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Reasoning segmentation enables open-set object segmentation via implicit text queries, therefore serving as a foundation for embodied agents that should operate autonomously in real-world environments. However, existing methods for…
We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the…
Image segmentation is widely used in a variety of computer vision tasks, such as object localization and recognition, boundary detection, and medical imaging. This thesis proposes deep learning architectures to improve automatic object…
Dilated convolution with learnable spacings (DCLS) is a recent convolution method in which the positions of the kernel elements are learned throughout training by backpropagation. Its interest has recently been demonstrated in computer…
Obtaining a useful estimate of an object from highly incomplete imaging measurements remains a holy grail of imaging science. Deep learning methods have shown promise in learning object priors or constraints to improve the conditioning of…
In online classification, a learner is presented with a sequence of examples and aims to predict their labels in an online fashion so as to minimize the total number of mistakes. In the self-directed variant, the learner knows in advance…
Self-attention has become an important and widely used neural network component that helped to establish new state-of-the-art results for various applications, such as machine translation and automatic speech recognition (ASR). However, the…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
Recent advances in visual representation learning allowed to build an abundance of powerful off-the-shelf features that are ready-to-use for numerous downstream tasks. This work aims to assess how well these features preserve information…
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…
We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…
Many machine learning tasks such as clustering, classification, and dataset search benefit from embedding data points in a space where distances reflect notions of relative similarity as perceived by humans. A common way to construct such…
The algebraic approach to the Constraint Satisfaction Problem (CSP) uses high order symmetries of relational structures -- polymorphisms -- to study the complexity of the CSP. In this paper we further develop one of the methods the…
As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated…