Abstract
In a joint work with D. Bennequin [8], we suggested that the (negative) minima of the 3-way multivariate mutual information correspond to Borromean links, paving the way for providing probabilistic analogs of linking numbers. This short note generalizes the correspondence of the minima of k multivariate interaction information with k Brunnian links in the binary variable case. Following [16], the negativity of the associated K-L divergence of the joint probability law with its Kirkwood approximation implies an obstruction to local decomposition into lower order interactions than k, defining a local decomposition inconsistency that reverses Abramsky’s contextuality local-global relation [1]. Those negative k-links provide a straightforward definition of collective emergence in complex k-body interacting systems or dataset.
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Acknowledgments
I thank warmly anonymous reviewer for helpful remarks improving the manuscript and Daniel Bennequin whose ideas are at the origin of this work.
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Baudot, P. (2021). On Information Links. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_68
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