#appliedcategorytheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #appliedcategorytheory, aggregated by home.social.
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🎓 Oh joy, a course on Applied Category Theory—because who doesn't want to spend their free time unraveling the mysteries of preorders and adjoints? 🙄 It's like the Avengers of abstract math concepts, minus the fun and special effects. Dive right in, they said—don't worry, there won't be any lifeguards. 🏊♂️
https://math.ucr.edu/home/baez/act_course/index.html #AppliedCategoryTheory #MathNerds #AbstractMath #LifeguardsNotIncluded #AvengersOfMath #HackerNews #ngated -
🎓 Oh joy, a course on Applied Category Theory—because who doesn't want to spend their free time unraveling the mysteries of preorders and adjoints? 🙄 It's like the Avengers of abstract math concepts, minus the fun and special effects. Dive right in, they said—don't worry, there won't be any lifeguards. 🏊♂️
https://math.ucr.edu/home/baez/act_course/index.html #AppliedCategoryTheory #MathNerds #AbstractMath #LifeguardsNotIncluded #AvengersOfMath #HackerNews #ngated -
CW: Hivemind: On the nature of mathematical proof in applied problems #PhilosophyOfMathematics #AppliedCategoryTheory
Mathematics is a formal system. The mathematician states axioms (that is, assumes the existence of some formal entities and relationships between them) and applies previously agreed formal inference rules to derive more relationships within the formal system.
Essentially, it's about making explicit the logical consequences that are implied by the original assumptions. Everything happens inside the formal system with no regard to anything outside that system. It's all about transforming meaningless symbols according to agreed rules that are concerned only with those symbols and not what they might correspond to outside that formal system.
In an applied problem, the mathematician maps elements of the external world to formal mathematical elements; mathematically manipulates the formal image of the external world to derive some implications; then inverse maps those formal implications back to the external world to make claims about implications in the external world.
The proofs in the formal systems are as proof-ish as any mathematics ever is. However, the external world and the mapping from the external world to the formal representation are not formal - so it seems to me that the proof in the formal representation are confined to that formal representation and can not extend back into the external world. That is, the chosen conceptualisation of the external world and the chosen mapping to its formal representation is assumed to be appropriate and the correctness of those assumptions is not able to be investigated from within the formal representation.
Consequently, I think the hardest part of applied maths for any problem domain would be finding a conceptualisation of the external world and mapping to the formal domain such that the formal manipulations actually tell us something about the external world, as a matter of fact. However, I don't see this discussed in the applied work that I read. The mappings are treated as self-evident.
This issue feels like it should be old-hat in the right literature. (It also feels a lot like the symbol grounding problem in #CognitiveScience.) I would greatly appreciate any pointers to literature with practical conclusions about this. (It also feels like something that #AppliedCategoryTheory people should have views about.)
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CW: Hivemind: On the nature of mathematical proof in applied problems #PhilosophyOfMathematics #AppliedCategoryTheory
Mathematics is a formal system. The mathematician states axioms (that is, assumes the existence of some formal entities and relationships between them) and applies previously agreed formal inference rules to derive more relationships within the formal system.
Essentially, it's about making explicit the logical consequences that are implied by the original assumptions. Everything happens inside the formal system with no regard to anything outside that system. It's all about transforming meaningless symbols according to agreed rules that are concerned only with those symbols and not what they might correspond to outside that formal system.
In an applied problem, the mathematician maps elements of the external world to formal mathematical elements; mathematically manipulates the formal image of the external world to derive some implications; then inverse maps those formal implications back to the external world to make claims about implications in the external world.
The proofs in the formal systems are as proof-ish as any mathematics ever is. However, the external world and the mapping from the external world to the formal representation are not formal - so it seems to me that the proof in the formal representation are confined to that formal representation and can not extend back into the external world. That is, the chosen conceptualisation of the external world and the chosen mapping to its formal representation is assumed to be appropriate and the correctness of those assumptions is not able to be investigated from within the formal representation.
Consequently, I think the hardest part of applied maths for any problem domain would be finding a conceptualisation of the external world and mapping to the formal domain such that the formal manipulations actually tell us something about the external world, as a matter of fact. However, I don't see this discussed in the applied work that I read. The mappings are treated as self-evident.
This issue feels like it should be old-hat in the right literature. (It also feels a lot like the symbol grounding problem in #CognitiveScience.) I would greatly appreciate any pointers to literature with practical conclusions about this. (It also feels like something that #AppliedCategoryTheory people should have views about.)
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I am always careful, when discussing the organization of organisms, because saying things like "the whole is not the sum of its parts" makes people think I'm talking about vitalism or religion or something, but I'm talking about non-cartesian products which lack projections #RM3 #SMCC #AppliedCategoryTheory
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Sad not to be in Oxford for Applied Category Theory this week. Hope you all have a blast!
#act #appliedcategorytheory -
This year's Joint Mathematics Meetings in San Francisco is going to be pretty chill for me. This is my fourth #JMM and my third in person. Last year I organized a session on #AppliedCategoryTheory, but this time around I'm just giving a couple talks on #MachineLearning and the history of the #Bourbaki group.
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This year's Joint Mathematics Meetings in San Francisco is going to be pretty chill for me. This is my fourth #JMM and my third in person. Last year I organized a session on #AppliedCategoryTheory, but this time around I'm just giving a couple talks on #MachineLearning and the history of the #Bourbaki group.
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As I prepare to head back home from #Cambridge, I'm reflecting on how much I've learned and on the hospitality shown to me by Jamie Vicary and his graduate students, @jonmsterling, and the computer lab as a whole. My first trip to the UK has been the experience of a lifetime and I look forward to seeing new friends I've made here again soon.
I was surprised to find that one person did a great deal to make me feel welcome despite the fact that I never met her. I noticed the pictured pride flag on my first day in the computer lab, and I assumed everyone signed it as part of some event. I don't talk much about being queer on Mastodon, but seeing this definitely helped me feel much more at ease in a place which was foreign to me, an American mathematician, in multiple senses.
(1/2)
#ComputerScience #CategoryTheory #AppliedCategoryTheory #queer
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As I prepare to head back home from #Cambridge, I'm reflecting on how much I've learned and on the hospitality shown to me by Jamie Vicary and his graduate students, @jonmsterling, and the computer lab as a whole. My first trip to the UK has been the experience of a lifetime and I look forward to seeing new friends I've made here again soon.
I was surprised to find that one person did a great deal to make me feel welcome despite the fact that I never met her. I noticed the pictured pride flag on my first day in the computer lab, and I assumed everyone signed it as part of some event. I don't talk much about being queer on Mastodon, but seeing this definitely helped me feel much more at ease in a place which was foreign to me, an American mathematician, in multiple senses.
(1/2)
#ComputerScience #CategoryTheory #AppliedCategoryTheory #queer
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My talk from yesterday on a categorical semantics for neural nets for the New York Category Theory Seminar has already been posted on YouTube! You can find it at https://www.youtube.com/watch?v=FKkpVKuspmA and you can see more about this seminar at https://www.sci.brooklyn.cuny.edu/~noson/Seminar/. The preprint I mention is https://arxiv.org/abs/2308.00677 and the talk by Joyal which was mentioned at the end can be found at https://www.youtube.com/watch?v=MxClaWFiGKw.
#CategoryTheory #AppliedCategoryTheory #AI #MachineLearning #ComputerScience #UniversalAlgebra #NeuralNets
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My talk from yesterday on a categorical semantics for neural nets for the New York Category Theory Seminar has already been posted on YouTube! You can find it at https://www.youtube.com/watch?v=FKkpVKuspmA and you can see more about this seminar at https://www.sci.brooklyn.cuny.edu/~noson/Seminar/. The preprint I mention is https://arxiv.org/abs/2308.00677 and the talk by Joyal which was mentioned at the end can be found at https://www.youtube.com/watch?v=MxClaWFiGKw.
#CategoryTheory #AppliedCategoryTheory #AI #MachineLearning #ComputerScience #UniversalAlgebra #NeuralNets
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In a couple hours I'll be giving a talk online for the New York Category Theory Seminar! This is going to be another iteration of "A categorical semantics for neural networks", which I first discussed last week at the Cambridge Logic and Semantics Seminar. I got some really helpful questions/feedback last week, so I'll have some new thoughts to share today.
In particular, I think I may want to use a horizontal categorification of clones, rather than traditional multicategories.
More info:
https://www.sci.brooklyn.cuny.edu/~noson/Seminar/#AppliedCategoryTheory #CategoryTheory #NeuralNets #AI #MachineLearning #ComputerScience
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In a couple hours I'll be giving a talk online for the New York Category Theory Seminar! This is going to be another iteration of "A categorical semantics for neural networks", which I first discussed last week at the Cambridge Logic and Semantics Seminar. I got some really helpful questions/feedback last week, so I'll have some new thoughts to share today.
