Related papers: Shortcut learning in geometric knot classification
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
Machine Learning (ML) is accelerating the progress of materials prediction and classification, with particular success in CGNN designs. While classical ML methods remain accessible, advanced deep networks are still challenging to build and…
Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…
Neural interfaces capable of multi-site electrical recording, on-site signal classification, and closed-loop therapy are critical for the diagnosis and treatment of neurological disorders. However, deploying machine learning algorithms on…
Face verification can be regarded as a 2-class fine-grained visual recognition problem. Enhancing the feature's discriminative power is one of the key problems to improve its performance. Metric learning technology is often applied to…
Given a maze populated with different objects, one may task a robot with a sequential goal completion task, e.g. 1) pick up a key then 2) unlock the door then 3) unlock the treasure chest. A typical machine learning (ML) solution would…
Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…
Cognitive map learners (CML) are a collection of separate yet collaboratively trained single-layer artificial neural networks (matrices), which navigate an abstract graph by learning internal representations of the node states, edge…
Machine learning (ML) holds great promise for improving healthcare, but it is critical to ensure that its use will not propagate or amplify health disparities. An important step is to characterize the (un)fairness of ML models - their…
Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches…
Recent studies have noted an intriguing phenomenon termed Neural Collapse, that is, when the neural networks establish the right correlation between feature spaces and the training targets, their last-layer features, together with the…
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Metric learning seeks perceptual embeddings where visually similar instances are close and dissimilar instances are apart, but learned representations can be sub-optimal when the distribution of intra-class samples is diverse and distinct…
Two fundamental objects in knot theory are the minimal genus surface and the least area surface bounded by a knot in a 3-dimensional manifold. When the knot is embedded in a general 3-manifold, the problems of finding these surfaces were…
The discovery of knotting in proteins and other macromolecular chains has motivated researchers to more carefully consider how to identify and classify knots in open arcs. Most definitions classify knotting in open arcs by constructing an…
Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading…
Quantum machine learning (QML) networks promise to have some computational (or quantum) advantage for classifying supervised datasets (e.g., satellite images) over some conventional deep learning (DL) techniques due to their expressive…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision…