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This paper addresses the problem of reassembling images from disjointed fragments. More specifically, given an unordered set of fragments, we aim at reassembling one or several possibly incomplete images. The main contributions of this work…
Recurrent Neural Networks (RNNs) have found widespread applications in machine learning for time series prediction and dynamical systems reconstruction, and experienced a recent renaissance with improved training algorithms and…
Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network…
The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
We show that finite parallel transports of vectors in Riemannian spaces, determined by the multiplication law in the deformed groups of diffeomorphisms, and sequences of infinitesimal parallel transports of vectors along geodesics are…
Ultrasound Localization Microscopy can resolve the microvascular bed down to a few micrometers. To achieve such performance microbubble contrast agents must perfuse the entire microvascular network. Microbubbles are then located…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
Deep Convolutional Neural Networks (DCNNs) commonly use generic `max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic convolution as a building…
A core challenge in Machine Learning is to learn to disentangle natural factors of variation in data (e.g. object shape vs. pose). A popular approach to disentanglement consists in learning to map each of these factors to distinct subspaces…
Diffusion models generate images with an unprecedented level of quality, but how can we freely rearrange image layouts? Recent works generate controllable scenes via learning spatially disentangled latent codes, but these methods do not…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
Convolutional networks for image classification progressively reduce resolution until the image is represented by tiny feature maps in which the spatial structure of the scene is no longer discernible. Such loss of spatial acuity can limit…
Speaker-independent speech separation has achieved remarkable performance in recent years with the development of deep neural network (DNN). Various network architectures, from traditional convolutional neural network (CNN) and recurrent…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
We analyze a few of the commonly used statistics based and machine learning algorithms for natural language disambiguation tasks and observe that they can be re-cast as learning linear separators in the feature space. Each of the methods…
Deep neural networks (DNNs) defy the classical bias-variance trade-off: adding parameters to a DNN that interpolates its training data will typically improve its generalization performance. Explaining the mechanism behind this ``benign…
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…