Ideal Paths for Approximating Logistic Gradient Descent Trajectories at Large Initialization

תקציר מקורי באנגליתarXiv:2610.04142v2 Announce Type: replace Abstract: Modern training on a new task often starts from a previously trained model rather than from scratch, raising the question of how this initialization affects the subsequent training trajectory. Classical implicit-bias results characterize the direction selected by prolonged training, but this direction alone does not provide information regarding the intermediate behavior. We address this question through a geometric approximation of full-batch logistic gradient descent (GD) trajectories on strictly linearly separable data, with large initialization of scale $R$ motivated by prior training. From any limiting normalized initial position, we use minimum-norm projection rules to construct a unique continuous ideal path consisting of finitely