## 1 Introduction  
Deep learning is a powerful approach for performing different types of computer vision tasks [1], such as object recognition [2; 3; 4; 5], image segmentation [6; 7; 8; 9], visual captioning [10], etc. Deep learning also enables other tasks, such as natural language processing (NLP) [11]. Deep networks pre-trained on large image datasets, e.g., ImageNet [12] have been used after fine-tuning for two important reasons [13]: First, the features learned by deep networks from large datasets help deep networks to generalize more effectively and rapidly; Second, pre-trained deep networks are successful at avoiding over-fitting during fine-tuning for smaller downstream tasks. It is well known that the performance of deep networks depends on their architecture as well as their training [14; 15; 16; 17]. A multitude of successful deep networks have been developed with a large number of parameters. To train these parameters, a very large number of training images are required; hence, the need for large-scale image datasets. Popular deep networks include AlexNet [18], VGG [19], GoogLeNet [20], ResNet [21], and DenseNet [22]. Popular large-scale image datasets include ImageNet [12] and OpenImage [23]. Deep networks have achieved state-of-the-art performance for many computer-vision applications [2; 6; 10; 24; 25; 26; 27; 28]. In spite of their success, the training of deep networks has become expensive and time-consuming. This is due to the laborious collection and manual annotation of the high volume of data required with large-scale datasets. For example, ImageNet [12], which is a popular dataset, has about 1.3 M annotated images with 1 K classes. In ImageNet, every image has been manually annotated and the annotation process is, therefore, substantial. In addition to this, collecting and annotating video data is more expensive still due to its temporal aspect. For example, the Kinetics video dataset [29] includes 500 K human action videos with 600 classes. Every video in the dataset is around 10 seconds long. Several Turkish Amazon workers were involved in the collection and annotation of this large-scale dataset. Bearing the above issues in mind, it is necessary to avoid lengthy and expensive manual annotation. To this end, different learning schemes have been proposed for training deep networks. These schemes include semi-supervised learning (SSL) [30; 31; 32; 33; 34; 35; 36; 37; 38; 39], weakly supervised learning (WSL) [40; 41; 42; 43; 44], unsupervised learning (USL) [45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57], and self-supervised learning [58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76]. The advantage of these schemes is that they can be used to train deep networks without the use of labeled data; hence, the expensive manual annotation process can be avoided. This can save time as well as expense. A promising supervised learning scheme, which involves use of synthetic images with auto-generated labels, is formula-driven supervised learning (FDSL) [77]. This learning scheme automates the dataset creation process and has produced promising results when used for pre-training. FDSL represents a viable alternative to other learning schemes which offer training using unlabeled data. FDSL has the potential to alter the way in which large-data models are trained, i.e., without manual collection or manual annotation. This potentially critical development, opening a new area of research, motivated us to conduct a literature survey on FDSL. It is hoped that, through such surveys, improved strategies for addressing the critical issues associated with the training of large-data models will emerge and become widely applied. The main contributions of the paper can be summarized as follows:  
* A detailed review of recent supervised learning schemes with respect to formula-driven supervised learning is presented. * Extensive manual data collection and annotation methods for training large-data models based on FDSL are discussed using synthetic datasets.