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Whats the different between Logistic regression and perceptron?

In a binary classification problem, if both logistic regression and a single preceptron uses Sigmoid function, what's the difference in classification results, since they will have the same decision ...
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From the Perceptron rule to Gradient Descent: How are Perceptrons with a sigmoid activation function different from Logistic Regression?

Essentially, my question is that in multilayer Perceptrons, perceptrons are used with a sigmoid activation function. So that in the update rule $\hat{y}$ is calculated as $$\hat{y} = \frac{1}{1+\exp(...
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