arXiv subjects

Alex Rodriguez

Publications and source records attributed to Alex Rodriguez.

At least 19 recordsLinked to original sources

arXiv2026

Machine learning the non-radiative decay modes in photochemical processes

Non-radiative decay in photoexcited molecular systems is driven by nuclear motion toward conical intersections (CIs), where electronic states become degenerate and nonadiabatic transitions occur. Identifying the nuclear degrees of freedom responsible for CI access from nonadiabatic molecular dynamics (NAD) simulations remains challenging because the underlying motions are high-dimensional and collective. Here, we introduce an unsupervised, information-theoretic framework based on Differentiable Information Imbalance (DII) to identify the nuclear coordinates governing CI access directly from trajectory surface hopping (TSH) simulations. By quantifying correlations between structural descriptors and electronic observables, including energy gaps and oscillator strengths, the method ranks nuclear degrees of freedom by predictive relevance. A multi-step protocol then extracts low-dimensional, physically interpretable modes associated with non-radiative decay. We apply the framework to the methaniminium cation, furan, L-glutamine, L-pyroglutamine-ammonium, and a photoactive molecular motor. Across all systems, the method recovers known mechanistic coordinates while revealing the relative importance of competing modes when multiple structural distortions contribute to CI access. The analysis also reveals a systematic distinction between observables: energy gaps are typically governed by a small number of localized coordinates, whereas oscillator strengths depend on more collective and distributed structural rearrangements. Overall, the DII-based framework combines predictive power with direct interpretability, providing a general and scalable route for extracting mechanistic insight from high-dimensional NAD data and constructing reduced-dimensional models of excited-state dynamics.

physics.chem-ph↗

arXiv2026

Flexible curves and Hausdorff dimension

We show that given a log-singular circle homeomorphism $h$ and given any $s\in[1,2]$, there is a flexible curve of Hausdorff dimension $s$ with welding $h$. We also see that there is another curve with welding $h$ and positive area. In particular, this implies that given a flexible curve $\Gamma$, there is a homeomorphism of the plane $\phi\colon\mathbb{C}\to\mathbb{C}$, conformal off $\Gamma$, so that $\phi(\Gamma)$ has positive area. This answers a particular case of the corresponding conjecture for general non-conformally removable sets, for a class of curves that is residual in the space of all Jordan curves.

math.CV↗

arXiv2025

Density-Informed VAE (DiVAE): Reliable Log-Prior Probability via Density Alignment Regularization

We introduce Density-Informed VAE (DiVAE), a lightweight, data-driven regularizer that aligns the VAE log-prior probability $\log p_Z(z)$ with a log-density estimated from data. Standard VAEs match latents to a simple prior, overlooking density structure in the data-space. DiVAE encourages the encoder to allocate posterior mass in proportion to data-space density and, when the prior is learnable, nudges the prior toward high-density regions. This is realized by adding a robust, precision-weighted penalty to the ELBO, incurring negligible computational overhead. On synthetic datasets, DiVAE (i) improves distributional alignment of latent log-densities to its ground truth counterpart, (ii) improves prior coverage, and (iii) yields better OOD uncertainty calibration. On MNIST, DiVAE improves alignment of the prior with external estimates of the density, providing better interpretability, and improves OOD detection for learnable priors.

cs.LG↗

arXiv2025

Beyond single-model XAI: aggregating multi-model explanations for enhanced trustworthiness

The use of Artificial Intelligence (AI) models in real-world and high-risk applications has intensified the discussion about their trustworthiness and ethical usage, from both a technical and a legislative perspective. The field of eXplainable Artificial Intelligence (XAI) addresses this challenge by proposing explanations that bring to light the decision-making processes of complex black-box models. Despite being an essential property, the robustness of explanations is often an overlooked aspect during development: only robust explanation methods can increase the trust in the system as a whole. This paper investigates the role of robustness through the usage of a feature importance aggregation derived from multiple models ($k$-nearest neighbours, random forest and neural networks). Preliminary results showcase the potential in increasing the trustworthiness of the application, while leveraging multiple model's predictive power.

cs.LG↗

arXiv2025

Assessing reliability of explanations in unbalanced datasets: a use-case on the occurrence of frost events

The usage of eXplainable Artificial Intelligence (XAI) methods has become essential in practical applications, given the increasing deployment of Artificial Intelligence (AI) models and the legislative requirements put forward in the latest years. A fundamental but often underestimated aspect of the explanations is their robustness, a key property that should be satisfied in order to trust the explanations. In this study, we provide some preliminary insights on evaluating the reliability of explanations in the specific case of unbalanced datasets, which are very frequent in high-risk use-cases, but at the same time considerably challenging for both AI models and XAI methods. We propose a simple evaluation focused on the minority class (i.e. the less frequent one) that leverages on-manifold generation of neighbours, explanation aggregation and a metric to test explanation consistency. We present a use-case based on a tabular dataset with numerical features focusing on the occurrence of frost events.

