An SAE with sufficiently many features can relatively accurately reconstruct an arc-shaped manifold by assigning feature activations to points along it.

“does it sort of fit the intrinsic geometry of it and so if we go back to this example of like an arc say i'm kind of with sufficiently many points you know with sufficiently many like lines i can say i've captured the manifold you know for any point on this manifold i have an sae feature which i can say oh it activates such and so amount and i've kind of relatively accurately captured captured in the sense of reconstruction this manifold”