Learning extreme models with the Coupled Free Energy

Hello, welcome everyone. This is Active Inference Model Stream number 20.1 on January 30th, 2026. And we will be discussing learning extreme models with a coupled free energy by Kenrick Nelson here and colleagues. So Kenrick, thanks a lot for joining. You will provide a presentation. And if anyone is watching live, feel free to put any questions in the live chat and I will read them when we have a discussion. So thanks again for joining and to you for the presentation. Thank you, Daniel. Really appreciate you hosting this talk. Folktrek has been doing a deep dive into Active Inference, including reading the new book that's come out in the last few years. And so we're looking forward to talking with your community about our own work in modeling extremes and how that can be used to improve artificial intelligence. My colleagues that worked on this presentation with me are Igor Olivera from Brazil and Amina Al-Najafi from Iraq. And so what I'm going to go through is sort of an introduction to complex systems and why they have properties that are unique in terms of trying to do modeling in AI. And then I'm going to go through a variety of entropy measures, including the standard ones of the Shannon entropy, but also generalizations that apply to complex systems. And then show why there's a unique one that I call the coupled entropy and how we can use that in variational inference to generalize the free energy function and thereby be able to model quite extreme environments and their distributions. And we'll go over some machine learning about results for that. And then I look forward to discussing it with you and the community. So FOTREC is building capabilities and risk aware intelligence. There's a couple aspects of that. There's a technical aspect, which I'm going to brief today with regard to our work in machine learning and risk risk. There's also a Dow governance piece in terms of using ideas from complex systems regarding how you design protocols for our communities to make good decisions. And then we see these two threads coming together in terms of how we can better mitigate extreme risks like the issues around climate change. The team is diverse. I'm in the Cambridge, Massachusetts area, but we have working partners around the globe. And then we also collaborate with universities. I was on the faculty at Boston University, collaborating with Mark Khan for several years and Eugene Stanley. And then I have also collaborated with Sabir Umaroff at the University of New Haven. And then we have several other university partners. I was in Turkey for two months this year collaborating with Ugar Turknali, which was a fantastic opportunity. So here's the challenge. When it comes to catastrophic risk, we know that it's that those very low probability events that have high impact that are a real concern. But machine learning has grown out of traditions in statistics that revolve around what's called the exponential family and the Gaussian being the most popular example of that. And even the metrics are based on the inverse of that, which is the logarithmic function. That gives us the maximum likelihood metric that gives us the Boltzmann gives Shannon entropy. But these distributions and these metrics don't really account for the heavy tailed properties and the nonlinear properties that we experience in complex systems. And they're quite difficult because the moments can diverge. So there can be situations where you can't measure the variance, which is the most common thing that you're trying to characterize in in machine learning. So we need ways to account for this. And just just as one example to visualize this, you know, the cryptocurrency space is one of the areas that we work in as a community. And Bitcoin is notoriously very volatile. And you can see that in these spikes that are not modeled by a Gaussian distribution. Here we have in the middle an agent based model where in red, you would see something like a Gaussian…