In particular, I think I may want to use a horizontal categorification of clones, rather than traditional multicategories.
More info:
https://www.sci.brooklyn.cuny.edu/~noson/Seminar/#AppliedCategoryTheory #CategoryTheory #NeuralNets #AI #MachineLearning #ComputerScience
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I will be giving a talk on a functorial semantics for neural nets on Friday at the #Cambridge computer lab's Logic and Semantics Seminar. If you happen to be in the area at the time, consider checking it out!
This will be my first talk on a synthesis of my paper on discrete neural nets (https://arxiv.org/abs/2308.00677) and the categorified invariant theory appearing in my thesis (https://aten.cool/documents/thesis.pdf).
Abstract and other info: https://www.cst.cam.ac.uk/seminars/list/208831
#CategoryTheory #AppliedCategoryTheory #AI #MachineLearning #ComputerScience #logic #math #combinatorics #UniversalAlgebra
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I will be giving a talk on a functorial semantics for neural nets on Friday at the #Cambridge computer lab's Logic and Semantics Seminar. If you happen to be in the area at the time, consider checking it out!
This will be my first talk on a synthesis of my paper on discrete neural nets (https://arxiv.org/abs/2308.00677) and the categorified invariant theory appearing in my thesis (https://aten.cool/documents/thesis.pdf).
Abstract and other info: https://www.cst.cam.ac.uk/seminars/list/208831
#CategoryTheory #AppliedCategoryTheory #AI #MachineLearning #ComputerScience #logic #math #combinatorics #UniversalAlgebra
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Good morning UK! In two weeks I'll be visiting #Cambridge for about two weeks. Please let me know if there's anything cool I should check out while I'm there.
I'll be speaking at this seminar (https://talks.cam.ac.uk/show/index/6375) about a functorial semantics for neural nets. I still need to send in an abstract, so my talk isn't listed yet. This topic is a synthesis of my preprint «Discrete neural nets and polymorphic learning» (https://arxiv.org/abs/2308.00677) as well as some of the results from my thesis (https://aten.cool/documents/thesis.pdf).
I am planning on making a trip to #Nottingham at some point, as well.
#AI #MachineLearning #AppliedCategoryTheory #Combinatorics #CategoryTheory
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Good morning UK! In two weeks I'll be visiting #Cambridge for about two weeks. Please let me know if there's anything cool I should check out while I'm there.
I'll be speaking at this seminar (https://talks.cam.ac.uk/show/index/6375) about a functorial semantics for neural nets. I still need to send in an abstract, so my talk isn't listed yet. This topic is a synthesis of my preprint «Discrete neural nets and polymorphic learning» (https://arxiv.org/abs/2308.00677) as well as some of the results from my thesis (https://aten.cool/documents/thesis.pdf).
I am planning on making a trip to #Nottingham at some point, as well.
#AI #MachineLearning #AppliedCategoryTheory #Combinatorics #CategoryTheory
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I'm giving another talk on discrete neural nets and polymorphic learning at the #CUBoulder PALS seminar (https://math.colorado.edu/algebralogic) at 230pm MDT today! You can find the preprint I'm discussing at https://arxiv.org/abs/2308.00677. As usual, a recording will be available in case you'd like to watch later.
#AI #CategoryTheory #algebra #AbstractAlgebra #Combinatorics #ComputerScience #AppliedCategoryTheory
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I'm giving another talk on discrete neural nets and polymorphic learning at the #CUBoulder PALS seminar (https://math.colorado.edu/algebralogic) at 230pm MDT today! You can find the preprint I'm discussing at https://arxiv.org/abs/2308.00677. As usual, a recording will be available in case you'd like to watch later.
#AI #CategoryTheory #algebra #AbstractAlgebra #Combinatorics #ComputerScience #AppliedCategoryTheory
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"This talk is an invitation to embark on a journey to solve one of the most naive yet insanely convoluted open question in #software architecture: the problem of unit systems and physical quantities. As surprising as it may seem, in 2023, there is still no software library available in any of the most common programming languages that covers the issue in its full complexity including its myriad of edge cases. In the context of a standardization effort within the #cpp programming language committee #WG21 on the topic of units this talk constitutes an attempt to reach out to the #appliedcategorytheory community in order to approach the subject from a new angle.
