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Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that…
Electromagnetismlike Optimization (EMO) is a global optimization algorithm, particularly well suited to solve problems featuring nonlinear and multimodal cost functions. EMO employs searcher agents that emulate a population of charged…
Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are…
The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…
High mobility environment leads to severe Doppler effects and poses serious challenges to the conventional physical layer based on the widely popular orthogonal frequency division multiplexing (OFDM). The recent emergence of orthogonal time…
This thesis examines self-attention training through the lens of Optimal Transport (OT) and develops an OT-based alternative for tabular classification. The study tracks intermediate projections of the self-attention layer during training…
Algebraic data types (ADTs) are a construct classically found in functional programming languages that capture data structures like enumerated types, lists, and trees. In recent years, interest in ADTs has increased. For example, popular…
In this paper we study the expectation maximization (EM) technique for one-bit MIMO-OFDM detection (OMOD). Arising from the recent interest in massive MIMO with one-bit analog-to-digital converters, OMOD is a massive-scale problem. EM is an…
Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear…
Variational Neural Machine Translation (VNMT) is an attractive framework for modeling the generation of target translations, conditioned not only on the source sentence but also on some latent random variables. The latent variable modeling…
We consider a general optimization problem of minimizing a composite objective functional defined over a class of probability distributions. The objective is composed of two functionals: one is assumed to possess the variational…
The problem of Cloud resource provisioning for component-based applications consists in the allocation of virtual machines (VMs) offers from various Cloud Providers to a set of applications such that the constraints induced by the…
Mixture-of-Experts (MoE) models improve transformer efficiency but lack a unified theoretical explanation, especially when both feed-forward and attention layers are allowed to specialize. To this end, we study the Mixture-of-Transformers…
High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as…
Recent advances in automatic music transcription (AMT) have achieved highly accurate polyphonic piano transcription results by incorporating onset and offset detection. The existing literature, however, focuses mainly on the leverage of…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this…
The Fast Fourier Transform (FFT) is widely used in applications such as MRI, CT, and interferometry; however, because of its dependence on uniformly sampled data, it requires the use of gridding techniques for practical implementation. The…