Mentor: Prof. Karthik C. S.

Over the past few decades, randomization has become one of the most pervasive paradigms with applications to algorithm design, cryptography, and combinatorial constructions. But can we reduce or even eliminate the use of randomness in these settings? In many scenarios, we can answer this question in the affirmative by using highly non-trivial extremal combinatorial objects such as expanders, error correcting codes, small biased sets, extractors, dispersers, almost independent sets, and so on. In this project, the student will first survey the known constructions of many of these objects, which in many cases uses simple and yet rich ideas in algebra, geometry, number theory, and combinatorics. Next, the we will explore if we can propose constructions which are better than the state-of-the-art parameters for one or more of these objects.

**Students on this project**: Surya Mantha, Keya Patel, Elijah Rubin

Mentor: Prof. Yipeng Huang

**Students on this project**: Arpan Gupta, Cyrus Majd

Mentor: Prof. Yipeng Huang

**Students on this project**: Alex Miralles-Cordal

Mentor: Prof. Santosh Nagarakatte

**Students on this project**: Pranav Kalapala

Mentor: Prof. Konstantinos Michmizos

Imagine using your brain to control a robotic hand. In our lab, we a) wonder how our brain moves our limbs, and b) study how we can be inspired by our knowledge about our brain to develop algorithms that move a robotic hand. There are 5 areas of knowledge required for succeeding in this project - computer science, neuroscience, robotics, mathematics, and machine learning. When you come (or when you leave), you are expected to have some knowledge in at least three of these areas. Specifically, you are expected to get familiar with some of the hardware that we currently use in the lab, that includes an 128-channel EEG system, the Wonik Allegro robotic hand, our in-house robotic head, a robotic hexapod, and the Bionik Arm rehabilitation robot. You will also read – and digest – the relevant papers on EEG-driven robotic systems, including our own (e.g., Kumar & Michmizos, Nature Scientific Reports, 2022). And you will hopefully help us in extending our current methods and applications. If successful, your Capstone project will develop novel brain-inspired methods and algorithms that can reach clinical applications, such as those of rehabilitation robotics and neuro-prosthetics.

**Students on this project**: Qihan Jin

Mentor: Prof. Karl Stratos

Recently, the field of natural language processing (NLP) has been galvanized by the seemingly astounding capabilities of large-scale pretrained language models (PLMs) to solve unknown tasks (i.e., zero-shot learning) as long as they can be framed in natural language (e.g., provide the input "Translate the following sentence to German: [sentence]" to a PLM, expect a German translation of [sentence] as output). This approach, also known as "prompting", has generated a number of papers trying to use and better understand it, but most are superficial applications and analyses which do not offer a satisfying explanation for why prompting works and how. In this project, we will thoroughly chart the current landscape of prompting prominent PLMs (e.g., GPT-3, T0) by systematic experiments on standard zero-shot performance benchmarks (e.g., T0 datasets) and aim to develop a new understanding and methods of prompting.

**Students on this project**: Alex Rashduni, Akshaj Tyagi