Competitive One-Step-Ahead Control of Friedkin--Johnsen Networks: Potential Games, Stability, and the Price of Competition
arXiv:2608.27623
2026
Dynamics
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper provides a constructive stability mechanism for competitive one-step control: the Nash equilibrium is the solution of a symmetric positive-definite potential problem, while parallel best-response updates converge if and only if an exact Jacobi spectral-radius condition holds. This transfers naturally to neural networks with multiple competing parameter blocks, adapters, experts, or objectives that update against a shared frozen representation. The most useful implementation is a block-coordinate optimizer that estimates the cross-player coupling matrix, switches from parallel to damped or sequential updates when the predicted Jacobi radius approaches one, and tests whether the observed convergence boundary matches the spectral prediction.
Ideas from this paper
✗ Failed on benchmark
2026
Partition neural-network parameters into competing blocks, such as LoRA adapters, mixture-of-experts heads, or task-specific heads, and update each block by minimizing its local quadratic model while holding the other blocks fixed. Use the exact Jacobi coupling spectral radius to decide whether simultaneous updates are stable; near the boundary, apply damping or fall back to sequential Gauss-Seidel updates.
Useful7/10
Difficulty5/10
Novelty7/10