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The phase-amplitude framework extends the classical phase reduction method by incorporating amplitude coordinates (or isostables) to describe transient dynamics transverse to the limit cycle in a simplified form. While the full set of amplitude coordinates provides an exact description of oscillatory dynamics, it maintains the system's original dimensionality, limiting the advantages of simplification. A more effective approach reduces the dynamics to the slow attracting invariant submanifold associated with the slowest contracting direction, achieving a balance between simplification and accuracy. In this work, we present an efficient numerical method to compute the parameterization of the attracting slow submanifold of hyperbolic limit cycles and the simplified dynamics in its induced coordinates. Additionally, we compute the infinitesimal Phase and Amplitude Response Functions (iPRF and iARF, respectively) restricted to this manifold, which characterize the effects of perturbations on phase and amplitude. These results are obtained by solving an invariance equation for the slow manifold and adjoint equations for the iPRF and iARF. To solve these functional equations efficiently, we employ the Floquet normal form to solve the invariance equation and propose a novel coordinate transformation to simplify the adjoint equations. The solutions are expressed as Fourier-Taylor expansions with arbitrarily high accuracy. Our method accommodates both real and complex Floquet exponents. Finally, we discuss the numerical implementation of the method and present results from its application to a representative example.

We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensional case, this constant is even optimal. From these inequalities, we derive concentration results, which allow concluding the case of the pathological dimension two.

This article introduces a groundbreaking analytical workflow designed for the holistic characterisation, modelling and physical simulation of device heterostructures. Our innovative workflow autonomously, comprehensively and locally characterises the crystallographic information and 3D orientation of the crystal phases, the elemental composition, and the strain maps of devices from (scanning) transmission electron microscopy data. It converts a manual characterisation process that traditionally takes days into an automatic routine completed in minutes. This is achieved through a physics-guided artificial intelligence model that combines unsupervised and supervised machine learning in a modular way to provide a representative 3D description of the devices, materials structures, or samples under analysis. To culminate the process, we integrate the extracted knowledge to automate the generation of both 3D finite element and atomic models of millions of atoms acting as digital twins, enabling simulations that yield essential physical and chemical insights crucial for understanding the device's behaviour in practical applications. We prove this end-to-end workflow with a state-of-the-art materials platform based on SiGe planar heterostructures for hosting coherent and scalable spin qubits. Our workflow connects representative digital twins of the experimental devices with their theoretical properties to reveal the true impact that every atom in the structure has on their electronic properties, and eventually, into their functional quantum performance. Notably, the versatility of our workflow is demonstrated through its successful application to a wide array of materials systems, device configurations and sample morphologies.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference., Comment: To be published in Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS 2025)

The ubiquitous phenomena of crystallization and melting occur in various geophysical contexts across many spatial and temporal scales. In particular, they take place in the iron core of terrestrial planets and moons, profoundly influencing their dynamics and magnetic field generation. Crystallization and melting entail intricate multiphase flows, buoyancy effects, and out-of-equilibrium thermodynamics, posing challenges for theoretical modeling and numerical simulations. Besides, due to the inaccessible nature of the planetary deep interior, our understanding relies on indirect data from seismology, mineral physics, geochemistry, and magnetism. Consequently, phase-change-driven flows in planetary cores constitute a compelling yet challenging area of research. This paper provides an overview of the role of laboratory fluid dynamics experiments in elucidating the solid-liquid phase change phenomena occurring thousands of kilometers beneath our feet and within other planetary depths, along with their dynamic repercussions. Drawing parallel with metallurgy, it navigates through all scales of phase change dynamics, from microscopic processes (nucleation and crystal growth) to macroscopic consequences (solid-liquid segregation and large-scale flows). The review delves into the two primary planetary solidification regimes, top-down and bottom-up, and elucidates the formation of mushy and/or slurry layers in the various relevant configurations. Additionally, it outlines remaining challenges, including insights from ongoing space missions poised to unveil the diverse planetary regimes., Comment: 40 pages; 16 figures

Machine Translation (MT) evaluation metrics assess translation quality automatically. Recently, researchers have employed MT metrics for various new use cases, such as data filtering and translation re-ranking. However, most MT metrics return assessments as scalar scores that are difficult to interpret, posing a challenge to making informed design choices. Moreover, MT metrics' capabilities have historically been evaluated using correlation with human judgment, which, despite its efficacy, falls short of providing intuitive insights into metric performance, especially in terms of new metric use cases. To address these issues, we introduce an interpretable evaluation framework for MT metrics. Within this framework, we evaluate metrics in two scenarios that serve as proxies for the data filtering and translation re-ranking use cases. Furthermore, by measuring the performance of MT metrics using Precision, Recall, and F-score, we offer clearer insights into their capabilities than correlation with human judgments. Finally, we raise concerns regarding the reliability of manually curated data following the Direct Assessments+Scalar Quality Metrics (DA+SQM) guidelines, reporting a notably low agreement with Multidimensional Quality Metrics (MQM) annotations., Comment: Accepted at EMNLP 2024 Main Conference. 26 pages

