Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics

What the math gives to ML

The paper provides a transferable mechanism of delayed threshold crossing combined with bistability: an effective control parameter relaxes toward a target with finite rate, while the state can remain trapped in a competing attractor even after the parameter returns below the local instability threshold. For neural networks, this suggests separating commanded optimizer or recurrent-network parameters from their actually applied values, predicting implementation lag analytically, and triggering interventions before the effective system crosses a dangerous spectral boundary. A second transfer is hysteresis-aware stability control for recurrent or state-space networks: monitoring only the local threshold is insufficient, so training should also probe basin membership and apply stronger damping until the trajectory has demonstrably returned to the desired attractor.