cs.LG↗

arXiv2025

Opportunities and Challenges in Unsupervised Learning: The Case of Aqueous Electrolyte Solutions

Machine learning has emerged as a powerful tool in atomistic simulations, enabling the identification of complex patterns in molecular systems limiting human intervention and bias. However, the practical implementation of these methods presents significant technical challenges, particularly in the selection of hyperparameters and in the physical interpretability of machine-learned descriptors. In this work, we systematically investigate these challenges by applying an unsupervised learning protocol to a fundamental problem in physical chemistry namely, how ions perturb the local structure of water. Using the Smooth Overlap of Atomic Positions(SOAP) descriptors, we demonstrate how the intrinsic dimension (ID) serves as a guide for selecting hyperparameters and interpreting structural complexity. Furthermore, we construct a high-dimensional free energy landscape encompassing all water environments surrounding different ions. This analysis reveals how the physical properties of ions are intricately reflected in their hydration shells, shaping the landscape through specific connections between different minima. Our findings highlight the difficulty in balancing algorithmic automation with the need of employing both physical and chemical intuition, particularly for the construction of meaningful descriptors and for the interpretation of final results. By critically assessing the methodological hurdles associated with unsupervised learning, we provide a road map for researchers looking to harness these techniques for studying electrolyte and aqueous solutions in general.

physics.chem-ph↗

arXiv2025

Every circle homeomorphism is the composition of two weldings

We show that every orientation-preserving circle homeomorphism is a composition of two conformal welding homeomorphisms, which implies that conformal welding homeomorphisms are not closed under composition. Our approach uses the log-singular maps introduced by Bishop. The main tool that we introduce are log-singular sets, which are zero capacity sets that admit a log-singular map that maps their complement to a zero capacity set.

math.CV↗

arXiv2024

Unsupervised detection of semantic correlations in big data

In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to semantic roles and are naturally recognized by both the human brain and artificial neural networks. This recognition enables, for instance, the prediction of missing parts of an image or text based on their context. We present a method to detect these correlations in high-dimensional data represented as binary numbers. We estimate the binary intrinsic dimension of a dataset, which quantifies the minimum number of independent coordinates needed to describe the data, and is therefore a proxy of semantic complexity. The proposed algorithm is largely insensitive to the so-called curse of dimensionality, and can therefore be used in big data analysis. We test this approach identifying phase transitions in model magnetic systems and we then apply it to the detection of semantic correlations of images and text inside deep neural networks.

cs.LG↗

arXiv2024

Advances in Privacy Preserving Federated Learning to Realize a Truly Learning Healthcare System

The concept of a learning healthcare system (LHS) envisions a self-improving network where multimodal data from patient care are continuously analyzed to enhance future healthcare outcomes. However, realizing this vision faces significant challenges in data sharing and privacy protection. Privacy-Preserving Federated Learning (PPFL) is a transformative and promising approach that has the potential to address these challenges by enabling collaborative learning from decentralized data while safeguarding patient privacy. This paper proposes a vision for integrating PPFL into the healthcare ecosystem to achieve a truly LHS as defined by the Institute of Medicine (IOM) Roundtable.

cs.CR↗

arXiv2024

Density Estimation via Binless Multidimensional Integration

We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences between neighbouring data points. Subsequently, such differences are integrated, weighted by their associated uncertainties, using a maximum-likelihood formulation. This procedure can be seen as an extension to a multidimensional setting of the thermodynamic integration, a technique developed in statistical physics. The method leverages the manifold hypothesis, estimating quantities within the intrinsic data manifold without defining an explicit coordinate map. It does not rely on any binning or space partitioning, but rather on the construction of a neighbourhood graph based on an adaptive bandwidth selection procedure. BMTI mitigates the limitations commonly associated with traditional nonparametric density estimators, effectively reconstructing smooth profiles even in high-dimensional embedding spaces. The method is tested on a variety of complex synthetic high-dimensional datasets, where it is shown to outperform traditional estimators, and is benchmarked on realistic datasets from the chemical physics literature.

stat.ML↗

arXiv2024

Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear nature, which makes them challenging to detect using standard methods. This paper exploits the entanglement between intrinsic dimensionality and correlation to propose a metric that quantifies the (potentially nonlinear) correlation between high-dimensional manifolds. We first validate our method on synthetic data in controlled environments, showcasing its advantages and drawbacks compared to existing techniques. Subsequently, we extend our analysis to large-scale applications in neural network representations. Specifically, we focus on latent representations of multimodal data, uncovering clear correlations between paired visual and textual embeddings, whereas existing methods struggle significantly in detecting similarity. Our results indicate the presence of highly nonlinear correlation patterns between latent manifolds.

cs.LG↗

arXiv2024

When Can You Trust Your Explanations? A Robustness Analysis on Feature Importances

