Related papers: Manifold Function Encoder: Identifying Different F…

Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth manifolds. Round fold maps were introduced as stable fold…

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…

Multilayer perceptrons (MLPs) learn high frequencies slowly. Recent approaches encode features in spatial bins to improve speed of learning details, but at the cost of larger model size and loss of continuity. Instead, we propose to encode…

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic…

Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…

The authors define a class of functions on Riemannian manifolds, which is called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions and some of its properties…

We formulate the manifold learning problem as the problem of finding an operator that maps any point to a close neighbor that lies on a ``hidden'' $k$-dimensional manifold. We call this operator the correcting function. Under this…

It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for…

Understanding how agents learn to generalize -- and, in particular, to extrapolate -- in high-dimensional, naturalistic environments remains a challenge for both machine learning and the study of biological agents. One approach to this has…

Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of…

We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data's modes of variation in amplitude and phase. Based on this manifold,…

We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…

Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent…

How to learn discriminative video representation from unlabeled videos is challenging but crucial for video analysis. The latest attempts seek to learn a representation model by predicting the appearance contents in the masked regions.…

The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning…

We present EmbodiedMAE, a unified 3D multi-modal representation for robot manipulation. Current approaches suffer from significant domain gaps between training datasets and robot manipulation tasks, while also lacking model architectures…