We derive explicit restriction and continuation formulas between n-dimensional (Anti)-de Sitter spaces and the (n + 1)-dimensional Minkowskian ambient space for the codifferential and Laplace-de Rham operators acting on p-forms., Comment: 9 pages, v2: typos corrected

Entity Linking (EL) and Relation Extraction (RE) are fundamental tasks in Natural Language Processing, serving as critical components in a wide range of applications. In this paper, we propose ReLiK, a Retriever-Reader architecture for both EL and RE, where, given an input text, the Retriever module undertakes the identification of candidate entities or relations that could potentially appear within the text. Subsequently, the Reader module is tasked to discern the pertinent retrieved entities or relations and establish their alignment with the corresponding textual spans. Notably, we put forward an innovative input representation that incorporates the candidate entities or relations alongside the text, making it possible to link entities or extract relations in a single forward pass and to fully leverage pre-trained language models contextualization capabilities, in contrast with previous Retriever-Reader-based methods, which require a forward pass for each candidate. Our formulation of EL and RE achieves state-of-the-art performance in both in-domain and out-of-domain benchmarks while using academic budget training and with up to 40x inference speed compared to competitors. Finally, we show how our architecture can be used seamlessly for Information Extraction (cIE), i.e. EL + RE, and setting a new state of the art by employing a shared Reader that simultaneously extracts entities and relations., Comment: Findings of the Association for Computational Linguistics ACL 2024

Advances in medical imaging technologies have enabled the collection of longitudinal images, which involve repeated scanning of the same patients over time, to monitor disease progression. However, predictive modeling of such data remains challenging due to high dimensionality, irregular sampling, and data sparsity. To address these issues, we propose ImageFlowNet, a novel model designed to forecast disease trajectories from initial images while preserving spatial details. ImageFlowNet first learns multiscale joint representation spaces across patients and time points, then optimizes deterministic or stochastic flow fields within these spaces using a position-parameterized neural ODE/SDE framework. The model leverages a UNet architecture to create robust multiscale representations and mitigates data scarcity by combining knowledge from all patients. We provide theoretical insights that support our formulation of ODEs, and motivate our regularizations involving high-level visual features, latent space organization, and trajectory smoothness. We validate ImageFlowNet on three longitudinal medical image datasets depicting progression in geographic atrophy, multiple sclerosis, and glioblastoma, demonstrating its ability to effectively forecast disease progression and outperform existing methods. Our contributions include the development of ImageFlowNet, its theoretical underpinnings, and empirical validation on real-world datasets. The official implementation is available at https://github.com/KrishnaswamyLab/ImageFlowNet., Comment: Accepted to ICASSP 2025

Using high resolution scanning transmission electron microscopy and low-loss electron energy loss spectroscopy, we correlate the local bandgap (Eg), indium concentration, and strain distribution across multiple InxGa1-xAs quantum wells (QWs), on a GaAs substrate, within a metamorphic laser structure. Our findings reveal significant inhomogeneities, particularly near the interfaces, for both the indium and strain distribution, and subtle variations in the Eg across individual QWs. The interplay between strain, composition, and Eg was further explored by density functional theory simulations, indicating that variations in the Eg are predominantly influenced by the indium concentration, with strain playing a minor role. The observed local inhomogeneities suggest that differences between individual QWs may affect the collective emission and performance of the final device. This study highlights the importance of spatially resolved analysis in understanding and optimising the electronic and optical properties for designing of next-generation metamorphic lasers with multiple QWs as the active region.

We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates.

Identities pertaining to the de Rham codifferential {\delta} in differential geometry are scattered in the literature. This article gathers such formulas involving usual differential operators (Lie derivative, Schouten-Nijenhuis bracket, ...), while adding a few new ones using a natural extension of the interior product, to provide a compact handy summary., Comment: Revtex 8 pages, v2: typo corrected

Proteins are essential for almost all biological processes and derive their diverse functions from complex 3D structures, which are in turn determined by their amino acid sequences. In this paper, we exploit the rich biological inductive bias of amino acid sequences and introduce FoldFlow-2, a novel sequence-conditioned SE(3)-equivariant flow matching model for protein structure generation. FoldFlow-2 presents substantial new architectural features over the previous FoldFlow family of models including a protein large language model to encode sequence, a new multi-modal fusion trunk that combines structure and sequence representations, and a geometric transformer based decoder. To increase diversity and novelty of generated samples -- crucial for de-novo drug design -- we train FoldFlow-2 at scale on a new dataset that is an order of magnitude larger than PDB datasets of prior works, containing both known proteins in PDB and high-quality synthetic structures achieved through filtering. We further demonstrate the ability to align FoldFlow-2 to arbitrary rewards, e.g. increasing secondary structures diversity, by introducing a Reinforced Finetuning (ReFT) objective. We empirically observe that FoldFlow-2 outperforms previous state-of-the-art protein structure-based generative models, improving over RFDiffusion in terms of unconditional generation across all metrics including designability, diversity, and novelty across all protein lengths, as well as exhibiting generalization on the task of equilibrium conformation sampling. Finally, we demonstrate that a fine-tuned FoldFlow-2 makes progress on challenging conditional design tasks such as designing scaffolds for the VHH nanobody., Comment: Presented at NeurIPS 2024

Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, L\'eonard & Zambrini (AIHP PS 2020), we study a problem of entropic minimization on the path space when the reference measure is a generic Feller semimartingale. We show that, under some regularity condition, our problem connects naturally with a, possibly non-local, version of the Hamilton-Jacobi-Bellman equation. Additionally, we study existence of minimizers when the reference measure in a Ornstein-Uhlenbeck process., Comment: 13 pages, comments welcome!

Differentially-private (DP) mechanisms can be embedded into the design of a machine learning algorithm to protect the resulting model against privacy leakage. However, this often comes with a significant loss of accuracy due to the noise added to enforce DP. In this paper, we aim at improving this trade-off for a popular class of machine learning algorithms leveraging the Gini impurity as an information gain criterion to greedily build interpretable models such as decision trees or rule lists. To this end, we establish the smooth sensitivity of the Gini impurity, which can be used to obtain thorough DP guarantees while adding noise scaled with tighter magnitude. We illustrate the applicability of this mechanism by integrating it within a greedy algorithm producing rule list models, motivated by the fact that such models remain understudied in the DP literature. Our theoretical analysis and experimental results confirm that the DP rule lists models integrating smooth sensitivity have higher accuracy that those using other DP frameworks based on global sensitivity, for identical privacy budgets.

Machine learning techniques are increasingly used for high-stakes decision-making, such as college admissions, loan attribution or recidivism prediction. Thus, it is crucial to ensure that the models learnt can be audited or understood by human users, do not create or reproduce discrimination or bias, and do not leak sensitive information regarding their training data. Indeed, interpretability, fairness and privacy are key requirements for the development of responsible machine learning, and all three have been studied extensively during the last decade. However, they were mainly considered in isolation, while in practice they interplay with each other, either positively or negatively. In this Systematization of Knowledge (SoK) paper, we survey the literature on the interactions between these three desiderata. More precisely, for each pairwise interaction, we summarize the identified synergies and tensions. These findings highlight several fundamental theoretical and empirical conflicts, while also demonstrating that jointly considering these different requirements is challenging when one aims at preserving a high level of utility. To solve this issue, we also discuss possible conciliation mechanisms, showing that a careful design can enable to successfully handle these different concerns in practice.

We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lema\^itre-Robertson-Walker spaces, in $\mathbb{R}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of $\mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of the ambient space reduces to conformal transformations on the submanifolds., Comment: 6 pages, no figures, v2: close match to published version

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Macroscopic oscillations in the brain are involved in various cognitive and physiological processes, yet their precise function is not not completely understood. Communication Through Coherence (CTC) theory proposes that these rhythmic electrical patterns might serve to regulate the information flow between neural populations. Thus, to communicate effectively, neural populations must synchronize their oscillatory activity, ensuring that input volleys from the presynaptic population reach the postsynaptic one at its maximum phase of excitability. We consider an Excitatory-Inhibitory (E-I) network whose macroscopic activity is described by an exact mean-field model. The E-I network receives periodic inputs from either one or two external sources, for which effective communication will not be achieved in the absence of control. We explore strategies based on optimal control theory for phase-amplitude dynamics to design a control that sets the target population in the optimal phase to synchronize its activity with a specific presynaptic input signal and establish communication. The control mechanism resembles the role of a higher cortical area in the context of selective attention. To design the control, we use the phase-amplitude reduction of a limit cycle and leverage recent developments in this field in order to find the most effective control strategy regarding a defined cost function. Furthermore, we present results that guarantee the local controllability of the system close to the limit cycle.

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce FoldFlow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions -- i.e. the group $\text{SE}(3)$ -- enabling accurate modeling of protein backbones. We first introduce FoldFlow-Base, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\text{SE}(3)$. We next accelerate training by incorporating Riemannian optimal transport to create FoldFlow-OT, leading to the construction of both more simple and stable flows. Finally, we design FoldFlow-SFM, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\text{SE}(3)$. Our family of FoldFlow, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\text{SE}(3)$. Empirically, we validate FoldFlow, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples., Comment: ICLR 2024 Spotlight

Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such disclosure may directly conflict with privacy, a precise quantification of the privacy impact of such breach is a fundamental problem. For instance, previous work have shown that the structure of a decision tree can be leveraged to build a probabilistic reconstruction of its training dataset, with the uncertainty of the reconstruction being a relevant metric for the information leak. In this paper, we propose of a novel framework generalizing these probabilistic reconstructions in the sense that it can handle other forms of interpretable models and more generic types of knowledge. In addition, we demonstrate that under realistic assumptions regarding the interpretable models' structure, the uncertainty of the reconstruction can be computed efficiently. Finally, we illustrate the applicability of our approach on both decision trees and rule lists, by comparing the theoretical information leak associated to either exact or heuristic learning algorithms. Our results suggest that optimal interpretable models are often more compact and leak less information regarding their training data than greedily-built ones, for a given accuracy level.

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic generative modeling as a Schr\"odinger bridge problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data. Our code is available in the TorchCFM package at https://github.com/atong01/conditional-flow-matching., Comment: AISTATS 2024. Code: https://github.com/atong01/conditional-flow-matching

Abstract Meaning Representation (AMR) is a Semantic Parsing formalism that aims at providing a semantic graph abstraction representing a given text. Current approaches are based on autoregressive language models such as BART or T5, fine-tuned through Teacher Forcing to obtain a linearized version of the AMR graph from a sentence. In this paper, we present LeakDistill, a model and method that explores a modification to the Transformer architecture, using structural adapters to explicitly incorporate graph information into the learned representations and improve AMR parsing performance. Our experiments show how, by employing word-to-node alignment to embed graph structural information into the encoder at training time, we can obtain state-of-the-art AMR parsing through self-knowledge distillation, even without the use of additional data. We release the code at \url{http://www.github.com/sapienzanlp/LeakDistill}., Comment: ACL 2023. Please cite authors correctly using both lastnames ("Mart\'inez Lorenzo", "Huguet Cabot")

In this paper, we examine the current state-of-the-art in AMR parsing, which relies on ensemble strategies by merging multiple graph predictions. Our analysis reveals that the present models often violate AMR structural constraints. To address this issue, we develop a validation method, and show how ensemble models can exploit SMATCH metric weaknesses to obtain higher scores, but sometimes result in corrupted graphs. Additionally, we highlight the demanding need to compute the SMATCH score among all possible predictions. To overcome these challenges, we propose two novel ensemble strategies based on Transformer models, improving robustness to structural constraints, while also reducing the computational time. Our methods provide new insights for enhancing AMR parsers and metrics. Our code is available at \href{https://www.github.com/babelscape/AMRs-Assemble}{github.com/babelscape/AMRs-Assemble}., Comment: ACL 2023. Please cite authors correctly using both lastnames ("Mart\'inez Lorenzo", "Huguet Cabot")

Relation Extraction (RE) is a task that identifies relationships between entities in a text, enabling the acquisition of relational facts and bridging the gap between natural language and structured knowledge. However, current RE models often rely on small datasets with low coverage of relation types, particularly when working with languages other than English. In this paper, we address the above issue and provide two new resources that enable the training and evaluation of multilingual RE systems. First, we present SRED$^{\rm FM}$, an automatically annotated dataset covering 18 languages, 400 relation types, 13 entity types, totaling more than 40 million triplet instances. Second, we propose RED$^{\rm FM}$, a smaller, human-revised dataset for seven languages that allows for the evaluation of multilingual RE systems. To demonstrate the utility of these novel datasets, we experiment with the first end-to-end multilingual RE model, mREBEL, that extracts triplets, including entity types, in multiple languages. We release our resources and model checkpoints at https://www.github.com/babelscape/rebel, Comment: ACL 2023. Please cite authors correctly using both lastnames ("Huguet Cabot", "Ngonga Ngomo")

Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain activity. They are associated to various brain disorders such as migraine and ischemia. We consider a reduced version of a biophysical model of a neuron-astrocyte network for the initiation and propagation of CSD waves (Huguet et al., Biophys. J. , 2016), consisting of reaction-diffusion equations. The reduced model considers only the dynamics of the neuronal and astrocytic membrane potentials and the extracellular potassium concentration, capturing the instigation process implicated in such waves. We present a computational and mathematical framework based on the parameterization method and singular perturbation theory to provide semi-analytical results on the existence of a wave solution and to compute it jointly with its velocity of propagation. The traveling wave solution can be seen as an heteroclinic connection of an associated system of ordinary differential equations with a slow-fast dynamics. The presence of distinct time scales within the system introduces numerical instabilities, which we successfully address through the identification of significant invariant manifolds and the implementation of the parameterization method. Our results provide a methodology that allows to identify efficiently and accurately the mechanisms responsible for the initiation of these waves and the wave propagation velocity., Comment: 36 pages, 13 figures