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.
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Springer Monographs in Mathematics
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Positive Lyapunov exponents can block natural-innovation synchronization (hence usable functional dependence) for uniformly ergodic AR maps, even though Doeblin splitting always yields a geometric Bernoulli representation on an enlarged space.
Residual network Jacobians under Frobenius normalization have singular spectra that form trace-normalized Cartan orbits satisfying slack-aware margin inequalities bounding exponent drift to order (log M)/L in zero-slack cases.
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Bayesian updates from coalgebraic determinisation
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.
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Functional dependence and synchronous coupling in ergodic autoregressions
Positive Lyapunov exponents can block natural-innovation synchronization (hence usable functional dependence) for uniformly ergodic AR maps, even though Doeblin splitting always yields a geometric Bernoulli representation on an enlarged space.
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Geometric and Spectral Alignment for Deep Neural Network I
Residual network Jacobians under Frobenius normalization have singular spectra that form trace-normalized Cartan orbits satisfying slack-aware margin inequalities bounding exponent drift to order (log M)/L in zero-slack cases.