"LyapunovGCN"

"Graph Convolutional Networks (GCNs) suffer from numeri-cal instability and signal explosion in deep architectures, often relyingon layer-wise normalization for control. We propose LyapunovGCN, anormalization-free framework that constrains feature dynamics withinthe [0, 1] interval by combining column stochastic weight matrices witha shifted dead-zone activation(SDZA). Inspired by Wolfowitzs theorem,our formulation guarantees bounded propagation and stable deep train-ing.Empirically, LyapunovGCN reduces gradient variance by over 3\u00d7and limits signal gain from exponential growth to near constant mag-nitude in deep networks. It consistently outperforms strong baselinesacross six benchmarks, achieving up to +4.61% improvement on het-erophilous graphs. Moreover, the model maintains accuracy under 72%parameter reduction and benefits from its inherently bounded featurerange, making it well-suited for low-precision training and inference.These results establish a principled and hardware-efficient solution forstable deep graph learning."