Researchers from institutions across the United States are contributing to innovative projects at the NSF-Simons National Institute for Theory and Mathematics in Biology. These research projects focus on developing mathematical frameworks that illuminate emergent capabilities of biological systems. The NSF-Simons NITMB is developing the theory and mathematics needed to highlight the fundamental roles of physical, chemical, and biological constraints as organizing principles for understanding biological mechanisms. In order to highlight the diversity of experts developing NITMB Supported Research and the significance of their contributions, we will share insight into our growing community of researchers as part of the NITMB Spotlight series.
Xaq Pitkow is an associate professor of computational neuroscience at Carnegie Mellon University. He is in the Neuroscience Institute and, by courtesy, the Department of Machine Learning. Pitkow’s LAB (Lab for the Algorithmic Brain) aims to understand how the brain works using mathematical principles. The LAB develops theories of neural computation and collaborates with experimentalists to test such predictions. Xaq Pitkow is also part of the NITMB supported research project, ‘Impact of higher order structures on the dynamics of neural networks.’ This project works to explain how higher-order structure in the connectivity of neural networks shapes both local and global aspects of their dynamics, and, ultimately, shapes their function.
We spoke with Xaq Pitkow to explore his research directions and the opportunities for future work integrating ecological psychology, neuroscience, and AI.
What is a big question you’ve been asking throughout your research?
“I’m interested in principles of intelligence in brains and machines. What structured computations explain the brain and, hopefully, lead to better generalization? I especially focus on the algorithmic level, trying to bridge between the performance goals of computation and the neural mechanisms. There are many ways to solve a given problem that can differ in those mechanisms, and I try to identify the key abstract properties that are shared by all equivalent solutions.”
What disciplines does your research integrate?
“My research draws from many disciplines, especially neuroscience, statistics, physics, computer science, and cognitive science.”
Where do you find inspiration?
“I love to think about geometry, imagining the computational dynamics on neural manifolds that transform sensory inputs to behavior. I also find inspiration from nature, thinking about the clever solutions that animals have discovered to thrive.”
What aspects of your research could be interesting to mathematicians or applied to biology?
“I mentioned working at the algorithm level. Mathematically it’s interesting to consider what structures lead to equivalently structured computations. This is naturally described as dynamics on a foliation. But more generally, there’s a fundamental challenge: complexity. Computation on natural problems, whether by either brains or machines, must account for lots of complex, niche-specific structures. That makes it hard to extract simple, general principles. Still, that’s the aspiration of the field. There’s hope because despite the complexity, the natural world does have significant structure, and we expect the brain to mirror that in some way.”
What about the NITMB do you find exciting?
“I like the research themes that NITMB focuses on, and I think they are compelling domains to look for unifying principles amidst the diversity. NITMB also brings together a community of researchers with a wonderful set of perspectives, and who are eager to open doors and share knowledge.”
What career achievement are you most proud of?
“I’m fond of a number of my published studies, but I’m most proud of a framework for connecting encoding, recoding, and decoding. This framework enables me to think about, and quantitatively analyze, the entire stream of brain computations acting on a low-dimensional task-relevant manifold.”
Outside of your research, what other interests do you have?
“I like to do music and art. I like to improvise on a bunch of musical instruments, especially piano but also including instruments from around the world. I’m a graphic illustrator and visual artist, and I particularly enjoy mathematical sculpture.”
What are you hoping to work on in the future?
“I’m excited about integrating the fields of ecological psychology, neuroscience, and AI, and I’ve been involved in an amazing international team that is gearing up to test some fundamental hypotheses from these fields.”
The NITMB is enthusiastic to have Xaq Pitkow as a contributor to NITMB supported research improving our understanding of the dynamics of neural networks. More information about Xaq Pitkow’s work is available on the LAB website, and more information on Pitkow’s NITMB supported research project, ‘Impact of higher order structure on the dynamics of neural networks,’ is available on the NITMB website.