Mathematical Neuroscience Lab

Departments of Bioengineering and Neurosciences
Center for Engineered Natural Intelligence

The brain as a system.
From theory to engineering.

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We want to understand how the brain works as an engineered system. The foundational principles by which the brain computes. How it learns, internally represents information, and makes meaningful decisions. And how information processing differs in neurodevelopmental disorders such as autism spectrum disorder.

Using this understanding, we are also exploring new forms of computation and machine learning. We create new machine learning algorithms from the neurophysiology. We want to change how humans interact with technology by creating an augmented and personalized human-machine experience. AI built for the individual.

Our publications

Full text PDF’s of our published work.

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Our Research


We use mathematics and engineering to understand the brain as an engineered system. And develop next generation machine learning from the brain.

We are interested in mathematical models and algorithms capable of one-shot adaptive online learning that do not require training or prior exposure to data classes. In particular, models derived from functionally accurate neurophysiological mechanisms. At a foundational level, the key questions involve understanding how and why learning works in these models, and what classes of problems they are uniquely suited for that the existing state of the art in machine learning cannot solve. What classes of functions can these models operate on? How computationally robust are they? Under what constraints and conditions are convergent unique solutions guaranteed?

And how can principles of neural plasticity (facilitation and depression) and neural morphology and architecture allow such models to adapt in contextually relevant ways (e.g. due to changing external queries or other considerations) in real time, without any training?

At the same time, we have a strong interest in how thinking about machine learning from a neuroscience perspective can inform neuroscience itself. On-going work in our group aims to understand what happens when there is a breakdown in signaling in neurodevelopmental disorders; in particular as autism spectrum disorder. Much of our focus is in studying how network geometric and topological structure constrains and determines dynamic function. We also have an interest in the development of advanced brain machine interfaces and neural prosthesis that adapt and learn to new data in order to modulate their outputs.

Our lab


Who we are

The individuals in our lab come from a diverse and varied backgrounds, training, and experiences. We have hosted visiting faculty on sabbatical, and visiting scholars from industry. We have trained research scientists, postdoctoral fellows, clinicians, graduate students, medical students, and undergraduate students.

Who we were

Our lab alumni have gone on to do great things and great careers. They have gone to medical school, graduate school, and industry. Some are faculty or research scientists and engineers at other institutions. Others have gone into research, management, or executive positions in industry. And some are entrepreneurial and have started companies of their own. 

Professor Gabriel A. Silva

Gabe Silva is the lab’s director and Principal Investigator. He is a Professor of Bioengineering and Neurosciences, the Founding Director of the Center for Engineered Natural Intelligence (CENI), and a Jacobs Faculty Endowed Scholar in Engineering.


Historical manuscripts


The pursuit of scientific knowledge and understanding is a dynamic, constantly evolving life long quest. In fact, it is longer than any one lifetime, and therefore bigger than any one individual seeking its pursuit. What we know today is a reflection of what we knew yesterday and the day before. It builds on itself. This is at the core of the pursuit of scientific knowledge. In the course of this search there is an inherent beauty not just in the rewards of finding the answers, but in the struggle and enlightenment of the search itself. It is one of the fundamental things that make us human.

The collection of manuscripts reproduced here represent important historical and seminal works in areas of mathematics, physics, and neuroscience. This is the work from yesterday on which the foundation of today is built. Some of these papers are relatively recent, while some are much older. In a number of cases they are rare high-resolution PDF versions of the original manuscripts. But in all cases they reflect conceptually and technically ground breaking ideas and work. Human creativity, imagination, and ingenuity at its very best. Enjoy.

The incorrectness and weaknesses of a theory cause other minds to formulate the problems more exactly and in this way scientific progress is made.
— Robert Barany, Nobel Prize in Physiology or Medicine, 1914

Top panel: Group picture of the attendees of the 1926 Solvay conference. Left panel: Emmy Noether at work. The woman who changed physics. Center panel: Albert Einstein's office a mere hours after he passed away, as he left it, April 18th 1955. See the story by Ralph Morse, Time Magazine photographer here. Right panel: Santiago Ramon y Cajal. The father of modern neuroscience.