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The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed…
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…
Metric learning algorithms aim to learn a distance function that brings the semantically similar data items together and keeps dissimilar ones at a distance. The traditional Mahalanobis distance learning is equivalent to find a linear…
Physics-guided deep learning (PG-DL) via algorithm unrolling has received significant interest for improved image reconstruction, including MRI applications. These methods unroll an iterative optimization algorithm into a series of…
Measuring the generalization performance of a Deep Neural Network (DNN) without relying on a validation set is a difficult task. In this work, we propose exploiting Latent Geometry Graphs (LGGs) to represent the latent spaces of trained DNN…
We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…
A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…
Large language models (LLMs) can internalize private or harmful content, motivating unlearning that removes a forget set while preserving retaining knowledge. However, forgetting updates often cause collateral degradation on retaining…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical…
This article surveys the growing interest in utilizing Deep Learning (DL) as a powerful tool to address challenging problems in earthquake engineering. Despite decades of advancement in domain knowledge, issues such as uncertainty in…
This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…
Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…
Learning methods for relative camera pose estimation have been developed largely in isolation from classical geometric approaches. The question of how to integrate predictions from deep neural networks (DNNs) and solutions from geometric…
Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods…
Deep learning (DL) methods are widely used to extract high-dimensional patterns from the sequence features of radar echo signals. However, conventional DL algorithms face challenges such as redundant feature segments, and constraints from…