Miracle-dz/UniFAR-FTUs huggingface dataset:
Riemannian geometry of matrix manifolds for Lagrangian uncertainty quantification of stochastic fluid flows

This work focuses on developing theory and methodologies for the analysis of material transport in stochastic fluid flows. In a first part, two dominant classes of techniques for extracting Lagrangian Coherent Structures are reviewed and compared and some improve-ments are suggested for their pragmatic applications on realistic high-dimensional deter-ministic ocean velocity fields. In the stochastic case, estimating the uncertain Lagrangian motion can require to evaluate an ensemble of realizations of the flow map associated with a random velocity flow field, or equivalently realizations of the solution of a related transport partial differential equation. The Dynamically Orthogonal (DO) approximation is applied as an efficient model order reduction technique to solve this stochastic advection equation. With the goal of developing new rigorous reduced-order advection schemes, the second part of this work investigates the mathematical foundations of the method. Riemannian geometry providing an appropriate setting, a framework free of tensor notations is used to analyze the embedded geometry of three popular matrix manifolds, namely the fixed rank manifold, the Stiefel manifold and the isospectral manifold. Their extrinsic curvatures are characterized and computed through the study of the Weingarten map. As a spectacular by-product, explicit formulas are found for the differential of the truncated Singular Value Decomposition, of the Polar Decomposition, and of the eigenspaces of a time dependent symmetric matrix. Convergent gradient flows that achieve related algebraic operations are provided. A generalization of this framework to the non-Euclidean case is provided, al-lowing to derive analogous formulas and dynamical systems for tracking the eigenspaces of non-symmetric matrices. In the geometric setting, the DO approximation is a particular case of projected dynamical systems, that applies instantaneously the SVD truncation to optimally constrain the rank of the reduced solution. It is obtained that the error commit-ted by the DO approximation is controlled under the minimal geometric condition that the original solution stays close to the low-rank manifold. The last part of the work focuses on the practical implementation of the DO methodology for the stochastic advection equation. Fully linear, explicit central schemes are selected to ensure stability, accuracy and efficiency of the method. Riemannian matrix optimization is applied for the dynamic evaluation of the dominant SVD of a given matrix and is integrated to the DO time-stepping. Finally the technique is illustrated numerically on the uncertainty quantification of the Lagrangian motion of two bi-dimensional benchmark flows.
Neural-Symbolic Recommendation with Graph-Enhanced Information

The recommendation system is not only a problem of inductive statistics from data but also a cognitive task that requires reasoning ability. The most advanced graph neural networks have been widely used in recommendation systems because they can capture implicit structured information from graph-structured data. However, like most neural network algorithms, they only learn matching patterns from a perception perspective. Some researchers use user behavior for logic reasoning to achieve recommendation prediction from the perspective of cognitive reasoning, but this kind of reasoning is a local one and ignores implicit information on a global scale. In this work, we combine the advantages of graph neural networks and propositional logic operations to construct a neuro-symbolic recommendation model with both global implicit reasoning ability and local explicit logic reasoning ability. We first build an item-item graph based on the principle of adjacent interaction and use graph neural networks to capture implicit information in global data. Then we transform user behavior into propositional logic expressions to achieve recommendations from the perspective of cognitive reasoning. Extensive experiments on five public datasets show that our proposed model outperforms several state-of-the-art methods, source code is avaliable at [https://github.com/hanzo2020/GNNLR].
Mechanism and kinetics of bacteria-killing in a batch study in presence of Ag impregnated activated carbon

A mathematical model based on classical species balance equation has been developed to explain the experimental observation on E.Coli cell-killing in a batch reactor and to extract information on cell-killing mechanism. Maximum likelihood optimization method has been used to obtain the best fit to the experimental data to extract ten unknown kinetic and thermodynamic parameters, which is otherwise practically impossible. Bacteria killing kinetics is found to be dominated by contact killing mechanism with approximately one order difference between contact-and bulk-killing kinetics. The order of Ag-bacteria interaction is highly non-linear and thus the interaction is highly complex in manner. Concentration of Ag on the outer surface of AC controls the kinetics of bacteria killing. Mechanism of release of Ag from the inner surface of pores does has minimal impact on the bacteria killing kinetics. Activity of silver seems to remain preserved after cell killing and the surface concentration of Ag used in the experiment is so high that bacteria killing kinetics is independent of whether Ag remains active or not.
Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives

