adjoint VS Category_Theory_Machine_Learning

This idea shows up in essentially all scientific fields. It’s the idea of adjointness. Together with norm, they give you the idea of fixed points, (invariants, spectra, embeddings, braids etc).I'm

Lawvere's fixed point theorem is I think the best formulation of the idea

https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore...

I've been putting together a brain dump on the topic

https://github.com/adamnemecek/adjoint/

Join the discord https://discord.gg/mr9TAhpyBW

I’ve always thought that the completeness theorem was more interesting.

Also I really like approaching this from Lawvere’s fixed point theorem. https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem

I have been thinking about some of this stuff

https://github.com/adamnemecek/adjoint

Yeah I have been realizing this lately as well. I have written up a bit on this

https://github.com/adamnemecek/adjoint/

Check the raw source there’s a bunch of links.

Fixed points, diagonalizations and eigenshit are all the same thing.

I think that there are like three concepts in math or the world, the concepts being the adjoint, norm and fixed point.

https://github.com/adamnemecek/adjoint

The concept of a fixed point is so ubiquitous.

Game theory, just liek essentially everything in math, physics and probability, and cs is about adjoints, norms, and fixed points https://github.com/adamnemecek/adjoint/

Nash equilibrium is a fixed point.

For me it was the idea of adjoint functors which is the central idea of category theory.

I wrote up a bit on it here https://github.com/adamnemecek/adjoint

For those that don't know Bruno, he's one of the organizers for https://cats.for.ai/

He also maintains an "Awesome-$X" like Github page for ML and Category Theory: https://github.com/bgavran/Category_Theory_Machine_Learning

I have no association with him and I doubt he knows who I am. But I thought there is enough interest here in both ML and Category Theory that others might be interested in this.

There's also the cats.for.ai group and this nice github: https://github.com/bgavran/Category_Theory_Machine_Learning

## More Links

1. https://github.com/geniusrise/geniusrise - core framework

2. https://github.com/geniusrise/geniusrise-huggingface - hf modules

3. https://github.com/geniusrise/geniusrise-openai - openai modules

4. https://github.com/geniusrise/geniusrise-listeners - streaming data input

5. https://github.com/geniusrise/geniusrise-databases - database input

6. https://github.com/geniusrise/geniusrise-prompt-actions - functional integrations (RAG-able and GPT function call-able, WIP)

7. https://github.com/geniusrise/geniusrise-indexing - vectorizing for RAG usecases (WIP)

8. https://github.com/geniusrise/geniusrise-exit-proxy - cached LLM interface with MITM-auditing (WIP)

## Asides

I think the core framework can be AGPL but the modules must be MIT / Apachev2.

I really wanted to create an elaborate example in the guides but could not find time, - something like load and vectorize SNOMED-CT or UMLS and use it to NER / RAG EHR docs. Or maybe a usecase of doctor communicating to patient in another language (a major problem in India), with reverse translation verifying translated output using the KG. These kinds of stuff are soon to come. Or discourse segmentation for better chunking for RAG usecases.

I'm not sure if I should add cyberpunk-ed scientists as banner images. I tried with mathematicians like Voevodsky to Andre Joyal to John Baez, but couldn't. Actual geniuses tend to not be famous, hence SDXL fails I guess.

I plan to also write this framework in scala. The category-theorizing of neural networks is amazing!!! https://github.com/bgavran/Category_Theory_Machine_Learning. I hope Bartosz Milewski approves.

I love Alan Turing, but cuz of "The Chemical Basis of Morphogenesis". It introduced me to the wonderful world of complex systems. Hence, his image as banner.

I'm also working on a cli library called "isomorphic", wraps over argparse and provides cli, api, yaml, json interfaces.

Yes, gradio integration is also underway.

Finally, to huggingface.

Also check out the curated list of papers on the intersection of CT and ML: https://github.com/bgavran/Category_Theory_Machine_Learning