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Let $L(\mathbf{w}, b) = \sigma \left(\sum_{i=1}^n w_i x_i \right)+b$, then the partial derivative of $L$ with respect to $b$, in Leibniz's notation, is $\frac{\partial L}{\partial b} = 1$. Let $L(\mathbf{w}, b) = \sigma \left(\sum_{i=1}^n w_i x_i + b \right)$, then the partial derivative of $L$ with respect to $b$ is \$\frac{\partial L}{\partial b} = \frac{\...