Sandbox 10

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



Homotopic Information Theory


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