Throughout the presentation, a particular attention will be put on the underlying reasons behind the emerging complexity of the subject and why applied category theory may be key to disentangle this apparent complexity. This will be illustrated by concrete applications in computational #physics and metrology, including particularly pathological cases that will put into question the very notion of what a unit is. Exploring conceptual boundaries through edge cases will help putting constraints on the mathematical structures that may be used to abstract the problem. Beyond the mere scope of being able to standardize a unit systems software library, the challenge raised in this talk represents a gateway to deep questions about physics, its language, its structure, and how to translate it into #typetheory. It also constitutes a perfect playground for applied category theory, going from a naive and well-framed question to an interdisciplinary open problem at the intersection of physics, computer science, and mathematics with broad impacts for programming languages and international standards."
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Love to see #AppliedCategoryTheory in the Linux space:
#Linux API for Software Disagnostics
Accelerated with #CategoryTheory in View
by Dmitry Vostokov
https://www.patterndiagnostics.com/accelerated-linux-api-book -
@abuseofnotation There are at least two reasons that categories aren't usually covered during an introduction to abstract algebra.
1) While the modern upper-level undergraduate curriculum does push a lot more abstraction than appeared a century ago, this is still balanced with the psychological need for students to not go up too many levels too quickly. Even though categories are some kind of algebraic structure generalizing groups and lattices, the standard examples are categories of other mathematical objects one has already studed (sets, groups, etc.). For students this is conceptually quite different from the more concrete situation of finite symmetry groups, for example.
2) The applications of categories (separately from the special cases of groups/lattices/monoids/posets/etc.) don't yet appear enough for the average person with a bachelor's in math to need to know them. This may change as #AppliedCategoryTheory, #TopologicalDataAnalysis, #FunctionalProgramming, and so forth continue to mature and have greater impacts outside of academia.
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@abuseofnotation There are at least two reasons that categories aren't usually covered during an introduction to abstract algebra.
1) While the modern upper-level undergraduate curriculum does push a lot more abstraction than appeared a century ago, this is still balanced with the psychological need for students to not go up too many levels too quickly. Even though categories are some kind of algebraic structure generalizing groups and lattices, the standard examples are categories of other mathematical objects one has already studed (sets, groups, etc.). For students this is conceptually quite different from the more concrete situation of finite symmetry groups, for example.
2) The applications of categories (separately from the special cases of groups/lattices/monoids/posets/etc.) don't yet appear enough for the average person with a bachelor's in math to need to know them. This may change as #AppliedCategoryTheory, #TopologicalDataAnalysis, #FunctionalProgramming, and so forth continue to mature and have greater impacts outside of academia.
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#MIT "spin outs" are such a clever form of intellectual sabotage. Whether its #Lisp, or #AppliedCategoryTheory, MIT's manifold "private ventures" so often seem to be employed as a means to subdue and suffocate genuinely novel research currents under the ruse of increased investment, as most serious theoretical activity is more or less destined to suboptimal demand in a capitalist market
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I'm an associate professor at ELSI in Tokyo. I'm into #ComplexSystems, #ArtificialLife, #OriginOfLife and #AppliedCategoryTheory.
Lately I'm really into the question of "what is an agent" and the foundations of Bayesian reasoning and decision making. This means my interests overlap quite a bit with the #aialignment crowd, although my main motivation is understanding where agency came from in biology.
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I'm an associate professor at ELSI in Tokyo. I'm into #ComplexSystems, #ArtificialLife, #OriginOfLife and #AppliedCategoryTheory.
Lately I'm really into the question of "what is an agent" and the foundations of Bayesian reasoning and decisition making. This means my interests overlap quite a bit with the #aialignment crowd, although my main motivation is understanding where agency came from in biology.
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I'm a post-doctoral at Aix-Marseille University. I just finished my PhD with the Quantum Group at the University of Oxford. I'm the main developer of DisCoPy, a Python library for computing with string diagrams.
My research focuses on the following topics:
#QuantumComputing
#ArtificialIntelligence
#NaturalLanguageProcessing
#CategoryTheory
#AppliedCategoryTheory -
I'm a post-doctoral at Aix-Marseille University. I just finished my PhD with the Quantum Group at the University of Oxford. I'm the main developer of DisCoPy, a Python library for computing with string diagrams.
My research focuses on the following topics:
#QuantumComputing
#ArtificialIntelligence
#NaturalLanguageProcessing
#CategoryTheory
#AppliedCategoryTheory
