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3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…

Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance…

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in $n$-dimensional…

In distributed systems, knowledge of the network structure of the connections among the unitary components is often a requirement for an accurate prediction of the emerging collective dynamics. However, in many real-world situations, one…

In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…

Multimodal transformers integrate diverse data types like images, audio, and text, advancing tasks such as audio-visual understanding and image-text retrieval; yet their high parameterization limits deployment on resource-constrained edge…

This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a…

Large machine learning models trained on diverse data have recently seen unprecedented success. Federated learning enables training on private data that may otherwise be inaccessible, such as domain-specific datasets decentralized across…

Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

Skip connections made the training of very deep networks possible and have become an indispensable component in a variety of neural architectures. A completely satisfactory explanation for their success remains elusive. Here, we present a…

Collecting large-scale medical datasets with fine-grained annotations is time-consuming and requires experts. For this reason, weakly supervised learning aims at optimising machine learning models using weaker forms of annotations, such as…

This paper focuses on the challenging task of learning 3D object surface reconstructions from single RGB images. Existing methods achieve varying degrees of success by using different geometric representations. However, they all have their…

Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…

The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…

We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…

Recent advancements in low-cost ensemble learning have demonstrated improved efficiency for image classification. However, the existing low-cost ensemble methods show relatively lower accuracy compared to conventional ensemble learning. In…

The phenomenon of linear mode connectivity (LMC) links several aspects of deep learning, including training stability under noisy stochastic gradients, the smoothness and generalization of local minima (basins), the similarity and…

We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local…