Paolo Perrone
@paolopmath.bsky.social
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📥 47
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Mathematician & Math Teacher
pinned post!
My book is out!
www.worldscientific.com/worldscibook...
about 1 year ago
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More on the relationship between string diagrams and probabilistic graphical models. New work by Antonio Lorenzin and Fabio Zanasi.
arxiv.org/abs/2512.09908
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Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective
Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian netw...
https://arxiv.org/abs/2512.09908
23 days ago
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New work by Bart Jacobs, Márk Széles and Dario Stein.
arxiv.org/abs/2512.00209
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Compositional Inference for Bayesian Networks and Causality
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables...
https://arxiv.org/abs/2512.00209
about 1 month ago
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Descent in Probability Theory: the first steps down
youtu.be/VG2RTE1R0BY?...
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[Oxford Seminar] Paolo Perrone | Descent in Probability Theory: the first steps downward
YouTube video by Topos Institute
https://youtu.be/VG2RTE1R0BY?si=mgRJ2cBgPyrH919n
about 2 months ago
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Anyone in Milan tomorrow?
about 2 months ago
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"Independent States Are Orthogonal", a talk at GSI 2025 bridging probability and geometry.
youtu.be/mUPJEt3FeiU
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Paolo Perrone - Independent States Are Orthogonal - GSI 2025
YouTube video by Paolo Perrone
https://youtu.be/mUPJEt3FeiU
about 2 months ago
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New introduction to Categorical Probability for Physicists, by Tomáš Gonda:
www.youtube.com/live/eVfFuIG...
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TOMAS GONDA: Introduction to Categorical Probability
YouTube video by IQOQI Vienna
https://www.youtube.com/live/eVfFuIGEZxc?feature=shared
3 months ago
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Great work by Areeb Shah-Mohammed on partial morphisms in Markov categories.
arxiv.org/abs/2509.05094
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Partializations of Markov categories
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier mod...
https://arxiv.org/abs/2509.05094
4 months ago
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We should call it 'connecting the DOTS'.
5 months ago
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A categorical definition of independence! Here is a recording of the talk I gave at CT 2025, for anyone who might have missed it.
youtu.be/ls6zOX8L1eI
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Categories of relations which compose independently - Paolo Perrone
YouTube video by Paolo Perrone
https://youtu.be/ls6zOX8L1eI
5 months ago
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New paper out!
arxiv.org/abs/2508.01146
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Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories
Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the categ...
https://arxiv.org/abs/2508.01146
5 months ago
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The document that started categorical probability, part of secret work from 1962, has reappeared, together with new commentaries of its author, Bill Lawvere.
lawverearchives.com/wp-content/u...
Thanks to Tobias Fritz and to the Lawvere Archives for the work.
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https://lawverearchives.com/wp-content/uploads/2025/07/1962.probmap.pdf
5 months ago
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I'm excited to be in Bologna for the week! (If anyone is here and wants to meet, write me an email.)
7 months ago
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Me, every time the EU "wants to attract researchers":
8 months ago
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We start in 10 minutes!
8 months ago
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What are point-free measurable spaces, and what is their quantum equivalent? Great work by Tobias Fritz and Antonio Lorenzin.
arxiv.org/abs/2504.13708
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Categories of abstract and noncommutative measurable spaces
Gelfand duality is a fundamental result that justifies thinking of general unital $C^*$-algebras as noncommutative versions of compact Hausdorff spaces. Inspired by this perspective, we investigate wh...
https://arxiv.org/abs/2504.13708
9 months ago
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We finally have the strong law of large numbers in Markov categories.
arxiv.org/abs/2503.21576
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Empirical Measures and Strong Laws of Large Numbers in Categorical Probability
The Glivenko-Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying dist...
https://arxiv.org/abs/2503.21576
9 months ago
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To all my UK-based mutual are into 'cybernetics', I very strongly recommend this exhibition in London.
www.tate.org.uk/whats-on/tat...
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Electric Dreams | Tate Modern
https://www.tate.org.uk/whats-on/tate-modern/electric-dreams
10 months ago
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New great work by Dario Stein.
arxiv.org/abs/2503.02477
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Random Variables, Conditional Independence and Categories of Abstract Sample Spaces
Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). ...
https://arxiv.org/abs/2503.02477
10 months ago
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What do Beck-Chevalley monads have to do with conditional probability?
arxiv.org/abs/2502.14941
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Categorical algebra of conditional probability
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this p...
https://arxiv.org/abs/2502.14941
10 months ago
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reposted by
Paolo Perrone
julesh
11 months ago
If there was anybody competent in charge in Europe we would be passing emergency legislation this week so that starting next week we poach every scientist from the US who was previously funded by NSF, NIH etc. Oh well, we can dream.
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Never forget that you do can do natural gradient descent in Haskell!
github.com/alex404/goal
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GitHub - alex404/goal: The Geometric OptimizAtion Libraries
The Geometric OptimizAtion Libraries. Contribute to alex404/goal development by creating an account on GitHub.
https://github.com/alex404/goal
11 months ago
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Excited to be in Seattle for the JMM! Besides ACT today and categorical probability on Saturday, which sessions are my fellow category theorists attending?
12 months ago
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Here's a lecture at MIT on Markov categories, symmetries, and generative AI by Rob Cornish and myself.
youtu.be/ozN4zLEUCgs?...
#touchdesigner
#streamdiffusion
#bananas
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ACT4ED Special Lecture - Paolo Perrone, Rob Cornish (Oxford): Markov Categories, Symmetries, & GenAI
YouTube video by Zardini Lab
https://youtu.be/ozN4zLEUCgs?feature=shared
about 1 year ago
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New paper on Markov categories, proving Aldous-Hoover categorically, by Leihao Chen, Tobias Fritz, Tomáš Gonda, Andreas Klingler, Antonio Lorenzin.
arxiv.org/abs/2411.12840
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The Aldous--Hoover Theorem in Categorical Probability
The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equality in distribution,...
https://arxiv.org/abs/2411.12840
about 1 year ago
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The smartest thing the EU can do now is release a ton of funding for scientists, and relative visas. And I mean immediately.
about 1 year ago
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My book is out!
www.worldscientific.com/worldscibook...
about 1 year ago
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