Sandbox 10

PORTAL EXAMPLE Our projects. Kolmogorov-Hopfield Correspondence Program Aiming to link algorithmic information theory and statistical mechanics in weakly coupled systems and to further bridge notions of Shannon and Boltzmann entropy even in absence of a well-defined energy conservation functional, (such as in case of cellular automata and Turing machines). Contemporary Memetics / Noospherics Developing tools for social statistical modeling on local scale. Developing a formal physics of social influence and propagation, as well as how and if latent space representations can be employed as a "semiotic microscope". Developing a notion of "noosphere" through signifier mean-field theory. Sheaf-Theoretic Topological Deep Learning To further develop, both theoretically and in practice, sheaf neural networks and applied spectral sheaf theory as a way to generalize statistical data structures. In what cases can the harmonic cochain problem be simplified? Developing a theory of discrete tangent bundles in statistical contexts and broader connections between Hodge theory and information geometry. Unsupervised Invariant Distillation/Detection Can unsupervised learning models and their latent space representations be used in statistical detection and classification of invariants through Monte-Carlo probing of rich configuration spaces (such as ones in Representation Theory and Low-Dimensional Topology)? In what cases can human intuition be assisted by unsupervised learning models? Spin-Glass Error Program <todo> Homotopic Information Theory <todo>