# MATH 789R - RTG Seminar on Computational Mathematics for Data Science

## Theme: Computational Methods for Robust, Scalable, and Fair Deep Learning

Despite the widespread and increasing use of deep learning in a wide range of areas, including (but not limited) to data science, the development of its mathematical and computational foundations remains an urgent and very active field of research. Contributing to a better understanding and improved algorithms is one of the focus areas of Emory’s NSF-funded Research Training Group (RTG) on Computational Mathematics for Data Science at Emory.

This RTG seminar seeks to expose graduate students, research-oriented undergraduate students, and early career researchers to recent developments of deep learning and its applications in data science (e.g., large-scale data analysis, inverse problems, data assimilation) and scientific machine learning (e.g., solving partial differential equations, optimal control problems).

The overarching goal of this seminar is to help participants develop new research ideas and design projects that further advance computational methods for deep learning. We are particularly interested in mathematically sound approaches that help increase its robustness (e.g., learning from small data sets, adversarial attacks), scalability (e.g., more efficient architectures, learning algorithms, …), and fairness (e.g., bias mitigation, …).

## Expectations and Grading

The class provides 3 credit hours for students that enroll on an S/U basis. I expect students to participate in the following ways:

### Reading

Students are expected to read each paper from the reading list before participating in online and in-class discussions.

### Online Discussions

There is one in-person meeting per week that covers the paper discussed in the seminar. Students need to post one answer to the discussion prompt (typically due by Monday) and provide a constructive comment to at least one other post (typically due by Wednesday). Although I will grade the posts only as complete/incomplete, you may find it helpful to consider this sample rubric while working on these assignments. One incomplete or late submission will be tolerated.

### Moderation

Participants must moderate the discussion of at least one paper of their choice. Papers will be assigned on a first-come-first-serve basis. Moderators should start reading the paper before the associated discussion on Canvas will be opened and are encouraged to propose questions for the prompt to guide the discussion. Each session should start with a short (10 minute) presentation that summarizes the paper and common threads of the online discussion. The remaining time can be used in various ways and should include some active elements such as discussion in small groups, quizzes, creation of online material. I will help in the preparation process and expect the presenter to send me a complete draft of their slides and a roadmap for the session at least one week ahead of time. **Participants that want to take the class need to select a paper from the list below by September 1. **

### Poster Presentation

During the final session of the course, participants will present a poster that gives an overview of a research project developed in this course. Participants can work in groups of up to three students. The poster session will be advertised to all students, postdocs, and faculty in the Departments of Mathematics and Computer Science.

### Proposal

As a final outcome of the course, participants (in groups of up to three) will submit a research proposal of up to five pages, which will be due about two weeks after the poster session to allow revisions based on the discussions during that event. The proposal must be focused on new research ideas developed during this course. The proposal must provide references to state-of-the-art approaches and clearly identify the research gap tackled by the work.

The proposal should also give some idea about how the project will be carried out. In addition to ‘standard’ research projects resulting in PhD theses or academic papers, we also welcome ideas that could be used for a Data Science contest or that could become homework projects for existing courses in computational mathematics.