Re: Categorical Foundations of Generative AI [reader]

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.
>>>
>>