# Amortized Bayesian Meta-Learning with Accelerated Gradient Descent Steps
## 4 Experiments
### ShapeNet Dataset View Reconstruction
Table 4 shows MSE and SSIM comparisons for view reconstruction results, where MSE denotes the mean square error (the lower the better) and SSIM denotes the structural similarity index (the higher the better). We observe that the measurements show improvements for both SIN and Versa as the shot number increases to 5. To provide a qualitative analysis for the ShapeNet dataset, we plot the normalized MSE with the increase in training epochs in Figure 13. Observe that there is a descending MSE trend as the training epochs grow, which shows the convergence of the proposed method for both 5-shot and 1-shot learning. This also validates the fast convergence principle of ABML-SIN. Table 4 displays the details of the training performance comparisons of different meta-learning approaches. We used a personal computer with a 4-core Intel i5-8200 CPU and a NVIDIA-GTX 1060 6 GB GPU. The training epochs were set to 20,000 and 35,000 separately. The support size and query size for meta-training were set at (1, 15) and (2, 25) for memory and training time comparisons, respectively. We used five-way, one-shot for accurate recording. Our method (SIN) exhibits top-tier accuracy among the compared methods after 20k and 30k epochs (Figure 14). However, it costs a little more in terms of GPU memory usage and training parameters since it uses the knowledge distillation approach with the 'teacher and student' architecture introduced. In conclusion, our method achieves better performance with fast gradient descent steps, owing to the optimized training architectural designs. To further see the performance metrics of the training time and computational resources of these meta-learning methods, they were based on PyTorch/TensorFlow architectures. We recorded the training time and GPU memory consumption through memory probe tools. Model parameters were recorded through PyTorch/TensorFlow. Also, the accuracy factor was recorded via training epochs and training time. Table 5 shows the details of  
Figure 11: Qualitative analysis of the normalized MSE with the increase in the training epochs on the ShapeNet dataset. the training performance comparisons in different meta-learning approaches. Observe that the proposed method performs competitively among the compared methods. It requires the least training time to meet the target epoch with the best accuracy. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Method** & **MSE** & **SSIM** \\ \hline C-VAE [33] 1-shot & 0.0277 & 0.5923 \\ C-VAE 5-shot & 0.0265 & 0.5639 \\ Versa [7] 1-shot & 0.0108 & 0.7893 \\ Versa 5-shot & 0.0069 & 0.8483 \\ \hline SIN 1-shot & 0.0065 & 0.8492 \\ SIN 5-shot & **0.0061** & **0.8521** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: View reconstruction test results. (MSE and SSIM comparisons between different methods). Figure 12: Results for ShapeNet view reconstruction for unseen test objects. **(I)–(VI)** represents six categories: plane, lamp, bench, car, metal box, chair. Top row: The ground truth. **(a)** C-VAE [33]. **(b)** Versa [21]. **(c)** SIN. \begin{table}
\begin{tabular}{l l} \hline \hline
**Output Size** & **Layers** \\ \hline \(32\times 32\times 1\) & input image \\ \(16\times 16\times 64\) & conv2d (\(3\times 3\), stride = 1, padding = SAME), pool \\ \(8\times 8\times 64\) & conv2d (\(3\times 3\), stride = 1, padding = SAME), pool \\ \(4\times 4\times 64\) & conv2d (\(3\times 3\), stride = 1, padding = SAME), pool \\ \(2\times 2\times 64\) & conv2d (\(3\times 3\), stride = 1, padding = SAME), pool \\ \(d_{\phi_{7}}\), \(256\times 1\) & full connection layer, activation=ReLU \\ \hline \(d_{\phi_{7}}\), \(256\times 1\) & input layer \\ \(256\times 128\) & dense, activation = Tanh \\ \(128\times 64\) & dense, activation = Tanh \\ \(\theta_{0}^{t}\), \(64\times 1\) & full connection layer, activation = ReLU \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The structure of feature network \(f\) with amortization network \(\phi\) for ShapeNet with few-shot learning.