## 2 Materials and Methods
### cDCGAN
#### 2.2.2 One-Hot and Distributed Representation  
1. One-Hot Representation  
One of the most commonly used methods in NLP is One-Hot Representation, which uses a multi-bit state register to encode multiple states. In this method, word text is discretized and represented as a vector with only some non-zero dimensions, with each word using a different dimension. The characteristic of One-Hot Representation is that all words are independent. Clearly, this representation of the One-Hot Representation has a number of issues [36]. A word vector is a mathematical way used to represent human language, and the simplest vector approach is the One-Hot Representation form. For example, for the typical sedimentary facies in Table 2, the first element of \(1\) represents braided river facies, the fourth element of \(1\) represents anastomosing river facies, and the sixth element of \(1\) represents fan delta facies. In the One-Hot Representation, there is no semantic information, so it is impossible to express the difference of semantic association. For instance, the meaning of \"Braided River Facies\" is similar to that of \"Meandering River Facies\" and \"Straight River Facies\". However, in this representation space, all word vectors are orthogonal. In this case, if the similarity of words is measured by cosine distance, then the similarity is \(0\). If Euclidean distance is used to measure the similarity of words, then all the words have the same meaning. The distances between words with similar meanings as well as unrelated words are the same. Moreover, to represent n words, it is necessary to set the length of a word expression to n, so that n words can be distinguished. This expression method loses the information related to the meaning between words. In particular, the vocabulary will increase exponentially when geometric parameters and information about the direction of the object source are added to the concept. The One-Hot Representation dimension will be increased accordingly, resulting in a dimensional catastrophe. As a result, One-Hot Representation is often confronted with the problems of exploding parameters and sparse data in practical applications. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sedimentary Facies** & **One-Hot Representation** \\ \hline Braided River Facies & \([1,0,0,0,0,0]\) \\ Meandering River Facies & \([0,1,0,0,0,0]\) \\ Straight River Facies & \([0,0,1,0,0,0]\) \\ Anastomosing River Facies & \([0,0,0,1,0,0]\) \\ Braided River Delta Facies & \([0,0,0,0,1,0]\) \\ Fan Delta Facies & \([0,0,0,0,0,1]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Example of One-Hot Representation. Distributed Representation is a good way to overcome the problem of dimension disaster. Moreover, it is able to compute the similarity directly from the distance between two words. The reduction in the number of parameters is of great significance, since it not only reduces computation but also allows for a relatively few sample sizes to avoid overfitting [38]. Comparison between One-Hot and Distributed Representation  
Figure 3 shows the two types of clustering. In the local representation (Figure 3a), each area is relatively independent, and a set of parameters is needed to characterize each area individually. In Distributed Representation (Figure 3b), different from the previous one, the parameters that describe the characteristics are shared, and each area can be characterized by a category representation 1-3. The ability of neural networks to learn distributed data representations is one of the main reasons why deep learning can be very effective for many different types of problems. Labeling with a combination of One-Hot and Distributed Representation  
Distributed Representation can be used to represent words with low dimensional density vectors, which can make it more difficult to differentiate between words. The One-Hot Representation has the advantages of simplicity, high efficiency, and better discrimination than Distributed Representation.