Re: Categorical Foundations of Generative AI [reader]

Dear Paola,

I can only give you a very general outline, because I am in the process of
resuming my academic studies after decades. I am in the process of
evaluating some fast track equivalence programs offered by some European
Universities to convert my academic degree dating from an older academic
era into a current BSc degree and move on to obtaining a MSc degree, and if
possible go on to a PhD.

I have been busy organizing my notes and research and have been asked to
provide insight into what I have been doing so far and see how this can be
utilized or fit into a tailor made program for me with my research serving
as subject matter for a thesis.

The rules for sharing information in W3 Community Groups and having a W3C
user account and the fact that email threads are publicly visible makes
sharing information subject to careful consideration criteria.

I will provide a very general outline, but it will take some time to put it
together to make sure I explain just enough without giving away too much of
the underlying ongoing research.

Milton Ponson
Rainbow Warriors Core Foundation
CIAMSD Institute-ICT4D Program
+2977459312
PO Box 1154, Oranjestad
Aruba, Dutch Caribbean


On Tue, Jun 25, 2024 at 9:40 PM Paola Di Maio <paoladimaio10@gmail.com>
wrote:

>
> *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.
>>>>>
>>>>