Separation Capacity of Scattering Networks on Low-Dimensional Datasets

What the math gives to ML

The paper gives an exact geometric characterization of separation capacity: it is twice the smallest linear dimension occupied by the feature image on any positive-measure subset of the data. This identifies a concrete failure mode for neural representations that global variance metrics miss: a feature map may have high overall rank while collapsing large local or semantic subsets into low-dimensional subspaces. The most transferable construction is a local anti-collapse objective that maximizes the effective span dimension of feature vectors, especially for fixed-filter CNN or scattering-style encoders whose filters are the main design variables.