<ul><li>Researchers have developed a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions.</li><li>The correspondence is based on connecting the Ehrhard-Regnier derivative from linear logic with the role of geometry in Watanabe's singular learning theory.</li><li>By embedding ordinary (discrete) Turing machine codes into a family of noisy codes, a smooth parameter space is formed.</li><li>The structure of the Turing machine and its associated singularity is related to Bayesian inference, implying that the Bayesian posterior can discriminate between different algorithmic implementations.</li></ul>

Programs as Singularities

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