Distributed Nash Equilibrium Seeking with Logarithmic Bit Rates over Digital Channels

What the math gives to ML

The paper offers a constructive quantized distributed-control mechanism: a passivity-based iteration is combined with time-varying scaling of an ultimate-boundedness quantization error, allowing geometric convergence despite low-bit communication. The transferable asset is a quantizer whose resolution decreases at a rate compatible with the contraction rate of the underlying optimization dynamics. A direct neural-network application is quantized decentralized or federated training in which workers transmit sparsified model or gradient-tracking states while the quantizer scale shrinks geometrically. The key falsifiable prediction is that geometric quantization preserves linear convergence when its decay rate is below one, whereas fixed-resolution quantization produces a nonzero error floor.