## 1 Introduction  
The beauty-related industries have witnessed significant expansion globally, owing to their multifarious beneficial applications in the entertainment, digital media, plastic surgery, and cosmetic sectors. To this end, various studies have been conducted by researchers, medical practitioners, and artists to investigate and measure facial beauty [1, 2, 3]. The task of predicting facial attractiveness is a complex and important undertaking in the field of computer vision and machine learning. Building robust and effective FBP models is challenging due to the variability of facial appearance and the complexity of human perception. Conventional methods for predicting face beauty were based on hand-crafted features; these features are manually extracted and then fed to a classifier or a regressor [4]. Facial geometry, color, texture, and other local characteristics are some examples of feature-based representation. Nonetheless, the effectiveness of statistical and traditional machine-learning techniques for extracting and predicting beauty features diminishes with the emergence of sophisticated deep neural networks [5]. The remarkable capability of CNNs to learn discriminative features has led to significant advancements in computer vision. In addition, both deep and machine learning are characterized by applying statistical methods to allow computers to learn from the data supplied. The machine-learning predictions error is measured using loss and cost functions. Loss functions quantify the error per observation, whereas cost functions quantify the error across all observations. Therefore, loss functions are the core aspects of the training process in the machine-learning system. The ideal values of parameters are derived by mitigating the mean value of the loss, given a labeled training set; hence, selecting the appropriate loss function is the greatest priority. FBP may assume various forms, including classification, regression, or ranking problems [6]. However, CNN is mostly used in classification-based applications, and its implementation in regression studies is still developing. Thus, predicting a collection of dependent, continuous variables is the focus of the latest suggested deep-learning techniques that tackle the facial-image-attractiveness assessment task. Consequently, choosing a loss function that matches the specific predictive modeling issue, such as classification or regression, is critical so that CNN models can learn from the data. The mean square error (MSE), which is based on L2 loss, is commonly employed for regression problems, aiming to reduce the squared difference between the predicted and the actual values. However, it is sensitive to outliers, making it hard to generalize based on how many outliers might be present via the training phase [7]. While the mean absolute error (MAE) based on L1 loss can cover the MSE downside as it takes the absolute value into account, the errors will be penalized linearly, and it is less sensitive to outliers [8]. However, with the MAE, all errors are equally weighted. In addition, it is not a differentiable function. A viable solution was proposed in [9] to manage the actual and predicted values when data are susceptible to unknown noise distributions by applying the logarithmic hyperbolic cosine (Incosh) as a loss function. This outcome makes sense, given that the Log-cosh function takes advantage of L2 loss for small values and the L1 loss for large ones. Moreover, the Log-cosh loss function is a type of robust loss function that does not require the adjustment of hyperparameters. This contrasts with other robust loss functions, such as Huber loss [10] and Tukey loss [11], which require tuning hyperparameters for optimal performance. Additionally, the Log-cosh loss function has a smooth gradient, which allows for more efficient optimization and convergence during model training. The Log-cosh loss function provides a simple yet effective solution for robust regression tasks, without extensive hyperparameter tuning.