Doctor of Philosophy in

The course covers the following topics:

• The theory of NP-completeness and its relationship to the complexity classes P and NP.
• Circuit complexity and alternations.
• SAT, the complexity of counting, and algebraic circuit complexity.
• Circuit complexity lowerbound, hardness vs randomness, ironic complexity, and interactive proof systems.

This course covers a broad overview of the many diverse types of data structures, including persistent, retroactive, geometric data structures, like a map, and temporal data structures, as in storage that happens over a time series. A comprehensive study of these data structures is a vital component of this subject. It also covers dictionaries, static trees, strings, succinct structures, and dynamic graphs. Finally, the course will cover the major directions of research for a wide variety of such data structures.

Randomized algorithms went from being a tool in computational number theory to finding widespread application in many types of algorithms. Two benefits of randomization have spearheaded this growth: simplicity and speed. This course discusses the basic and advanced concepts of randomized signals. Specifically, it includes random sampling, tail inequalities, probabilistic methods, algebraic methods, and random walks. Further, it also covers linear programming, graph algorithms and approximate counting topics.

This course covers the topic of polyhedra, including various mathematical concepts and algorithms such as Farkas lemma, duality, complementary slackness, and decomposition of polyhedra. The course also covers topics like integer polyhedra, matrices, matching (bipartite and non-bipartite), graphs, matroids, polymatroids and submodular functions. The course will also cover the application of these concepts in machine learning.

This course introduces students to the diverse landscape of biological data, including its types and characteristics and explores the foundational principles of single-cell omics bioinformatics, encompassing key methodologies, tools, and computational workflows, with an emphasis on the development of foundation models for single cell omics data from a research perspective. Single cell omics technologies are a new and fast-growing family of biological assays that enables measuring the molecular contents of individual cells with very high resolution and is key to advancing precision medicine. The course covers essential bioinformatics aspects for working with single cell omics data.

This course provides an introduction to 3D geometry processing, an important field that intersects computer vision, computer graphics, and discrete geometry. With 3D vision systems becoming increasingly sophisticated, object recognition and modeling is no longer limited to abstracted feature representations but are often high-fidelity digitization of real-world objects and environments. While 3D geometry processing has evolved significantly in the areas of visual effects and interactive games, they are impacting other domains, ranging from metaverse technologies to robotics, biomedicine, and additive manufacturing. Augmented/virtual reality systems are using 3D scanned virtual avatars to enable immersive communication, autonomous cars are capturing their 3D surroundings in real-time, and Google earth is digitizing entire worlds using satellite and geospatial data. With the emergence of 3D scanning, real-time depth sensors, and 3D printing technologies, polygonal meshes have become the de-factor standard for 3D surface representation. This course will cover the mathematical foundations for studying 3D surfaces from a discrete differential geometric standpoint and present the full geometry processing pipeline: from 3D data capture, mesh smoothing, surface reconstruction, parameterization, registration, shape analysis (correspondence, symmetry, matching), data-driven synthesis, interactive manipulation, to 3D printing. We will also illustrate this course with important applications and recent AI advances in this field, especially with new developments in 3D deep learning, deep generative models for 3D objects, and differentiable rendering. In analogy to image processing for which inputs are 2D images and video, 3D Geometry processing involves the treatment of 3D depth maps, point clouds, polygonal meshes and volumetric data and involves many techniques from linear algebra, differential geometry, signal processing, and numerical optimization. This course will offer practical coding exercises to understand basic geometry processing algorithms and exciting project around data capture and geometry processing.

Training the largest Machine Learning (ML) programs requires petaFLOPs (1015) to exaFLOPs (1018) of computing operations, as well as multiple terabytes (1012) of hardware accelerator memory. Accordingly, 100s to 1000s of these accelerators are needed to satisfy both the computing and memory requirements of the large-scale ML. This course covers systems architecture design, communication strategies and algorithmic modifications required to execute ML training in a parallel and distributed fashion across many network-connected hardware accelerators. In the first part of the course, students will learn a comprehensive set of principles, representations, and performance metrics for parallelizing ML programs and learning algorithms, as well as learn how to compare and evaluate different parallel ML strategies composed out of basic parallel ML “aspects”. In the second part of the course, students will apply these skills to read and critique peer-reviewed literature on parallel and distributed ML systems.

The course introduces students to the topic of natural language generation and related emerging topics in the field. The course prepares them to perform research that advances the state of the art in this research area.

This course focuses on recent research in Natural Language Processing and on developing skills for performing research to advance the state of the art in Natural Language Processing.

This course focuses on recent topics in Natural Language Processing and on developing skills for performing research to advance the state of the art in Natural Language Processing. Specifically, this course will cover fundamentals of LLMs such as Transformers architecture, methods on training and evaluating LLMs via distributed training and efficiency methods, and application in multilinguality, translation and multimodality.

This course provides a comprehensive introduction to Speech Processing. It focuses on developing knowledge about the state of the art in a wide range of Speech Processing tasks, and readiness for performing research to advance the state of the art in these topics. Topics include speech production, speech signal analysis, automatic speech recognition, speech synthesis, neural speech recognition and synthesis, and recent topics in foundation models and speech processing.

This course focuses on recent topics in Natural Language Processing and on developing skills for performing research to advance the state of the art in Natural Language Processing.

This course explores the cutting-edge techniques and methodologies in the field of speech processing. The course covers advanced topics such as Automatic Speech Recognition, Language Modeling and Decoding, Speech Synthesis, Speaker Identification, Speech Diarization, Paralinguistic analysis, Speech Translation & Summarization, Multilinguality and low-resource languages and Spoken Dialog Systems. Students will delve into modern models and frameworks for the different speech tasks. The course emphasizes both theoretical understanding and practical implementation, fostering skills necessary for innovative research and development in speech technologies.

The course introduces students to advanced topics in natural language processing concerning the robustness and trustworthiness of language models (LMs), specifically world knowledge in LMs, safety and inclusivity of LMs, and inner workings of LMs. The course prepares them to perform research that advances the state of the art in these research areas.

PhD thesis research exposes students to cutting-edge and unsolved research problems, where they are required to propose new solutions and significantly contribute towards the body of knowledge. Students pursue an independent research study, under the guidance of a supervisory panel, for a period of 3 to 4 years. PhD thesis research helps train graduates to become leaders in their chosen area of research through partly supervised study, eventually transforming them into researchers who can work independently or interdependently to carry out cutting-edge research.

This course will prepare students to produce professional-quality research and solve a practical research challenge in an organization based on an innovative, sustainable, and entrepreneurial research topic. This course will provide exposure to a variety of special topics, research integrity, ethics, organizational challenges, and needs related to various disciplines. Students will design and implement a research project suitable for conference presentation or journal submission relevant to their field of interest, in addition to peer-reviewing a paper. The instructor, and guest lecturers, as appropriate, will present topics necessary to develop well-rounded researchers, innovators, and entrepreneurs in the AI disciplines.

PhD Internship (up to four months)