Geometry, SFMs and FEP

[Item: 7b35a6f1-6434-4659-ba9d-43d6b101efad]

https://www.tangramvision.com/blog/the-deceptively-asymmetric-unit-sphere

Interesting tour of differential geometry. Deep reinforcement learning approaches similar manifold oriented problems as in SFMs and active inference (the latter has non Euclidean geometry because probability distribution parameter space is not Euclidean)

https://arxiv.org/pdf/1210.2354v2 describes the two univariate Gaussian case in detail

Friston’s FEP says action choice follows shortest path ie geodesics in those spaces. Maybe links to fluidity: low fluidity is choosing long geodesics between states, and high fluidity is choosing short geodesics. So fluidity is a signature of information geometry of rest state manifold, which is the internal model Q in FEP

☕️☕️