Re: Categorical Foundations of Generative AI [reader]

*V mentioned constructibility theory, because it defines a formal framework
to create categories of universes for knowledge representation. Symplectic
geometry introduces elements to model theoretical physics and algebraic
topology to model field and string theories. *

Maybe you could put together a few slides to introduce these to us

On Tue, Jun 25, 2024 at 6:28 PM Milton Ponson <rwiciamsd@gmail.com> wrote:

> I totally agree that category theory has its limitations.
> But it is indispensable in creating the frameworks for defining the
> objects and the functors used. Now if we jump to the graph paradigm what
> this article introduces is a way to bind or connect ontology like
> structures to the vertices and have the functors define knowledge
> representation mappings.
> It is important to note that the article applies category theory to the
> issue of generative AI using specific methodologies as a case study.
> And I expect that category theory will also be used to find the
> generalizations.
> I mentioned constructibility theory, because it defines a formal framework
> to create categories of universes for knowledge representation. Symplectic
> geometry introduces elements to model theoretical physics and algebraic
> topology to model field and string theories.
> KR for AI, whether it's generative AI, AGI or any other form, the path has
> been shown for further progress and the usefulness  of category theory has
> been shown, as I have been saying all along.
>
>
> Milton Ponson
> Rainbow Warriors Core Foundation
> CIAMSD Institute-ICT4D Program
> +2977459312
> PO Box 1154, Oranjestad
> Aruba, Dutch Caribbean
>
>
> On Mon, Jun 24, 2024 at 10:20 PM Paola Di Maio <paoladimaio10@gmail.com>
> wrote:
>
>>
>>
>>
>> Thank you Milton
>> Yes, it can be generalized to address broader challenges
>> What I think is important here, is actually not category theory per se
>> (which has its limitation)
>> but that Gen AI is being anchored into KR/ontology of sorts
>> that is what this CG has been advoating all along and is nice to see
>> happen
>>
>> On Mon, Jun 24, 2024 at 6:08 PM Milton Ponson <rwiciamsd@gmail.com>
>> wrote:
>>
>>> Seems like more people have been exploring the same concepts. This GAIA
>>> model restricts itself to generative AI, but it can be generalized using
>>> category theory to all forms of knowledge representations.
>>>
>>> Combining constructibility theory, category theory, symplectic geometry
>>> and algebraic topology we can define universes of discourse that cover most
>>> of the knowledge representation methodologies using generalized graph
>>> concepts.
>>>
>>> Milton Ponson
>>> Rainbow Warriors Core Foundation
>>> CIAMSD Institute-ICT4D Program
>>> +2977459312
>>> PO Box 1154, Oranjestad
>>> Aruba, Dutch Caribbean
>>>
>>>
>>> On Fri, Jun 21, 2024 at 11:43 PM Paola Di Maio <paola.dimaio@gmail.com>
>>> wrote:
>>>
>>>>
>>>> Greetings,  W3C AI KR CG,  Happy Solstice
>>>>
>>>> a great way to start the summer by reading this paper
>>>> In my view this is a contribution towards neurosymbolic AI/KR and a
>>>> clear signal
>>>>
>>>> Enjoy
>>>> ----------------------------------------------------------------
>>>>
>>>> GAIA: Categorical Foundations of Generative AI
>>>> by Sridhar Mahadeva
>>>> https://arxiv.org/pdf/2402.18732
>>>>
>>>> In this paper, we propose GAIA, a generative AI architecture based on
>>>> category theory. GAIA is based on a hierarchical model where modules are
>>>> organized as a simplicial complex. Each simplicial complex updates its
>>>> internal parameters biased on information it receives from its superior
>>>> simplices and in turn relays updates to its subordinate sub-simplices.
>>>> Parameter updates are formulated in terms of lifting diagrams over
>>>> simplicial sets, where inner and outer horn extensions correspond to
>>>> different types of learning problems. Backpropagation is modeled as an
>>>> endofunctor over the category of parameters, leading to a coalgebraic
>>>> formulation of deep learning.
>>>>
>>>