ADRM

Adaptive Dynamic Recursive Mapping (ADRM)

$$s_{t+1}=\psi_{\alpha}(s_t)=s_t+\alpha\,(s_t-s_t^{2}),\quad \alpha\in[-1,1].$$

• $\alpha>0$ amplifies evidence for abnormality
• $\alpha<0$ suppresses false positives
• $\alpha=0$ leaves the score unchanged

Here, $s_t$ is the anomaly score at step $t$, and the adaptive decision parameter $\alpha$ is learned jointly with the backbone detector. By recursively mapping the score trajectory, ADRM stabilises detector outputs, magnifies truly anomalous segments, and damps noisy spikes, yielding more reliable video-level anomaly detection under weak supervision and heterogeneous federated settings.