Related papers: Geometry-informed neural atlas for boundary value …

Existing UV mapping algorithms are designed to operate on well-behaved meshes, instead of the geometry representations produced by state-of-the-art 3D reconstruction and generation techniques. As such, applying these methods to the volume…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…

We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces…

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…

The recent proliferation of 3D content that can be consumed on hand-held devices necessitates efficient tools for transmitting large geometric data, e.g., 3D meshes, over the Internet. Detailed high-resolution assets can pose a challenge to…

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…

Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…

We present a novel neural network architecture called AutoAtlas for fully unsupervised partitioning and representation learning of 3D brain Magnetic Resonance Imaging (MRI) volumes. AutoAtlas consists of two neural network components: one…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

The encoding of input parameters is one of the fundamental building blocks of neural network algorithms. Its goal is to map the input data to a higher-dimensional space, typically supported by trained feature vectors. The mapping is crucial…

Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…

In this paper, we develop novel, efficient 2D encodings for 3D geometry, which enable reconstructing full 3D shapes from a single image at high resolution. The key idea is to pose 3D shape reconstruction as a 2D prediction problem. To that…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Constitution-conditioned post-training can be analysed as a structured perturbation of a model's learned representational geometry. We introduce ATLAS, a geometry-first program that traces constitution-induced hidden-state structure across…