars of music, and organize the latent dimensions according to their relevance in describing music. We find that, on average, most latent neurons remain silent when fed real music tracks: we call these "noise" neurons. The remaining few dozens of latent neurons that do fire are called "music neurons". We ask which neurons carry the musical information and what kind of musical information they encode, namely something that can be identified as pitch, rhythm or melody. We find that most of the information about pitch and rhythm is encoded in the first few music neurons: the neural network has thus constructed a couple of variables that non-linearly encode many human-defined variables used to describe pitch and rhythm. The concept of melody only seems to show up in independent neurons for longer sequences of music.

Predicting the traffic flux in the city of Valencia with Deep Learning

Traffic congestion is a major urban issue due to its adverse effects on health and the environment, so much so that reducing it has become a priority for urban decision-makers. In this work, we investigate whether a high amount of data on traffic flow throughout a city and the knowledge of the road city network allows an Artificial Intelligence to predict the traffic flux far enough in advance in order to enable emission reduction measures such as those linked to the Low Emission Zone policies. To build a predictive model, we use the city of Valencia traffic sensor system, one of the densest in the world, with nearly 3500 sensors distributed throughout the city. In this work we train and characterize an LSTM (Long Short-Term Memory) Neural Network to predict temporal patterns of traffic in the city using historical data from the years 2016 and 2017. We show that the LSTM is capable of predicting future evolution of the traffic flux in real-time, by extracting patterns out of the measured data.

Symmetry meets AI

We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no information on symmetry is provided. We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance. As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.

Anomaly Awareness

We present a new Machine Learning algorithm called Anomaly Awareness. By making our algorithm aware of the presence of a range of different anomalies, we improve its capability to detect anomalous events, even those it had not been exposed to. As an example of use, we apply this method to searches for new phenomena in the Large Hadron Collider. In particular, we analyze events with boosted jets where new physics could be hiding.

Developing an App to interpret Chest X-rays to support the diagnosis of respiratory pathology with Artificial Intelligence

In this paper we present our work to improve access to diagnosis in remote areas where good quality medical services may be lacking. We develop new Machine Learning methodologies for deployment onto mobile devices to help the early diagnosis of a number of life-threatening conditions using X-ray images. By using the latest developments in fast and portable Artificial Intelligence environments, we develop a smartphone app using an Artificial Neural Network to assist physicians in their diagnostic.