Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
Disintegration and bayesian inversion via string diagrams.Mathematical Structures in Computer Science, 29(7):938–971
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In Cubical Agda, conditional independence is formalized as paths between kernels, Bayesian conditioning is made total on a full-support fragment, and Pearl's d-separation soundness is verified for finite DAGs, using a new generalized interchange axiom.
In integrable cones, De Finetti's theorem and the free exponential of Linear Logic are shown to be the same construction, yielding a characterization of total elements of !Bool as mixtures of i.i.d. Bernoulli sequences.
ULLER's three independent semantics are unified as instances of monads, enabling modular addition of new semantics and translations between them.
Causal sufficiency is identified with involutive closure plus Frobenius-copy preservation, but the equivalence is true by definition rather than by derivation.
Typed stochastic diagrams of Markov kernels form colored Markov polycategories, and expected-objective gradients decompose into expectations of local reverse-mode contributions.
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Multi-distribution Rényi divergences are positive integrals of coincidence divergences C_α over four strata (simplex interior, mixed-sign cones, tropical boundary, KL edges).
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A cubical formalisation of conditional independence, Bayesian conditioning, and Pearl's d-separation soundness
In Cubical Agda, conditional independence is formalized as paths between kernels, Bayesian conditioning is made total on a full-support fragment, and Pearl's d-separation soundness is verified for finite DAGs, using a new generalized interchange axiom.
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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)
In integrable cones, De Finetti's theorem and the free exponential of Linear Logic are shown to be the same construction, yielding a characterization of total elements of !Bool as mixtures of i.i.d. Bernoulli sequences.
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NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework
ULLER's three independent semantics are unified as instances of monads, enabling modular addition of new semantics and translations between them.
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Infinitesimal Causality
Causal sufficiency is identified with involutive closure plus Frobenius-copy preservation, but the equivalence is true by definition rather than by derivation.
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Colored Markov polycategories and diagrammatic differentiation
Typed stochastic diagrams of Markov kernels form colored Markov polycategories, and expected-objective gradients decompose into expectations of local reverse-mode contributions.