Learning LDPC codes with quantized density evolution over relaxed protographs

What the math gives to ML

The transferable asset is a principled relaxation of a discrete graph or connectivity design problem: each binary protograph entry is treated as a Bernoulli probability, while the objective is evaluated on the corresponding ensemble rather than only on a rounded architecture. This can turn expensive discrete search over sparse neural connectivity, graph structure, or expert-routing patterns into deterministic gradient optimization, provided the network dynamics admit a tractable mean-field or message-passing expectation. The safest neural use is a graph-neural-network architecture-search module in which relaxed edge probabilities are trained jointly with weights, then thresholded and re-evaluated on sampled binary graphs to test whether the relaxed objective predicts discrete performance.