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ABSTRACT This paper studies the transfer learning problem for convolutional neural network models. A phase transition phenomenon has been empirically validated: The convolutional layer shifts from general to specific with respect to the target task as its depth increases. The paper suggests measuring the generality of convolutional layers through an easy‐to‐compute and tuning‐free statistic named projection correlation. The non‐asymptotic upper bounds for the estimation error of the proposed generality measure have been provided. Based on this generality measure, the paper proposes a forward‐adding‐layer‐selection algorithm to select general layers. The algorithm aims to find a cut‐off in the pre‐trained model according to where the phase transition from general to specific happens. Then, we propose to transfer only the general layers as specific layers can cause overfitting issues and hence hurt the prediction performance. The proposed algorithm is computationally efficient and can consistently estimate the true beginning of phase transition under mild conditions. Its superior empirical performance has been justified by various numerical experiments.