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
Understanding the capabilities and limitations of beyond-binary states in quantum computing
Specialized accelerator computer hardware for scientific simulations
Correct and Efficient Math Libraries
Controlling a robotic hand – with your brain
Understanding the zero-shot learning capabilities of pretrained language models