Related papers: Intrinsic Universal Measurements of Non-linear Emb…

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

Intrinsic imaging or intrinsic image decomposition has traditionally been described as the problem of decomposing an image into two layers: a reflectance, the albedo invariant color of the material; and a shading, produced by the…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

In this work we consider the problem of data classification in post-classical settings were the number of training examples consists of mere few data points. We explore the phenomenon and reveal key relationships between dimensionality of…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Few-shot deep learning is a topical challenge area for scaling visual recognition to open ended growth of unseen new classes with limited labeled examples. A promising approach is based on metric learning, which trains a deep embedding to…

The escalating parameter counts in modern deep learning models pose a fundamental challenge to efficient training and resolution of overfitting. We address this by introducing the \emph{Mapping Networks} which replace the high dimensional…

Recent numerical experiments have demonstrated that the choice of optimization geometry used during training can impact generalization performance when learning expressive nonlinear model classes such as deep neural networks. These…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…

This paper proposed a new methodology for machine learning in 2-dimensional space (2-D ML) in inline coordinates. It is a full machine learning approach that does not require to deal with n-dimensional data in n-dimensional space. It allows…

Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…

Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…

Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we…

A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled…

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…