## 4 Experimental Results
### Characteristics of Augmented Essays  
We set two baseline models of data-augmentation for comparisons with EssayGAN. Random is a data-augmentation model that generates a new essay by composing randomly selected sentences from essays with the same target score. All sentences in each essay in the training dataset were assumed to be sequentially numbered. Random\({}_{\text{Order}}\) generates a new essay by collecting sentences in non-decreasing order from essays with the same target score to ensure minimal coherence between sentences. First of all, we observed the characteristics and statistics of the augmented essays, which are summarized in Tables 3 and 4. We introduced the 'number of source essays' and the 'number of sentences in reversed order' to examine the consistency and coherence of the augmented essays according to the augmentation techniques used. We augmented the same numbers of essays as those in the training data for each prompt. Figure 4 depicts an example of the number of source essays and the number of sentences in reversed order to help readers fully understand these concepts. The number of source essays refers to the number of essays from which sentences of a newly generated essay are extracted. We can reason that the consistency of contents in a newly generated essay scarcely remains when the number of source essays is too large. The number of sentences in reversed order refers to the frequency of the occurrence of a decreasing order of sentences in a newly generated essay. This measurement indirectly indicates how well a newly generated essay is organized to maintain coherence. In the example shown in Figure 4, Generator-3 was trained to compose new essays with a score of 3. In the essay database, each sentence \(s_{ij}\) in a source essay indicates a \(j\)-th sentence in an \(i\)-th essay. The augmented essay has three different source essays (1, 2, and 3) and one sentence in reversed order between \(s_{26}\) and \(s_{14}\). Table 3 represents the number of source essays according to the augmentation techniques. The Random and Random\({}_{\text{Order}}\) categories had almost the same numbers of source essays as the average number of sentences per essay because they collected sentences randomly from the source essays. EssayGAN had less than three source essays for prompts  
Figure 4: An example of an augmented essay, showing the number of source essays and the number of sentences in reversed order. 3-7, of which the average number of sentences was 4.63-11.64. EssayGAN trained without the \(t\)-step (in Algorithm 1) had a higher number of source essays than EssayGAN for all prompts. A comparison of the number of sentences in reversed order is shown in Table 4. Essays generated from RandomOrder did not have a reversed sentence order because they were composed under the strategy of monotonically increasing the sentence order. Random had an average of 5.73 sentences in reversed order in an augmented essay, whereas EssayGAN trained with and without the \(t\)-step had 0.51 and 1.01 on average, respectively. We can thus reason that EssayGAN can compose a new essay more coherently than the other augmentation techniques that were considered in this study. Next, we used a more explicit metric to examine the coherence of the augmented essays. Coherence is a property of well-organized texts that makes them easy to read and understand [19]. Semantic coherence, proposed in [19], quantifies the degree of semantic relatedness within a text.In this work, we adopted this metric for coherence measurements. The local coherence, as expressed in Equation (6), is a measure of the similarity between