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The paper uses a frame-theoretic setting to study the injectivity of aReLU-layer on the closed ball of $\mathbb{R}^n$ and its non-negative part. Inparticular, the interplay between the radius of the ball and the bias vector isemphasized. Together with a perspective from convex geometry, this leads to acomputationally feasible method of verifying the injectivity of a ReLU-layerunder reasonable restrictions in terms of an upper bound of the bias vector.Explicit reconstruction formulas are provided, inspired by the duality conceptfrom frame theory. All this gives rise to the possibility of quantifying theinvertibility of a ReLU-layer and a concrete reconstruction algorithm for anyinput vector on the ball.

Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction