Understanding resource-rational decision making with mathematical methods: A conversation with Sarah Marzen

Sarah Marzen is an Associate Professor of Physics at the Department of Natural Sciences and Kravis Department of Integrated Sciences at the Claremont Colleges in Southern California. Professor Marzen’s lab explores using machine learning to better understand biological data, interpreting biological organisms as machine learners, and using science to produce societally positive results.

We spoke with Sarah Marzen to learn more about how her work can drive discovery in biological functions such as decision-making, and how NITMB can inspire collaboration at the intersection of mathematics and biology.

What is a big question you’ve been asking throughout your research?

“I want to know how biological systems function. Everyone does. Everyone tackles the problem of understanding in a different way. Some people dive deep into one system and focus on nailing every single detail about that biological system. I took the opposite path and started trying to find biological principles that hold for all organisms at all scales of complexity. There are very few principles that survive, but one that I’m testing out is an optimality principle based on resource-rational decision making. All organisms are making decisions, but they have limited time and energy and memory, and as a result, their decisions are suboptimal—but maybe their decisions are optimally suboptimal, in that they are the best decisions you could possibly make given limited resources. It makes sense given evolution that something like this should be going on, but in my biased opinion, there’s too much handwaving when people talk about resource-rational decision making and not enough quantification. So, I’m trying to quantify this idea and test it out with a combination of reinforcement learning and rate-distortion theory. The idea has survived a few quantitative tests on everything from cultured neurons to humans.”

What disciplines does your research integrate?

“To investigate this question, we have to use information theory, dynamical systems and stochastic processes, machine learning, and of course biophysics. There’s a little bit of cognitive science in there as well, depending on which organism we are studying.”

Where do you find inspiration?

“Everywhere. Sometimes, I find inspiration in the oddest of places. For instance, I happen to be a schizophrenic with very complicated voices. The world of voices is so complicated and imaginative that it’d remind you of Harry Potter’s world. The social dynamics of Voiceland, the world of voices, is fascinating, and two papers have emerged from trying to model the world, as well as some songs and a lot of writing.”

What aspects of your work could be interesting to mathematicians or applied to biology?

“Mathematicians might be interested in how many beautiful mathematical conjectures and proof sketches (since I’m really a physicist) come out of considering biology. For instance, resource-rational decision making can, in some circumstances, be quantified by rate-distortion theory. We investigated a combination of random matrix theory and rate-distortion theory because we just didn’t know what the reward function of the real world was, so we took a guess that it was random. What resulted was a surprising universality result that we still can’t prove, but we can just show it is true numerically. And the cool part is that, like using random energies for the nucleus, this result might have biological implications.

For biologists, the key is that these crazy mathematical ideas actually reveal what’s going on with data if the mathematician manages to actually nail it. You wouldn’t think that esoteric information theory ideas like rate-distortion theory explain real data so well, but they do. Organisms appear to want to conserve resources in a way that you can quantify using bits in order to make decisions that, sometimes, you can quantify using bits. It’s surprising.”

What excites you about NITMB?

“I love the idea of mathematicians and biologists working together more. Mathematicians can take a lot of inspiration from biological problems, and biologists can rest assured that actually, math has something to say about what’s going on with organisms and populations of organisms. I think that NITMB will allow for nascent collaborations to become full-fledged collaborations in service of addressing these mathematical biology questions. And through workshops, perhaps NITMB can serve to bring some of these more niche mathematical biology ideas to light.”

What career achievement are you most proud of?

“Probably the most exciting thing that’s ever happened to me was to get a book contract with Princeton University Press for a biophysics textbook. As I said, I am at teaching colleges, and we put a lot of effort into our course preparation. It was just so gratifying to see that the course preparation really was as good as I delusionally thought. I’m not really sure what counts as a career achievement, but this seems to me to be the closest to an award or honor that I’m really quite proud of.”

Outside of your research, what other interests do you have?

“I like to write pop songs. My producer friend on the East Coast produces them for a discount when I come and visit every so often. I used to like to write, but I got very tired of writing at some point. I like to cook and try out new NYT Cooking recipes constantly.”

What are you hoping to work on in the future?

“I am particularly interested in seeing whether or not the fly connectome suggests to us that indeed, the flies are engaging in resource-rational decision-making. This would be a really strong test of resource-rational decision-making: Can you look at circuits in the brain and say, yes, this is what you would expect in sensory regions if the fly were trying to predict with limited memory? If the optimality principle fails to explain what we see, then oh well, but I’m hopeful.”

Is there anything else you would like the NITMB community to know about you?

“Please do email me out of the blue with crazy ideas. I love hearing about them.”

More information on Sarah Marzen’s work is available on her website.