Given a set of calibrated images of a scene, we present an approach that produces a simple, compact, and actionable 3D world representation by means of 3D primitives. While many approaches focus on recovering high-fidelity 3D scenes, we focus on parsing a scene into mid-level 3D representations made of a small set of textured primitives. Such representations are interpretable, easy to manipulate and suited for physics-based simulations. Moreover, unlike existing primitive decomposition methods that rely on 3D input data, our approach operates directly on images through differentiable rendering. Specifically, we model primitives as textured superquadric meshes and optimize their parameters from scratch with an image rendering loss. We highlight the importance of modeling transparency for each primitive, which is critical for optimization and also enables handling varying numbers of primitives. We show that the resulting textured primitives faithfully reconstruct the input images and accurately model the visible 3D points, while providing amodal shape completions of unseen object regions. We compare our approach to the state of the art on diverse scenes from DTU, and demonstrate its robustness on real-life captures from BlendedMVS and Nerfstudio. We also showcase how our results can be used to effortlessly edit a scene or perform physical simulations. Code and video results are available at https://www.tmonnier. com/DBW .
Decorrelation using Optimal Transport

Being able to decorrelate a feature space from protected attributes is an area of active research and study in ethics, fairness, and also natural sciences. We introduce a novel decorrelation method using Convex Neural Optimal Transport Solvers (Cnots) that is able to decorrelate a continuous feature space against protected attributes with optimal transport. We demonstrate how well it performs in the context of jet classification in high energy physics, where classifier scores are desired to be decorrelated from the mass of a jet. The decorrelation achieved in binary classification approaches the levels achieved by the state-of-the-art using conditional normalising flows. When moving to multiclass outputs the optimal transport approach performs significantly better than the state-of-the-art, suggesting substantial gains at decorrelating multidimensional feature spaces.
Pegasus Simulator: An Isaac Sim Framework for Multiple Aerial Vehicles Simulation

Developing and testing novel control and motion planning algorithms for aerial vehicles can be a challenging task, with the robotics community relying more than ever on 3D simulation technologies to evaluate the performance of new algorithms in a variety of conditions and environments. In this work, we introduce the Pegasus Simulator, a modular framework implemented as an NVIDIA Isaac Sim extension that enables real-time simulation of multiple multirotor vehicles in photo-realistic environments, while providing out-of-the-box integration with the widely adopted PX4-Autopilot and ROS2 through its modular implementation and intuitive graphical user interface. To demonstrate some of its capabilities, a nonlinear controller was implemented and simulation results for two drones performing aggressive flight maneuvers are presented. Code and documentation for this framework are also provided as supplementary material.
Piecing Together Clues: A Benchmark for Evaluating the Detective Skills of Large Language Models

Detectives frequently engage in information detection and reasoning simultaneously when making decisions across various cases, especially when confronted with a vast amount of information. With the rapid development of large language models~(LLMs), evaluating how these models identify key information and reason to solve questions becomes increasingly relevant. We introduces the DetectBench, a reading comprehension dataset designed to assess a model's ability to jointly ability in key information detection and multi-hop reasoning when facing complex and implicit information. The DetectBench comprises 3,928 questions, each paired with a paragraph averaging 190 tokens in length. To enhance model's detective skills, we propose the Detective Thinking Framework. These methods encourage models to identify all possible clues within the context before reasoning. Our experiments reveal that existing models perform poorly in both information detection and multi-hop reasoning. However, the Detective Thinking Framework approach alleviates this issue.
Enhancing Continuous Time Series Modelling with a Latent ODE-LSTM Approach

Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are difficult to model with standard Recurrent Neural Networks (RNNs), RNNs have been generalised to have continuous-time hidden dynamics defined by a Neural Ordinary Differential Equation (Neural ODE), leading to the ODE-RNN model. Another approach that provides a better modelling is that of the Latent ODE model, which constructs a continuous-time model where a latent state is defined at all times. The Latent ODE model uses a standard RNN as the encoder and a Neural ODE as the decoder. However, since the RNN encoder leads to difficulties with missing data and ill-defined latent variables, a Latent ODE-RNN model has recently been proposed that uses a ODE-RNN model as the encoder instead. Both the Latent ODE and Latent ODE-RNN models are difficult to train due to the vanishing and exploding gradients problem. To overcome this problem, the main contribution of this paper is to propose and illustrate a new model based on a new Latent ODE using an ODE-LSTM (Long Short-Term Memory) network as an encoder -- the Latent ODE-LSTM model. To limit the growth of the gradients the Norm Gradient Clipping strategy was embedded on the Latent ODE-LSTM model. The performance evaluation of the new Latent ODE-LSTM (with and without Norm Gradient Clipping) for modelling CTS with regular and irregular sampling rates is then demonstrated. Numerical experiments show that the new Latent ODE-LSTM performs better than Latent ODE-RNNs and can avoid the vanishing and exploding gradients during training.
Relativistic Real-Time Methods

Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle-field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies.
Predicting Outcomes in Long COVID Patients with Spatiotemporal Attention

Long COVID is a general term of post-acute sequelae of COVID-19. Patients with long COVID can endure long-lasting symptoms including fatigue, headache, dyspnea and anosmia, etc. Identifying the cohorts with severe long-term complications in COVID-19 could benefit the treatment planning and resource arrangement. However, due to the heterogeneous phenotype presented in long COVID patients, it is difficult to predict their outcomes from their longitudinal data. In this study, we proposed a spatiotemporal attention mechanism to weigh feature importance jointly from the temporal dimension and feature space. Considering that medical examinations can have interchangeable orders in adjacent time points, we restricted the learning of short-term dependency with a Local-LSTM and the learning of long-term dependency with the joint spatiotemporal attention. We also compared the proposed method with several state-of-the-art methods and a method in clinical practice. The methods are evaluated on a hard-to-acquire clinical dataset of patients with long COVID. Experimental results show the Local-LSTM with joint spatiotemporal attention outperformed related methods in outcome prediction. The proposed method provides a clinical tool for the severity assessment of long COVID.
Effective Whitney Stratification of Real Algebraic Varieties

We describe an algorithm to compute Whitney stratifications of real algebraic varieties. The basic idea is to first stratify the complexified version of the given real variety using conormal techniques, and then to show that the resulting stratifications admit a description using only real polynomials. This method also extends to stratification problems involving certain basic semialgebraic sets as well as real algebraic maps. One of the map stratification algorithms described here yields a new method for solving the real root classification problem.
Probabilistic Counterexample Guidance for Safer Reinforcement Learning (Extended Version)

Safe exploration aims at addressing the limitations of Reinforcement Learning (RL) in safety-critical scenarios, where failures during trial-and-error learning may incur high costs. Several methods exist to incorporate external knowledge or to use proximal sensor data to limit the exploration of unsafe states. However, reducing exploration risks in unknown environments, where an agent must discover safety threats during exploration, remains challenging. In this paper, we target the problem of safe exploration by guiding the training with counterexamples of the safety requirement. Our method abstracts both continuous and discrete state-space systems into compact abstract models representing the safety-relevant knowledge acquired by the agent during exploration. We then exploit probabilistic counterexample generation to construct minimal simulation submodels eliciting safety requirement violations, where the agent can efficiently train offline to refine its policy towards minimising the risk of safety violations during the subsequent online exploration. We demonstrate our method's effectiveness in reducing safety violations during online exploration in preliminary experiments by an average of 40.3% compared with QL and DQN standard algorithms and 29.1% compared with previous related work, while achieving comparable cumulative rewards with respect to unrestricted exploration and alternative approaches.
Articulated 3D Head Avatar Generation using Text-to-Image Diffusion Models

