Jul 24, 2023
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The paper uses a frame-theoretic setting to study the injectivity of a ReLU-layer on the closed ball of ℝ^n and its non-negative part.In particular, the interplay between the radius of the ball and the bias vector is emphasized, which, together with a perspective from convex geometry leads to a computationally feasible method of verifying the injectivity of a ReLU-layer under reasonable restrictions in terms of an upper bound of the bias vector. Explicit reconstruction formulas are provided, inspired by the duality concept from frame theory. All this leads to the possibility of quantifying the invertibility of a ReLU-layer and systematically reconstructing any vector on the ball.The paper uses a frame-theoretic setting to study the injectivity of a ReLU-layer on the closed ball of ℝ^n and its non-negative part.In particular, the interplay between the radius of the ball and the bias vector is emphasized, which, together with a perspective from convex geometry leads to a computationally feasible method of verifying the injectivity of a ReLU-layer under reasonable restrictions in terms of an upper bound of the bias vector. Explicit reconstruction formulas are provided, ins…
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