Unifilarisation of stochastic Mealy machines is an instance of coalgebraic determinisation over monads with support structure, producing causal stochastic behaviours rather than Moore-style output distributions.
Amari.Differential-Geometrical Methods in Statistics, vol
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Higher-order Fisher tensors in exponential-family coordinates of binned energy correlators are simultaneously local KL coefficients, connected cumulants, and hyperedge weights, enabling hypergraph constructions for jet substructure analysis.
The paper justifies the composite coherence metric in event-based narrative extraction via an information-geometric decomposition on the product manifold and an axiomatic uniqueness proof for the geometric mean.
Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.
Determines the GL(n,R)-invariant and Isom-invariant statistical connections on the centered Gaussian model and describes the corresponding moduli spaces under two categorical equivalence relations.
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The moduli spaces of left-invariant statistical structures on Lie groups
Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.