The ability to generate diverse 3D articulated head avatars is vital to a plethora of applications, including augmented reality, cinematography, and education. Recent work on text-guided 3D object generation has shown great promise in addressing these needs. These methods directly leverage pre-trained 2D text-to-image diffusion models to generate 3D-multi-view-consistent radiance fields of generic objects. However, due to the lack of geometry and texture priors, these methods have limited control over the generated 3D objects, making it difficult to operate inside a specific domain, e.g., human heads. In this work, we develop a new approach to text-guided 3D head avatar generation to address this limitation. Our framework directly operates on the geometry and texture of an articulable 3D morphable model (3DMM) of a head, and introduces novel optimization procedures to update the geometry and texture while keeping the 2D and 3D facial features aligned. The result is a 3D head avatar that is consistent with the text description and can be readily articulated using the deformation model of the 3DMM. We show that our diffusion-based articulated head avatars outperform state-of-the-art approaches for this task. The latter are typically based on CLIP, which is known to provide limited diversity of generation and accuracy for 3D object generation.
The $\hbar\to 0$ limit of open quantum systems with general Lindbladians: vanishing noise ensures classicality beyond the Ehrenfest time

Quantum and classical systems evolving under the same formal Hamiltonian $H$ may exhibit dramatically different behavior after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as $\hbar \to 0$. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$. The error is small when the strength of the diffusion $D$ associated to the Lindblad functions satisfies $D \gg \hbar^{4/3}$, in particular allowing vanishing noise in the classical limit. We use a time-dependent semiclassical mixture of variably squeezed Gaussian states evolving by a local harmonic approximation to the Lindblad dynamics. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel's principle. We present heuristic arguments suggesting the $4/3$ exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. Our presentation aims to be comprehensive and accessible to both mathematicians and physicists. In a shorter companion paper, we treat the special case of Hamiltonians of the form $H=p^2/2m + V(x)$ and linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.
On the Value of Chess Squares

We propose a neural network-based approach to calculate the value of a chess square–piece combination. Our model takes a triplet (color, piece, square) as the input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces (= ∞, = 9, = 5, = 3, = 3, = 1). We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of knights and bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research.
Synthetic Decomposition for Counterfactual Predictions

Counterfactual predictions are challenging when the policy variable goes beyond its pre-policy support. However, in many cases, information about the policy of interest is available from different ("source") regions where a similar policy has already been implemented. In this paper, we propose a novel method of using such data from source regions to predict a new policy in a target region. Instead of relying on extrapolation of a structural relationship using a parametric specification, we formulate a transferability condition and construct a synthetic outcome-policy relationship such that it is as close as possible to meeting the condition. The synthetic relationship weighs both the similarity in distributions of observables and in structural relationships. We develop a general procedure to construct asymptotic confidence intervals for counterfactual predictions and prove its asymptotic validity. We then apply our proposal to predict average teenage employment in Texas following a counterfactual increase in the minimum wage.
OpenAL: An Efficient Deep Active Learning Framework for Open-Set Pathology Image Classification

Active learning (AL) is an effective approach to select the most informative samples to label so as to reduce the annotation cost. Existing AL methods typically work under the closed-set assumption, i.e., all classes existing in the unlabeled sample pool need to be classified by the target model. However, in some practical clinical tasks, the unlabeled pool may contain not only the target classes that need to be fine-grainedly classified, but also non-target classes that are irrelevant to the clinical tasks. Existing AL methods cannot work well in this scenario because they tend to select a large number of non-target samples. In this paper, we formulate this scenario as an open-set AL problem and propose an efficient framework, OpenAL, to address the challenge of querying samples from an unlabeled pool with both target class and non-target class samples. Experiments on fine-grained classification of pathology images show that OpenAL can significantly improve the query quality of target class samples and achieve higher performance than current state-of-the-art AL methods. Code is available at https://github.com/miccaiif/OpenAL.