# Imitating Human Go Players via Vision Transformer
## 4 Experiments and Results
### Performance Evaluation for Imitating Human Moves  
#### 4.2.1 Top-k Accuracy  
To evaluate how well a model can imitate human players, we report both top-one and top-five accuracy. For a given board position, a prediction is considered correct for top-one accuracy if the model's highest-ranked move matches the human expert's move. For top-five accuracy, it is considered correct if the human expert's move is among the model's top five predicted moves. Formally, the top-\(k\) accuracy is defined as follows:  
\[\text{Top-kAcc.}=\frac{1}{N}\sum_{i=1}^{N}I(y_{i}\in\text{Top-k}(\hat{x}_{i})) \tag{5}\]  
where the variables have the following meanings:  
* \(N\) is the total number of instances in the dataset;
* \(y_{i}\) is the true label (human expert's move) for the \(i\)-th instance;
* \(\hat{x}_{i}\) represents the predicted scores or probabilities for the \(i\)-th input;
* Top-k(\(\hat{x}_{i}\)) is the set of \(k\) labels with the highest predicted scores or probabilities for the \(i\)-th instance;
* \(I(\cdot)\) is the indicator function, returning 1 if the condition inside is true and 0 otherwise.  
The results are summarized in Table 2, and test-time augmentation (TTA) leveraging the symmetric properties of Go was applied during evaluation. TTA is particularly effective for Go due to the game's symmetry, allowing the model to evaluate augmented versions of each position without additional training. This method significantly improved performance with no extra computational cost during training.  
Our evaluation shows that ViT models, even with eight encoder blocks, outperform both CNN-based models in top-one and top-five accuracy after incorporating TTA. The best-performing model, ViT/L-12, achieved a top-one accuracy of 51.49%.  
However, due to the computational cost, we limited our testing of ViT models to a maximum of 12 layers. As shown in Table 2, the results suggest that increasing the number of encoder blocks could further improve accuracy, indicating potential for even better performance with deeper models.  
We compare our results with existing Go move prediction studies [19; 20]. In [19], three different models were used: the Incep-Attention model, the Up-Down model, and an ensemble of the two models. Their top-one accuracy scores were 0.4074, 0.4420, and 0.4686, respectively. In [20], a mobile network was tested for Go move prediction, achieving a top-one accuracy of 0.4431. Compared to these studies, our approach demonstrates  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Symmetries** & **Top-1 Acc.** & **Top-5 Acc.** \\ \hline
12-layer CNN & 1 & 0.4911 & 0.8250 \\
12-layer CNN & 8 & 0.4921 & 0.8259 \\ \hline Policy network & 1 & 0.4924 & 0.8134 \\ Policy network & 8 & 0.5045 & 0.8209 \\ \hline ViT/L = 4 & 1 & 0.4513 & 0.7674 \\ ViT/L = 4 & 8 & 0.4726 & 0.7973 \\ ViT/L = 8 & 1 & 0.4860 & 0.8031 \\ ViT/L = 8 & 8 & 0.5050 & 0.8214 \\ ViT/L =superior performance in top-one accuracy. However, it is worth noting that ViT, while achieving higher accuracy, has a larger number of parameters, potentially leading to higher computational requirements and an increased system load.