Using category theory to assess the relationship between consciousness and integrated information theory

Hello, I'm Hayato Saigo. Okay. Just one second. I'll just make sure it's going. It's all good. All right. Welcome to both. It is June 13th at zero UTC. We're here in active guest stream number 44.1 with Hayato Saigo and Nausugu Tsuchiya. So really looking forward to this presentation and discussion. Hayato, please say hello and then we'll continue with Nausugu's presentation. Hello, I'm Hayato Saigo. I'm a mathematician and a mathematical physicist also interested in consciousness. I have worked a lot with Nao by using category theory and application to IIT or other consciousness theories. So Nao. All right. So my name is Nao Tsuchiya. I'm a professor in Monash University and also having a lab in ATR in Japan. And as a sort of introduction to this today's session, I'll give a brief talk on our recent project called the Quaria Structure, which Hayato and I will be collaborating and also a little bit on the quantum Quaria hypothesis. Both of them are hopefully relevant to active inference issue. So the Quaria structure project is the Japanese funding that we received recently and it's going to continue for five years. This will be to establish a super interdisciplinary research program to tackle the problem of consciousness, especially Quaria through the interdisciplinary research. We are planning to also host summer school for two to three weeks every year. And here's the fantastic members for this grant. And Hayato is basically working with me in the part of the mathematical approach to the consciousness and the Quaria. And so one of the problems, for example, we want to address is, for example, when you see this square, Daniel, what do you see here? Blue. Blue. Yeah. So you say blue and I say maybe owl in Japanese and the Hayato may say sunny in Russian, but we could mean the same experience, Quaria. But how do we know that we are actually experiencing the same thing? And I'm actually curious whether this kind of question is something that the free energy or active inference kind of style approach can ever tackle. And my approach is to go into that category theory kind of inspired direction. And here's the first study that published, you know, we published in a few years ago with Hayato and Shigeru together with also another category theorist, Steve Phillips, that in the category theory, there's an interesting lemma called Yoneza lemma that proves that all the relationship characterizes its internal intrinsic properties and we are using that idea to study the Quaria. That's the kind of inspiration of our approach. So instead of, you know, trying to characterize what the blue is or red is, we are trying to characterize all the relationship between a particular color or particular Quaria to other exhaustively. And then by finding the correspondence of this relationship, we try to identify what the actual blue is. So if you will say blue is similar to green, but also similar to red, then that's going to be very different from my blue. And that's the way how we detect this, you know, blueness is same or different. And one recent application of this kind of idea is this unsupervised alignment that we are using with another collaborator, Masa Fumi, Oizumi University of Tokyo. And I'll skip the detail. And I'll skip the detail. But basically what we are doing is to do some kind of experiment and then collect lots of data to obtain so-called similarity matrix between all the colors. And then without really knowing what color maps onto what we try to use on the relationship to predict what we are seeing. So in a sense, this is a purely category theoretical kind of, you know, approach to the problem of consciousness. So then I'll just skip the details here. And then, yeah, so we are doing this kind of approach on other types of the codec. And then this is the thing that we are planning to do for the next five years. And then another just brief kind of, you know, introduction. If you have some other question, we can come back later. So…