## 1 Introduction  
With recent advancements in information technology, there has been a rapid increase in the volume of data. Consequently, the importance of data protection and the security of personal information have become increasingly significant. In light of these developments, reversible data hiding has garnered attention. Reversible data hiding (RDH) is one of the techniques used to hide data, primarily applied to images or videos. This technique not only hides the secret data but also has the ability to extract and restore the hidden data on the receiver side. The main goal of reversible data hiding is to perfectly restore the original data when extracting the hidden data. This means preserving the original data without making any changes when hiding the data. Due to these characteristics, reversible data hiding is currently being used in various fields such as healthcare, military, and so on. Reversible data hiding has been explored through various approaches. One approach focuses on developing embedding methods that reduce data distortion. Another approach involves developing predictors to enhance prediction accuracy [1]. Embedding methods that reduce data distortion include techniques such as difference expansion (DE), where pixel value differences are increased to hide data and the original data are recovered using these differences [2; 3]. Histogram shifting (HS) is another technique that analyzes the histogram of the original data to find available space for hiding data and performs data embedding in that space [4; 5; 6; 7]. Prediction error expansion (PEE) is a technique where pixel values are predicted, and the difference between the predicted and actual values is used to embed data. During extraction, the prediction error values are used to recover the original data [8; 9; 10; 11]. The development of predictors includes the difference predictor (DP) (which predicts the difference between pixels to hide data [2]), the median edge direction predictor (MEDP) (which predicts the edge direction around pixels as the median value to hide data [11]), the gradient adaptive predictor (GAP) (which predicts the gradient values around pixels to hide data [12]), and pixel-value-ordering (PVO) (which is the method of arranging image pixel values in ascending order and hiding data afterwards [12; 13; 14]). However, the previous predictors have limitations in that they only refer to a few adjacent pixels to predict the target pixel. To overcome this limitation, predictors using CNN (Convolutional Neural Network) have recently been attracting attention [1; 15; 16; 17; 18; 19; 20]. A CNN-based method in [15], image scrambling, was performed on encrypted images using Arnold transform, and CNN was applied to extract the secret data. [PERSON] et al. 's method in [1], a predictor CNNP based on CNN, was proposed, and it showed better performance in terms of accuracy and prediction error compared to various existing predictors. Subsequently, ICNNP was developed in [16], which takes into account the complexity of pixels in the original CNNP, showing further improved performance. In the field of data hiding, predictor development and data embedding using CNN have been actively researched, showing superior performance compared to existing methods. However, there is a trade-off between the performance metrics of data hiding, such as PSNR (Peak Signal-to-Noise Ratio) and EC (Embedding Capacity). As the amount of data to be hidden increases, the distortion of the cover image becomes severe. To overcome these limitations, this paper proposes a new embedding algorithm utilizing predictors developed using CNN. In the proposed method, the cover image is predicted using the CNN predictor, and the gap between the generated predicted image and the cover image is calculated. Then, the secret data are embedded into the predicted image to the direction closer to the pixels of the cover image.