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Asymptotic approaches in inverse problems for depolymerization estimation
No full textInternational audienceDepolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer sizes, such as the total polymerised mass or the mean size of particles. The question analysed here is to link this measurement to the initial size distribution. To do so, we first derive, from the initial reaction systemtwo asymptotic models: at first order, a backward transport equation, and at second order, an advection-diffusion/Fokker-Planck equation complemented with a mixed boundary condition at x = 0. We estimate their distance to the original system solution. We then turn to the inverse problem, i.e., how to estimate the initial size distribution from the time measurement of an average quantity, given by a moment of the solution. This question has been already studied for the first order asymptotic model, and we analyse here the second order asymptotic. Thanks to Carleman inequalities and to log-convexity estimates, we prove observability results and error estimates for a Tikhonov regularization.We then develop a Kalman-based observer approach, and implement it on simulated observations. Despite its severely ill-posed character, the secondorder approach appears numerically more accurate than the first-order one.</p
Performance uncertainty in medical image analysis: a large-scale investigation of confidence intervals
No full textPerformance uncertainty quantification is essential for reliable validation and eventual clinicaltranslation of medical imaging artificial intelligence (AI). Confidence intervals (CIs) play a centralrole in this process by indicating how precise a reported performance estimate is. Yet, due tothe limited amount of work examining CI behavior in medical imaging, the community remainslargely unaware of how many diverse CI methods exist and how they behave in specific settings.The purpose of this study is to close this gap. To this end, we conducted a large-scale empiricalanalysis across a total of 24 segmentation and classification tasks, using 19 trained models pertask group, a broad spectrum of commonly used performance metrics, multiple aggregationstrategies, and several widely adopted CI methods. Reliability (coverage) and precision (width)of each CI method were estimated across all settings to characterize their dependence on studycharacteristics. Our analysis revealed five principal findings: 1) the sample size required forreliable CIs varies from a few dozens to several thousands of cases depending on study parameters;2) CI behavior is strongly affected by the choice of performance metric; 3) aggregation strategysubstantially influences the reliability of CIs, e.g. they require more observations for macrothan for micro; 4) the machine learning problem (segmentation versus classification) modulatesthese effects; 5) different CI methods are not equally reliable and precise depending on the usecase. These results form key components for the development of future guidelines on reportingperformance uncertainty in medical imaging AI
ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecasting
No full textInternational audienceWeather forecasting plays a vital role in today's society, from agriculture and logistics to predicting the output of renewable energies, and preparing for extreme weather events. Deep learning weather forecasting models trained with the next state prediction objective on ERA5 have shown great success compared to numerical global circulation models. However, for a wide range of applications, being able to provide representative samples from the distribution of possible future weather states is critical. In this paper, we propose a methodology to leverage deterministic weather models in the design of probabilistic weather models, leading to improved performance and reduced computing costs. We first introduce \textbf{ArchesWeather}, a transformer-based deterministic model that improves upon Pangu-Weather by removing overrestrictive inductive priors. We then design a probabilistic weather model called \textbf{ArchesWeatherGen} based on flow matching, a modern variant of diffusion models, that is trained to project ArchesWeather's predictions to the distribution of ERA5 weather states. ArchesWeatherGen is a true stochastic emulator of ERA5 and surpasses IFS ENS and NeuralGCM on all WeatherBench headline variables (except for NeuralGCM's geopotential). Our work also aims to democratize the use of deterministic and generative machine learning models in weather forecasting research, with academic computing resources. All models are trained at 1.5° resolution, with a training budget of 9 V100 days for ArchesWeather and 45 V100 days for ArchesWeatherGen. For inference, ArchesWeatherGen generates 15-day weather trajectories at a rate of 1 minute per ensemble member on a A100 GPU card. To make our work fully reproducible, our code and models are open source, including the complete pipeline for data preparation, training, and evaluation, at https://github.com/INRIA/geoarches
ArchesWeather: An efficient AI weather forecasting model at 1.5° resolution
No full textInternational audienceOne of the guiding principles for designing AI-based weather forecasting systems is to embed physical constraints as inductive priors in the neural network architecture. A popular prior is locality, where the atmospheric data is processed with local neural interactions, like 3D convolutions or 3D local attention windows as in Pangu-Weather. On the other hand, some works have shown great success in weather forecasting without this locality principle, at the cost of a much higher parameter count. In this paper, we show that the 3D local processing in Pangu-Weather is computationally sub-optimal. We design ArchesWeather, a transformer model that combines 2D attention with a column-wise attention-based feature interaction module, and demonstrate that this design improves forecasting skill. ArchesWeather is trained at 1.5° resolution and 24h lead time, with a training budget of a few GPU-days and a lower inference cost than competing methods. An ensemble of four of our models shows better RMSE scores than the IFS HRES and is competitive with the 1.4° 50-members NeuralGCM ensemble for one to three days ahead forecasting. Our code and models are publicly available at https://github.com/gcouairon/ArchesWeather
Simulated 5-HT2A receptor activation accounts for the high complexity of brain activity during psychedelic states
