CryptaMind & MosaicMind
MosaicMind
Do you ever wonder if the way ancient mosaics balance every shard could give us a clue about how to arrange neurons in a neural net?
CryptaMind
The patterns in mosaics are essentially handcrafted graphs; each shard connects to a few neighbors, just like a sparse weight matrix. If you treat the tiles as nodes and the seams as edges, you get a planar graph with local constraints. Neural nets can benefit from that: enforce locality, preserve symmetry, and reduce over‑parameterization. I can see an algorithm that derives a connectivity matrix from a tessellation, then optimizes it—no small talk needed.
MosaicMind
That’s a neat parallel—just like a tile that fits only with its exact neighbors, a neuron should only talk to the ones it truly cares about. If you build the weight matrix the way a Roman mosaic is laid out, you keep the planar symmetry and eliminate the extra edges that clutter up a neural net. I can already picture a tessellation of hexagons, each one a layer of the network, and the grout lines acting as the learning rules that keep everything in balance. It’s almost like arranging a living floor that never repeats its own flaws. Just be sure you choose the right grout; the wrong one in 1987 would make the whole design look… off.
CryptaMind
Hexagons give a natural, isotropic neighborhood; each tile touches six others, so the adjacency matrix is regular and sparse. If you let the grout be the learning rule, you could encode weight updates that respect that local structure. It’s just a matter of mapping each cell to a node and defining the update rule along the edges. I’ll run a test lattice and see if the planar constraint actually reduces the parameter count without hurting performance. Just make sure the grout isn’t too elastic—otherwise you’ll get a ripple effect that distorts the whole pattern.
MosaicMind
I love the hexagon idea—six neighbors, perfect symmetry, just like a well‑cut Roman tessera. Make sure you treat the grout like a strict teacher; if it’s too flexible, the whole lattice will wobble like a badly laid floor. Keep the updates local, and don’t let the network grow larger than the pattern itself; that’s how we preserve the planarity and avoid those “blank tragedies” of over‑parameterization. Good luck with the lattice test, and remember: every missing shard is a warning sign, not a curiosity.
CryptaMind
Thanks for the guidance. I’ll enforce the strict learning rule and keep the updates strictly local. The lattice will stay exactly the size of the hexagonal pattern, so the planarity stays intact. Missing a shard will trigger a recalculation, not a curiosity. I'll run the test now.