You can get a sense of the convolution idea from thinking about how you’d detect the encoded square is an interval of intervals, via detecting a pattern along the diagonal and the connective blocks.
I also have a few notes on connecting the concept to Curry-Howard:
The idea of connecting a geometric and algebraic representation is based on work by Michael Shulman — and the internal languages of toposes. And work on the ML side such as covering based models. (Having trouble finding references on my phone; sorry.)
The first two look at implementing shapes as diagrams as digital images:
https://www.zmgsabstract.com/whitepapers/shapes-as-digital-i...
https://www.zmgsabstract.com/whitepapers/shapes-have-operati...
You can get a sense of the convolution idea from thinking about how you’d detect the encoded square is an interval of intervals, via detecting a pattern along the diagonal and the connective blocks.
I also have a few notes on connecting the concept to Curry-Howard:
https://zmichaelgehlke.com/journals/2021-06-14-curry-howard-...
And some (messy) notes about general research direction:
https://zmichaelgehlke.com/journals/2021-01-30-intro-to-effe...
The idea of connecting a geometric and algebraic representation is based on work by Michael Shulman — and the internal languages of toposes. And work on the ML side such as covering based models. (Having trouble finding references on my phone; sorry.)