Limits on the computational expressivity of non-equilibrium biophysical processes

Abstract: Many biological decision-making processes can be viewed as performing a classification task over a set of inputs, using various chemical and physical processes as "biological hardware." In this context, it is important to understand the inherent limitations on the computational expressivity of classification functions instantiated in biophysical media. Here, we model biochemical networks as Markov jump processes and train them to perform classification tasks, allowing us to investigate their computational expressivity. We reveal several unanticipated limitations on the input-output functions of these systems, which we further show can be lifted using biochemical mechanisms like promiscuous binding. We analyze the flexibility and sharpness of decision boundaries as well as the classification capacity of these networks. Additionally, we identify distinctive signatures of networks trained for classification, including the emergence of correlated subsets of spanning trees and a creased "energy landscape" with multiple basins. Our findings have implications for understanding and designing physical computing systems in both biological and synthetic chemical settings.

This is joint work with Suri Vaikuntanathan, Arvind Murugan, and Aaron Dinner (https://arxiv.org/abs/2409.05827).

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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