The ergodicity-tracking conjecture for unexpectedness

Let xx be a situation, let CW(x)C_W(x) denote its causal or world complexity, and let CD(x)C_D(x) denote its description complexity. In the minimal frequentist core of Simplicity Theory, write

U(x)=CW(x)CD(x)=CDLTM(x)CDSTM(x),U(x)=C_W(x)-C_D(x)=C_D^{LTM}(x)-C_D^{STM}(x),

where LTMLTM and STMSTM denote long-term and short-term memory, respectively. Ergodicity-tracking conjecture. Unexpectedness, in its frequentist core, tracks changes in the ergodicity of the environment. The surrounding discussion interprets persistent positive unexpectedness as evidence that ergodicity is no longer satisfied, indicating non-stationarity or a bifurcation and prompting the selection or learning of a better generative mechanism. The source gives no proof or resolution.

Sources & referencesView supporting material

Primary source

Giovanni Sileno and Jean-Louis Dessalles, “Three Conjectures on Unexpectedeness”, arXiv:2311.08768 (2023).

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