The unique family of multi-distribution Rényi functionals is the positive integral of coincidence divergences C_α over the simplex interior, mixed-sign cones, tropical boundary, and KL edges.
Disintegration and bayesian inversion via string diagrams.Mathematical Structures in Computer Science, 29(7):938–971
6 Pith papers cite this work, alongside 72 external citations. Polarity classification is still indexing.
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Infinitesimal causality is defined via compatibility of categorical and geometric Frobenius structures in Markov categories, with interventions as tangent vectors deforming copy/discard operations and Lie brackets measuring preservation of information flow.
Cubical Agda formalization of conditional independence as paths, Bayesian conditioning, and soundness of Pearl's d-separation on arbitrary finite DAGs, plus a minimal generalization of the convex-algebra interchange axiom.
Colored Markov polycategories provide typed compositional semantics for stochastic systems and support diagrammatic differentiation of expected scalar objectives via local gradients at parameterized vertices.
ULLER's three independent semantics are unified as instances of monads, enabling modular addition of new semantics and translations between them.
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.
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The unique family of multi-distribution Rényi functionals is the positive integral of coincidence divergences C_α over the simplex interior, mixed-sign cones, tropical boundary, and KL edges.
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Infinitesimal Causality
Infinitesimal causality is defined via compatibility of categorical and geometric Frobenius structures in Markov categories, with interventions as tangent vectors deforming copy/discard operations and Lie brackets measuring preservation of information flow.
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A cubical formalisation of conditional independence, Bayesian conditioning, and Pearl's d-separation soundness
Cubical Agda formalization of conditional independence as paths, Bayesian conditioning, and soundness of Pearl's d-separation on arbitrary finite DAGs, plus a minimal generalization of the convex-algebra interchange axiom.
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Colored Markov polycategories and diagrammatic differentiation
Colored Markov polycategories provide typed compositional semantics for stochastic systems and support diagrammatic differentiation of expected scalar objectives via local gradients at parameterized vertices.
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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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Interpreting De Finetti's theorem in the Category of Integrable Cones (long version)
Establishes a formal connection between Jacobs-Staton categorical De Finetti theorem and Melliès free exponential in linear logic, instantiated in probabilistic coherence spaces, then characterizes total elements of !Bool.