Alpha-rectifying Frames:

Injectivity and Reconstruction of ReLU-layers

This repository contains routines related to the injectivity of ReLU-layers and $\alpha$-rectifying frames, accompanying our ICML23 paper Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction. It currently includes:

• polytope bias estimations (PBE) for different input data domains: given a collection of vectors (e.g. row vectors of a weight matrix), the PBE gives a bias vector $\alpha^\mathbb{K}$ such that any ReLU-layer with bias $b\leq\alpha^\mathbb{B}$ is injective on $K$
• reconstruction formulas for injective ReLU-layers