\begin{algorithmic}
\State Draw $X_b, Y_b, [Z_{k-1,b} \cdots Z_{0,b}]$ \Comment{Draw training batch and corresponding features from prior models}
\State $Z_{k,b} \gets f^l_k(X_b)$
\State $N, D \gets shape(Z_{k,b})$
\State $\hat{Y_b} \gets f_k(X_b)$
\State $\mathcal{L} \gets \mathcal{L}_{ce}(\hat{Y_b}, Y_b)$
\State $i \gets 0$
\While{$i \leq k-1$}
   \State $Z_1, Z_2 \gets Z_{k,b}, Z_{i,b}$
    \If {$t \sim Uniform[0,1] < 0.5$}
        $Z_1, Z_2 \gets Z_2, Z_1$
 \EndIf
\State $R \sim N(0,1/\sqrt{D}) \in \mathbb{R}^{D+1 \times r}$
\State $Z_1 \gets [Z_1, \mathbf{1}]R$
\State $\mathcal{L} \gets \mathcal{L} + \frac{\lambda}{k} \mathcal{L}_R(Z_1, Z_2)$ \Comment{Apply decorrelation loss from Equation \ref{eqn:LR}}
\State $i \gets i+1$
\EndWhile

\State $\theta_k \gets \theta_k - \eta \nabla_{\mathcal{L}} \theta_k$
\end{algorithmic}

\begin{algorithmic}
\State Draw $X_b, Y_b, [Z_{k-1,b} \cdots Z_{0,b}]$ \Comment{Draw training batch and corresponding features from prior models}
\State $Z_{k,b} \gets f^l_k(X_b)$
\State $N, D \gets shape(Z_{k,b})$
\State $\hat{Y_b} \gets f_k(X_b)$
\State $\mathcal{L} \gets \mathcal{L}_{ce}(\hat{Y_b}, Y_b)$
\State $i \gets 0$
\While{$i \leq k-1$}
\State $Z_1, Z_2 \gets Z_{k,b}, Z_{i,b}$
\If {$t \sim Uniform[0,1] < 0.5$}
$Z_1, Z_2 \gets Z_2, Z_1$
\EndIf
\State $R \sim N(0,1/\sqrt{D}) \in \mathbb{R}^{D+1 \times r}$
\State $Z_1 \gets [Z_1, \mathbf{1}]R$
\State $\mathcal{L} \gets \mathcal{L} + \frac{\lambda}{k} \mathcal{L}_R(Z_1, Z_2)$ \Comment{Apply decorrelation loss from Equation \ref{eqn:LR}}
\State $i \gets i+1$
\EndWhile
\State $\theta_k \gets \theta_k - \eta \nabla_{\mathcal{L}} \theta_k$
\end{algorithmic}
{
    "title": "decorrelative network architecture for robust electrocardiogram   classification",
    "id": "2207.09031",
    "abstract": "artificial intelligence has made great progress in medical data analysis, but the lack of robustness and trustworthiness has kept these methods from being widely deployed. as it is not possible to train networks that are accurate in all scenarios, models must recognize situations where they cannot operate confidently. bayesian deep learning methods sample the model parameter space to estimate uncertainty, but these parameters are often subject to the same vulnerabilities, which can be exploited by adversarial attacks. we propose a novel ensemble approach based on feature decorrelation and fourier partitioning for teaching networks diverse complementary features, reducing the chance of perturbation-based fooling. we test our approach on single and multi-channel electrocardiogram classification, and adapt adversarial training and dverge into the bayesian ensemble framework for comparison. our results indicate that the combination of decorrelation and fourier partitioning generally maintains performance on unperturbed data while demonstrating superior robustness and uncertainty estimation on projected gradient descent and smooth adversarial attacks of various magnitudes. furthermore, our approach does not require expensive optimization with adversarial samples, adding much less compute to the training process than adversarial training or dverge. these methods can be applied to other tasks for more robust and trustworthy models.",
    "categories": "cs.lg cs.ai",
    "doi": "",
    "created": "2022-07-18",
    "updated": "2024-02-16",
    "authors": [
        "christopher wiedeman",
        "ge wang"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2207.09031"
}
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