Gaussian blurring, often used as a denoising technique for images, employs a Gaussian distribution to establish a convolution matrix that's applied to the original image. The fundamental idea involves substituting the noisy pixel with a weighted average of surrounding pixel values.

In this setting, neural operators trained to minimize squared error losses, while capable of accurate short-term forecasts, often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results.

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The numbers of the lower and upper bounds in the binarization layer are both in{5,10,50}. We utilize the Adam (Kingma and Ba, 2014) method for the training process with a mini-batch size of 32. Onlargedata sets, RRL is trained for 100 epochs, and we decay the learning rate by a factor of 0.75 every 20 epochs. Theinverse of regularization strength is in {1, 4, 16, 32}. Figure 7 shows the scatter plots of F1 score against log(#edges) for rule-based models trained on the other ten data sets.

Ensemble methodsand fuzzy/soft rules are commonly used to improve performance, but they sacrifice the model interpretability.

"The right to be forgotten" ensured by laws for user data privacy becomes increasingly important.

We show that the proposed algorithms converge to the (regularized) global optimal solution, andmoreover,theirratesofconvergence areofpolynomial orderinthe online setting and exponential order inthe finite sample setting, respectively.