François Rousseau

Guillaume Morel, Lucas Drumetz, Simon Benaïchouche et al.

Normalizing Flows (NF) are powerful likelihood-based generative models that are able to trade off between expressivity and tractability to model complex densities. A now well established research avenue leverages optimal transport (OT) and looks for Monge maps, i.e. models with minimal effort between the source and target distributions. This paper introduces a method based on Brenier's polar factorization theorem to transform any trained NF into a more OT-efficient version without changing the final density. We do so by learning a rearrangement of the source (Gaussian) distribution that minimizes the OT cost between the source and the final density. We further constrain the path leading to the estimated Monge map to lie on a geodesic in the space of volume-preserving diffeomorphisms thanks to Euler's equations. The proposed method leads to smooth flows with reduced OT cost for several existing models without affecting the model performance.

Maik Dannecker, Steven Jia, Nil Stolt-Ansó et al.

Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI, high-resolution 3D reconstruction of the brain from motion-corrupted low-resolution 2D acquisitions is a prerequisite for accurate neurodevelopmental diagnosis. While implicit neural representations (INRs) have recently established state-of-the-art performance in self-supervised slice-to-volume reconstruction (SVR), they suffer from a critical computational bottleneck: accurately modeling the image acquisition physics requires expensive stochastic Monte Carlo sampling to approximate the point spread function (PSF). In this work, we propose a shift from neural network based implicit representations to Gaussian based explicit representations. By parameterizing the HR 3D image volume as a field of anisotropic Gaussian primitives, we leverage the property of Gaussians being closed under convolution and thus derive a \textit{closed-form analytical solution} for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($\mathbfΣ_{obs} = \mathbfΣ_{HR} + \mathbfΣ_{PSF}$), effectively bypassing the need for compute-intensive stochastic sampling while ensuring exact gradient propagation. We demonstrate that our approach matches the reconstruction quality of self-supervised state-of-the-art SVR frameworks while delivering a 5$\times$--10$\times$ speed-up on neonatal and fetal data. With convergence often reached in under 30 seconds, our framework paves the way towards translation into clinical routine of real-time fetal 3D MRI. Code will be public at {https://github.com/m-dannecker/Gaussian-Primitives-for-Fast-SVR}.

Le Minh Triet Tran, Sarah Reynaud, Ronan Fablet et al.

Inverse problems are often ill-posed and require optimization schemes with strong stability and convergence guarantees. While learning-based approaches such as deep unrolling and meta-learning achieve strong empirical performance, they typically lack explicit control over descent and curvature, limiting robustness. We propose a learned Majorization-Minimization (MM) framework for inverse problems within a bilevel optimization setting. Instead of learning a full optimizer, we learn a structured curvature majorant that governs each MM step while preserving classical MM descent guarantees. The majorant is parameterized by a lightweight recurrent neural network and explicitly constrained to satisfy valid MM conditions. For cosine-similarity losses, we derive explicit curvature bounds yielding diagonal majorants. When analytic bounds are unavailable, we rely on efficient Hessian-vector product-based spectral estimation to automatically upper-bound local curvature without forming the Hessian explicitly. Experiments on EEG source imaging demonstrate improved accuracy, stability, and cross-dataset generalization over deep-unrolled and meta-learning baselines.

David Vigouroux, Lucas Drumetz, Ronan Fablet et al.

We introduce an unsupervised approach for constructing a global reference system by learning, in the ambient space, vector fields that span the tangent spaces of an unknown data manifold. In contrast to isometric objectives, which implicitly assume manifold flatness, our method learns tangent vector fields whose flows transport all samples to a common, learnable reference point. The resulting arc-lengths along these flows define interpretable intrinsic coordinates tied to a shared global frame. To prevent degenerate collapse, we enforce a non-shrinking constraint and derive a scalable, integration-free objective inspired by flow matching. Within our theoretical framework, we prove that minimizing the proposed objective recovers a global coordinate chart when one exists. Empirically, we obtain correct tangent alignment and coherent global coordinate structure on synthetic manifolds. We also demonstrate the scalability of our method on CIFAR-10, where the learned coordinates achieve competitive downstream classification performance.

Ronan Fablet, Bertrand Chapron, Lucas. Drumetz et al.

This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using both supervised and unsupervised strategies. Our numerical experiments on Lorenz-63 and Lorenz-96 systems report significant gain w.r.t. a classic gradient-based minimization of the variational cost both in terms of reconstruction performance and optimization complexity. Intriguingly, we also show that the variational models issued from the true Lorenz-63 and Lorenz-96 ODE representations may not lead to the best reconstruction performance. We believe these results may open new research avenues for the specification of assimilation models in geoscience.

Ronan Fablet, Lucas Drumetz, Francois Rousseau

Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties. Recently, learning-based strategies have appeared to be very efficient for solving inverse problems, by learning direct inversion schemes or plug-and-play regularizers from available pairs of true states and observations. In this paper, we go a step further and design an end-to-end framework allowing to learn actual variational frameworks for inverse problems in such a supervised setting. The variational cost and the gradient-based solver are both stated as neural networks using automatic differentiation for the latter. We can jointly learn both components to minimize the data reconstruction error on the true states. This leads to a data-driven discovery of variational models. We consider an application to inverse problems with incomplete datasets (image inpainting and multivariate time series interpolation). We experimentally illustrate that this framework can lead to a significant gain in terms of reconstruction performance, including w.r.t. the direct minimization of the variational formulation derived from the known generative model.

K. Makki, B. Borotikar, M. Garetier et al.

The log Euclidean polyrigid registration framework provides a way to smoothly estimate and interpolate poly-rigid/affine transformations for which the invertibility is guaranteed. This powerful and flexible mathematical framework is currently being used to track the human joint dynamics by first imposing bone rigidity constraints in order to synthetize the spatio-temporal joint deformations later. However, since no closed-form exists, then a computationally expensive integration of ordinary differential equations (ODEs) is required to perform image registration using this framework. To tackle this problem, the exponential map for solving these ODEs is computed using the scaling and squaring method in the literature. In this paper, we propose an algorithm using a matrix diagonalization based method for smooth interpolation of homogeneous polyrigid transformations of human joints during motion. The use of this alternative computational approach to integrate ODEs is well motivated by the fact that bone rigid transformations satisfy the mechanical constraints of human joint motion, which provide conditions that guarantee the diagonalizability of local bone transformations and consequently of the resulting joint transformations. In a comparison with the scaling and squaring method, we discuss the usefulness of the matrix eigendecomposition technique which reduces significantly the computational burden associated with the computation of matrix exponential over a dense regular grid. Finally, we have applied the method to enhance the temporal resolution of dynamic MRI sequences of the ankle joint. To conclude, numerical experiments show that the eigendecomposition method is more capable of balancing the trade-off between accuracy, computation time, and memory requirements.

Pierre-Henri Conze, Ali Emre Kavur, Emilie Cornec-Le Gall et al.

Objective : Abdominal anatomy segmentation is crucial for numerous applications from computer-assisted diagnosis to image-guided surgery. In this context, we address fully-automated multi-organ segmentation from abdominal CT and MR images using deep learning. Methods: The proposed model extends standard conditional generative adversarial networks. Additionally to the discriminator which enforces the model to create realistic organ delineations, it embeds cascaded partially pre-trained convolutional encoder-decoders as generator. Encoder fine-tuning from a large amount of non-medical images alleviates data scarcity limitations. The network is trained end-to-end to benefit from simultaneous multi-level segmentation refinements using auto-context. Results : Employed for healthy liver, kidneys and spleen segmentation, our pipeline provides promising results by outperforming state-of-the-art encoder-decoder schemes. Followed for the Combined Healthy Abdominal Organ Segmentation (CHAOS) challenge organized in conjunction with the IEEE International Symposium on Biomedical Imaging 2019, it gave us the first rank for three competition categories: liver CT, liver MR and multi-organ MR segmentation. Conclusion : Combining cascaded convolutional and adversarial networks strengthens the ability of deep learning pipelines to automatically delineate multiple abdominal organs, with good generalization capability. Significance : The comprehensive evaluation provided suggests that better guidance could be achieved to help clinicians in abdominal image interpretation and clinical decision making.

Ronan Fablet, Lucas Drumetz, François Rousseau

For numerous domains, including for instance earth observation, medical imaging, astrophysics,..., available image and signal datasets often involve irregular space-time sampling patterns and large missing data rates. These sampling properties may be critical to apply state-of-the-art learning-based (e.g., auto-encoders, CNNs,...), fully benefit from the available large-scale observations and reach breakthroughs in the reconstruction and identification of processes of interest. In this paper, we address the end-to-end learning of representations of signals, images and image sequences from irregularly-sampled data, i.e. when the training data involved missing data. From an analogy to Bayesian formulation, we consider energy-based representations. Two energy forms are investigated: one derived from auto-encoders and one relating to Gibbs priors. The learning stage of these energy-based representations (or priors) involve a joint interpolation issue, which amounts to solving an energy minimization problem under observation constraints. Using a neural-network-based implementation of the considered energy forms, we can state an end-to-end learning scheme from irregularly-sampled data. We demonstrate the relevance of the proposed representations for different case-studies: namely, multivariate time series, 2D images and image sequences.

Francois Rousseau, Ronan Fablet

This paper addresses the understanding and characterization of residual networks (ResNet), which are among the state-of-the-art deep learning architectures for a variety of supervised learning problems. We focus on the mapping component of ResNets, which map the embedding space towards a new unknown space where the prediction or classification can be stated according to linear criteria. We show that this mapping component can be regarded as the numerical implementation of continuous flows of diffeomorphisms governed by ordinary differential equations. Especially, ResNets with shared weights are fully characterized as numerical approximation of exponential diffeomorphic operators. We stress both theoretically and numerically the relevance of the enforcement of diffeormorphic properties and the importance of numerical issues to make consistent the continuous formulation and the discretized ResNet implementation. We further discuss the resulting theoretical and computational insights on ResNet architectures.

Margarita Karkali, Francois Rousseau, Alexandros Ntoulas et al.

Novelty detection in text streams is a challenging task that emerges in quite a few different scenarios, ranging from email thread filtering to RSS news feed recommendation on a smartphone. An efficient novelty detection algorithm can save the user a great deal of time and resources when browsing through relevant yet usually previously-seen content. Most of the recent research on detection of novel documents in text streams has been building upon either geometric distances or distributional similarities, with the former typically performing better but being much slower due to the need of comparing an incoming document with all the previously-seen ones. In this paper, we propose a new approach to novelty detection in text streams. We describe a resource-aware mechanism that is able to handle massive text streams such as the ones present today thanks to the burst of social media and the emergence of the Web as the main source of information. We capitalize on the historical Inverse Document Frequency (IDF) that was known for capturing well term specificity and we show that it can be used successfully at the document level as a measure of document novelty. This enables us to avoid similarity comparisons with previous documents in the text stream, thus scaling better and leading to faster execution times. Moreover, as the collection of documents evolves over time, we use a temporal variant of IDF not only to maintain an efficient representation of what has already been seen but also to decay the document frequencies as the time goes by. We evaluate the performance of the proposed approach on a real-world news articles dataset created for this task. The results show that the proposed method outperforms all of the baselines while managing to operate efficiently in terms of time complexity and memory usage, which are of great importance in a mobile setting scenario.