For an input set of real images, we say that the set of layer activation forms a “manifold of interest”.

It has been long assumed that manifolds of interest in neural network could be embedded in low-dimensional subspaces.

The authors have highlighted two properties that are indicative of the requirement that the manifold of interest should lie in a low-dimensional subspace of the higher-dimensional activation space.

If the manifold of interest remains non-zero volume after ReLU transformation, it corresponds to a linear transformation.

ReLU is capable of preserving complete information about the manifold only if the input manifold lies in a low-dimensional subspace of the input space.

Assuming the manifold of interest is low-dimensional, we can capture this by inserting linear bottleneck layers.

Inverted Residuals

Inspired by the intuition that the bottlenecks actually contain all the necessary information, the authors use shortcuts directly between the bottlenecks.