On the unit sphere, gradient descent for logistic regression converges globally for every step size below the stability threshold only in one dimension; in higher dimensions, cycles persist despite the equal-norm restriction.
The Implicit Bias of Gradient Descent on Separable Data
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Gradient Descent on Logistic Regression: Do Large Step-Sizes Work with Data on the Sphere?
On the unit sphere, gradient descent for logistic regression converges globally for every step size below the stability threshold only in one dimension; in higher dimensions, cycles persist despite the equal-norm restriction.