Sparse autoencoders capture concept manifolds globally via compact feature groups or locally via selective tiling but typically recover them suboptimally in a fragmented dilution regime.
But this point does not correspond to any observation on the data manifold: 1 2 m1 + 1 2 m′ 1 is generically not a point on M1 (it is a chord, not an arc), and likewise for M2
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Do Sparse Autoencoders Capture Concept Manifolds?
Sparse autoencoders capture concept manifolds globally via compact feature groups or locally via selective tiling but typically recover them suboptimally in a fragmented dilution regime.