No full textSerotonergic psychedelics, such as LSD, psilocybin, and DMT, have strong effects on human brain activity, yet their mechanisms of action at the whole-brain level are only partially understood. Here, we present a biophysically-based meanfield model that integrates cellular and network-level details to simulate the effects of these compounds at different spatial scales. By incorporating the brain-wide distribution of 5-HT 2A receptors, our model mechanistically links receptor activation to a reduction in leak membrane potassium conductance, consistent with electrophysiological data. Our simulations reveal that this microscopic perturbation leads to the emergence of a brain state characterized by asynchronous and irregular dynamics with increased firing rates, as well as significant alterations in spectral power. Specifically, we find a robust decrease in power within the delta, theta, and alpha frequency bands, a result consistent with empirical findings. This change in dynamics is accompanied by an increase in spontaneous complexity, as quantified by the Lempel-Ziv complexity index, as observed experimentally. Furthermore, our model accurately replicates experimental findings regarding the Perturbational Complexity Index (PCI), demonstrating that PCI does not increase significantly by psychedelic drug administration. This crucial dissociation, where spontaneous complexity and spectral power are increased while perturbational complexity is preserved, highlights the distinct neurophysiological substrates underlying different metrics in psychedelic states. Our multiscale model provides a robust, mechanistic framework for understanding how serotoninergic psychedelics modulate global brain activity, offering new insights consistent with empirical neuroimaging and electrophysiological data..</div
Enhancing Variational Quantum Algorithms for Multicriteria Optimization
No full textThis paper presents methodological improvements to variational quantum algorithms (VQAs) for solving multicriteria optimization problems. We introduce two key contributions. First, we reformulate the parameter optimization task of VQAs as a multicriteria problem, enabling the direct use of classical algorithms from various multicriteria metaheuristics. This hybrid framework outperforms the corresponding single-criteria VQAs in both average and worst-case performance across diverse benchmark problems. Second, we propose a method that augments the hypervolume-based cost function with coverage-oriented indicators, allowing explicit control over the diversity of the resulting Pareto front approximations. Experimental results show that our method can improve coverage by up to 40\% with minimal loss in hypervolume. Our findings highlight the potential of combining quantum variational methods with classical population-based search to advance practical quantum optimization
Generating Efficiently Realistic Counterfactual Explanations
No full textInternational audienceThis article introduces VCNet -Variational CounterNet -a method for generating realistic counterfactuals, and its extension ImmutableVCNet. VCNet aims to generate counterfactuals that are representative of their predicted classes in the context of tabular data. Moreover, it aims to overcome the limitations related to the posthoc character and optimization procedure of the state-of-the-art approaches, by reducing the computing time of the counterfactual generation and reaching high levels of validity. However, state-of-the-art methods that succeed in overcoming the aforementioned limitations suffer from a lack of realism with regard to the counterfactuals generated. VCNet addresses this concern by adding realism constraints to the counterfactual generation process. Our approach is based on a conditional variational autoencoder (cVAE) to model the distributions for every class at once. Thus, generated counterfactuals not only belong to the data distribution but belong to the data distribution of a given class. The ImmutableVCNet extends VCNet to overcome the limitation of handling immutable features. We conducted several ablation studies to investigate the impact of the different choices within the VCNet architecture. Furthermore, we conducted empirical studies that demonstrate the significant benefits of our approach in generating realistic counterfactuals. We evaluate VCNet against ImmutableVCNet and also ImmutableVCNet against a variety of state-of-the-art counterfactual methods
Single-exponential bounds for diagonals of D-finite power series
No full textD-finite power series appear ubiquitously in combinatorics, number theory, and mathematical physics. They satisfy systems of linear partial differential equations whose solution spaces are finite-dimensional, which makes them enjoy a lot of nice properties. After attempts by others in the 1980s, Lipshitz was the first to prove that the class they form in the multivariate case is closed under the operation of diagonal. In particular, an earlier work by Gessel had addressed the D-finiteness of the diagonals of multivariate rational power series. In this paper, we give another proof of Gessel's result that fixes a gap in his original proof, while extending it to the full class of D-finite power series. We also provide a single exponential bound on the degree and order of the defining differential equation satisfied by the diagonal of a D-finite power series in terms of the degree and order of the input differential system
Machine Unlearning for Gibbs Supervised Learning Algorithms
No full textIn this report, a method for achieving exact unlearning for Gibbs supervised learning algorithms is proposed using a variational formulation inspired by empirical risk minimization subject to relative entropy regularization (ERM-RER). Such a method consists of maximizing the expected empirical risk over the dataset to be unlearned subject to a regularization by relative entropy with respect to the original algorithm. The optimization variable is a probability measure on the models; and the solution is another Gibbs probability measure that represents a new Gibbs supervised learning algorithm. The method guarantees exact unlearning in the sense that the new Gibbs algorithm coincides in distribution with the algorithm that would have been obtained by retraining from scratch on the dataset to be retained. As a byproduct, a framework for reweighting data points in ERM-RER by strategically choosing both the reference measure and the regularization factor is obtained. In this framework, exact unlearning is the special case in which zero-weight is assigned to the contribution of the data points to be unlearned. More generally, depending on the choice of certain parameters, data points can be up-weighted or down-weighted in ERM-RER problems for particular purposes, e.g., controlling the generalization error of Gibbs algorithms. This paves the way to new constructive or adversarial views on classical reweighting data points in ERM-RER
Doppler Frequency Estimation in Tensor-Based Modulation via Post-CPD Maximum Likelihood
No full textInternational audienceTensor-Based Modulation (TBM) is a novel wave-form design enabling efficient unsourced massive random access(UMAC) for future wireless networks. By leveraging tensoralgebra and Canonical Polyadic Decomposition (CPD), TBMallows to perform blind user separation at the receiver. However,the impact of Doppler frequency shifts on TBM has not yetbeen addressed. This paper shows that Doppler effects remainencoded mode-wise within the TBM factors, and hence do notdisrupt the blind user separation approach. Furthermore, theDoppler shifts associated to each user can be accurately esti-mated through a post-CPD per-user Maximum-Likelihood (ML)estimator. Simulation results show that the proposed approachonly requires a limited number pilot symbols while achievingaccurate Doppler recovery at low SNRs, thereby restoring thedecoding performance to a level nearly identical to the ideal zero-Doppler case. This makes the proposed approach well suited forshort-packet URLLC and IoT scenarios