Residual-Gated Streaming Adaptation

1. Exact integration point: freeze the backbone and condition discriminator after offline training; expose only LayerNorm or BatchNorm affine parameters, a small LoRA adapter, or the final linear fault head to online updates. For each incoming sample, compute the fault posterior, condition mean, condition variance, and a residual against either a measured operating condition or an EMA forecast. 2. Pseudocode: initialize $\bar c$ from the offline condition distribution; for each $x_t$, compute $(p_t,\hat c_t,v_t)$, set $r_t=(\hat c_t-\bar c)/\sqrt{v_t+\epsilon}$ if no sensor condition exists, set $g_t=1[|r_t|<\tau_r\land v_t<\tau_v]$, compute entropy or temporal-consistency loss $L_u=H(p_t)$ or $\|p_t-p_{t-1}\|^2$, and update $\alpha\leftarrow\alpha-\eta_a g_tq_t\nabla_\alpha L_u$. Clip the update norm and update $\bar c$. 3. Taken from the paper: continuous condition residuals as reliability signals and selective online adaptation. Estimated empirically: $\tau_r$, $\tau_v$, EMA coefficient $\rho$, and whether entropy minimization or consistency is safer. 4. First cheap experiment: use a frozen MLP or 1-D CNN on a rotating-machinery benchmark or synthetic signals with slowly drifting speed. Train offline on one speed range and stream through a held-out range with labels hidden during adaptation. Compare no adaptation, adapt-every-sample, confidence-gated adaptation, and residual-gated adaptation. Sweep $\tau_r\in\{1,1.5,2,2.5,3\}$. The predicted signature is lower parameter drift and lower post-adaptation loss for accepted samples; samples with $|r|>3$ should produce disproportionately large error and drift. Measure gate acceptance, cumulative admitted weight, parameter drift, accuracy, and catastrophic-drift frequency. The method is supported if drift scales approximately linearly with $\sum_tg_tq_t$ and accepted samples have lower subsequent loss than rejected samples.