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Lawrence Udeigwe uses elegant math to understand complex brain systems | MIT News


It’s a familiar story to many first-generation students: Neither of Lawrence Udeigwe’s parents had more than a sixth-grade education, yet they were willing to sacrifice anything to educate their children.

“My father,” Udeigwe said, “used to tell us, ‘I’m willing to sell everything so you can go to school.'”

Udeigwe says that in Nigeria at the time, achieving the kind of success and stability his parents hoped for meant studying something practical and working for the government. So he moved to the United States, enrolled at Duquesne University in Pittsburgh, and majored in computer science.

“But then I discovered mathematics,” he says, and his dream of a job as a Nigerian government programmer was replaced by something new.

Udeigwe went on to a successful career as a professor of mathematics at Manhattan College in New York, bridging disciplinary gaps between calculus, pure mathematics, and neuroscience. This year, Udeigwe is at MIT as a Martin Luther King (MLK) Visiting Professor and Scholar in the Department of Brain and Cognitive Sciences. He is one of nine professors, in research fields ranging from art to engineering, selected for their outstanding contributions in their fields to increase the presence of underrepresented scholars of color at MIT.

The journey to MIT for Udeigwe began at the University of Delaware graduate school. Although the program was called Applied Mathematics, he was technically studying pure mathematics until, as he explains with a laugh, he discovered that he was actually interested in applied mathematics, particularly its applications in biology.

Like his discovery of mathematics as an undergraduate, Udeigwe’s discovery of mathematical biology pushed him to shift gears. He returned to Pennsylvania at the University of Pittsburgh to pursue his doctorate where he got his first taste of mathematical neuroscience. From there he became a professor at Manhattan College, a liberal arts college in the Bronx. He says the position has been great for improving his teaching skills and working closely with students, but he often had to put his research on the back burner.

Despite the heavy course load, however, he remained intellectually engaged with the neuroscience community, attending lectures and watching lectures online. One such presentation, from the Center for Brain, Mind, and Machines at MIT, was given by James DiCarlo of MIT, Peter de Florez Professor of Neuroscience and, at the time, head of the Department of Brain and Cognitive Sciences.

Udeigwe was immediately drawn to DiCarlo’s research using advanced computer models to understand the complex brain systems that underlie vision. A cold email and several meetings later, DiCarlo and Udeigwe had applied to the MLK Scholars program to bring Udeigwe to MIT.

“I love Jim’s lab, his collegial nature,” says Udeigwe. “We’re all colleagues, trying to build something, trying to move our little part of the scientific enterprise forward.”

A fundamental aspect of this endeavor for Udeigwe has been bridging what DiCarlo describes as a tension in neuroscience. On the one hand, those with a classical background in mathematics and physics who want to create models to describe neural activity using elegant equations that are easy to understand (at least for anyone who thinks in terms of “simple” differential equations). On the other side are those like DiCarlo, who rely on simulation and brute force computation to create models that can be scaled to describe the entire complex system of vision but which are, as DiCarlo describes them, “opaque to humans”.

Udeigwe and DiCarlo hope that by working together they can find something in between.

“He is a mathematician. I’m more of an engineer and experimenter,” says DiCarlo. The two, he explains, have a lot to learn from each other about how the other approaches fundamental questions in neuroscience. They are also the perfect combination to jointly teach students to better understand the benefits – and potential shortcomings – of applying mathematical theories to complex systems like the brain.

The course they designed, a seminar for graduate and advanced undergraduate students, begins with a basic discussion establishing definitions and clarifying the differences between theories, models, assumptions, and frameworks. From there, they plan to examine “theories that worked,” as Udeigwe describes it, determining where those theories came from, what they can accomplish, and where they failed.

“Students will explore the advantages and disadvantages of these two toolkits,” says DiCarlo. “Are they going to go more towards the classic and elegant toolbox of differential equations? Will they turn to the more modern artificial network simulation toolkit? Or will they find bridges between these two approaches, as Lawrence tries to do?

To that end, Udeigwe worked with Tiago Marques, a postdoc in the lab, on a project to improve models of so-called ventral flow. Ventral flow is the series of brain processing steps that translates images into increasingly complex patterns of neural activity, so that the image striking the eye becomes an object recognized by the brain. The first processing step, called V1, is the best understood part of the path. A property of the V1 zone called “ambience suppression” is particularly interesting.

Scientists understand that each neuron in V1 is activated in response to a small region of an image. Standard visual processing computer models are designed to capture this fact. Surround suppression, however, means that the strength of each neuron is changed (usually suppressed, as the name suggests) by adding features into the image outside of that neuron’s primary region – features that stimulate neighboring neurons. Although such “surround” phenomena are empirically well understood, they are not explicitly incorporated into existing models of ventral flow.

Udeigwe’s goal is to change that by incorporating surround suppression into contemporary models derived from machine learning, in the hope that it will improve object recognition to be more human-like. In turn, these computational models – based on elegant mathematics – can be used to better understand object recognition in people.

DiCarlo says Udeigwe’s work is an ambitious step in trying to relate mathematical models at the scale of a single neuron to the functioning of the entire ventral processing flow. For Udeigwe, it is also an opportunity to bring MIT and Manhattan College closer together. Two of his students, Andrew Cirincione and Artiom Bic, work on research with Udeigwe and Marques and have visited MIT several times.

MLK fellows still have several months at MIT, but Udeigwe is already strategizing to foster his relationship with MIT beyond the fellowship period. He hopes to continue teaching the course developed with DiCarlo, expanding it around theory in science more broadly, and to leverage the relationships he is building this year for future collaborations. He also wants to further his research around the intersections of math and vision with small-scale projects that his Manhattan College students, such as Cirincione and Bic, can undertake.

Udeigwe also developed a research initiative for veterans and reservists at MIT. The idea was prompted both by his own lifelong interest in military service as a means of giving back to the country and by his experiences with veteran students at Manhattan College. Udeigwe hopes to foster opportunities for students to develop and undertake research projects on national security issues, informed by what he describes as the unique perspective and problem-solving skills they have learned through the military service.

As to whether his time at MIT converted him to DiCarlo’s more simulation-based approach to neuroscience, Udeigwe laughs that he remains “agnostic.”

“I am a mathematician. I like the conciseness of mathematical equations. It’s stylish, it’s portable in other areas. It’s easy to pass on to students,” he explains. “But, at the same time, not all beautiful equations lead to things that we can build…so I have to be open to different methodologies.”


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