An approach to the discrete inverse conductivity problem (electrical impedance tomography on a square-lattice resistor network) in which a feed-forward neural network is designed so that the recovered edge conductivities are encoded directly in its second-layer weights rather than in its output. The central result is that, given enough suitably chosen Cauchy data, every global minimizer of the training loss attains zero loss and shares the same second-layer weights, which coincide with the true conductivity, making the trained weights physically interpretable; the method is provably robust to noise and partial data, outperforming the classical Curtis-Morrow algorithm.
Electrical impedance tomography recovers an internal conductivity profile from boundary current-voltage measurements; in discrete form it means recovering the conductivities on the edges of a square-…