arXiv:2607.26483v1 Announce Type: new Abstract: A Noise-modulated Neural Network (NNN) learns and infers only in the presence of noise, treating noise as a computational resource rather than a disturbance. The noise lets it learn efficiently by backpropagation while transmitting spike-like signals, but backpropagation needs a reverse path through transposed weights, the weight transport problem, which undermines biological and neuromorphic plausibility. Forward-only alternatives typically substitute a different objective or fixed random feedback, sacrificing stability and accuracy. We show that backpropagation itself can be reconstructed in the NNN from forward-pass statistics alone: a weight mirror estimates each weight matrix from the covariance between a previous-layer unit's output and the next-layer unit's input, and combining it with local differential estimation inside the units propagates the output error recursively along the computational graph, with no transposed-weight read...