Recent legislative regulations have underlined the need for accountable and transparent artificial intelligence systems and have contributed to a growing interest in the Explainable Artificial Intelligence (XAI) field. Nonetheless, the lack of standardized criteria to validate explanation methodologies remains a major obstacle to developing trustworthy systems. We address a crucial yet often overlooked aspect of XAI, the robustness of explanations, which plays a central role in ensuring trust in both the system and the provided explanation. To this end, we propose a novel approach to analyse the robustness of neural network explanations to non-adversarial perturbations, leveraging the manifold hypothesis to produce new perturbed datapoints that resemble the observed data distribution. We additionally present an ensemble method to aggregate various explanations, showing how merging explanations can be beneficial for both understanding the model's decision and evaluating the robustness. The aim of our work is to provide practitioners with a framework for evaluating the trustworthiness of model explanations. Experimental results on feature importances derived from neural networks applied to tabular datasets highlight the importance of robust explanations in practical applications.

cs.LG↗

arXiv2024

Large disks touching three sides of a quadrilateral

We show that every Jordan quadrilateral $Q\subset\mathbb{C}$ contains a disk $D$ so that $\partial D\cap\partial Q$ contains points of three different sides of $Q$. As a consequence, together with some modulus estimates from Lehto and Virtanen, we offer a short proof of the main result obtained by Chrontsios-Garitsis and Hinkkanen in 2024 and it also improves the bounds on their result.

math.CV↗

arXiv2024

Aqueous Solution Chemistry In Silico and the Role of Data Driven Approaches

The use of computer simulations to study the properties of aqueous systems is, today more than ever, an active area of research. In this context, during the last decade there has been a tremendous growth in the use of data-driven approaches to develop more accurate potentials for water as well as to characterize its complexity in chemical and biological contexts. We highlight the progress, giving a historical context, on the path to the development of many-body and reactive potentials to model aqueous chemistry, including the role of machine learning strategies. We focus specifically on conceptual and methodological challenges along the way in performing simulations that seek to tackle problems in modeling the chemistry of aqueous solutions. In conclusion, we summarize our perspectives on the use and integration of advanced data-science techniques to provide chemical insights in physical chemistry and how this will influence computer simulations of aqueous systems in the future.

physics.chem-ph↗

arXiv2024

Beyond Local Structures In Critical Supercooled Water Through Unsupervised Learning

The presence of a second critical point in water has been a topic of intense investigation for the last few decades. The molecular origins underlying this phenomenon are typically rationalized in terms of the competition between local high-density (HD) and low-density (LD) structures. Their identification often require designing parameters that are subject to human intervention. Herein, we use unsupervised learning to discover structures in atomistic simulations of water close to the Liquid-Liquid Critical point (LLCP). Encoding the information of the environment using local descriptors, we do not find evidence for two distinct thermodynamic structures. In contrast, when we deploy non-local descriptors that probe instead heterogeneities on the nanometer length scale, this leads to the emergence of LD and HD domains rationalizing the microscopic origins of the density fluctuations close to criticality.

cond-mat.soft↗

arXiv2023

Machine Learning Catalysis of Quantum Tunneling

Optimizing the probability of quantum tunneling between two states, while keeping the resources of the underlying physical system constant, is a task of key importance due to its critical role in various applications. We show that, by applying Machine Learning techniques when the system is coupled to an ancilla, one optimizes the parameters of both the ancillary component and the coupling, ultimately resulting in the maximization of the tunneling probability. We provide illustrative examples for the paradigmatic scenario involving a two-mode system and a two-mode ancilla in the presence of several interacting particles. Physically, the increase of the tunneling probability is rooted in the decrease of the two-well asymmetry due to the coherent oscillations induced by the coupling to the ancilla. We also argue that the enhancement of the tunneling probability is not hampered by weak coupling to noisy environments.

quant-ph↗

arXiv2023

ZundEig: The Structure of the Proton in Liquid Water From Unsupervised Learning

The structure of the excess proton in liquid water has been the subject of lively debate from both experimental and theoretical fronts for the last century. Fluctuations of the proton are typically interpreted in terms of limiting states referred to as the Eigen and Zundel species. Here we put these ideas under the microscope taking advantage of recent advances in unsupervised learning that use local atomic descriptors to characterize environments of acidic water combined with advanced clustering techniques. Our agnostic approach leads to the observation of only a single charged cluster and two neutral ones. We demonstrate that the charged cluster involving the excess proton, is best seen as an ionic topological defect in water's hydrogen bond network forming a single local minimum on the global free-energy landscape. This charged defect is a highly fluxional moiety where the idealized Eigen and Zundel species are neither limiting configurations nor distinct thermodynamic states. Instead, the ionic defect enhances the presence of neutral water defects through strong interactions with the network. We dub the combination of the charged and neutral defect clusters as ZundEig demonstrating that the fluctuations between these local environments provide a general framework for rationalizing more descriptive notions of the proton in the existing literature.

cond-mat.mtrl-sci↗

arXiv2023

Network science Ising states of matter

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the $2$D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the $2$D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data.

cond-mat.dis-nn↗