2 ms·
You're right, that's a bit ambiguous. Instead of "all different manifolds" I should have written "all different ways to define a manifold". Also, now that I th
by moralestapia 3y ago
You're right, that's a bit ambiguous.
Instead of "all different manifolds" I should have written "all different ways to define a manifold". Also, now that I think about it, it may not necessarily be all of them.
The important thing here is that, however you define them and their transition maps, you'll find they're very much alike. As if there was some sort of general structure that is highly preferred over others ...
- evertedsphere 3y ago"if you look at the (chart) transition maps for different atlases on this manifold, they tend to look similar for different atlases" what is the manifold here and what evidence do you have for this / what does it look like when you "define" them?
- moralestapia 3y agoSee, https://transformer-circuits.pub/2023/may-update/index.html#feature-manifolds https://transformer-circuits.pub/2023/may-update/index.html#.... They also reference, https://distill.pub/2020/circuits/equivariance/ https://distill.pub/2020/circuits/equivariance/. I'd also add, https://distill.pub/2021/multimodal-neurons/ https://distill.pub/2021/multimodal-neurons/.