# Amortized Bayesian Meta-Learning with Accelerated Gradient Descent Steps
## 4 Experiments
### ShapeNet Dataset View Reconstruction  
In this sub-experiment, we use ShapeNet [32] as a 3D-object database, which covers 55 common object categories, including view reconstruction tests. According to the experiment by [PERSON] et al., we pruned this big dataset by concatenating from 12 categories with nearly 30,000 objects; 70% of the objects were chosen for training, 10% for validation, and the rest for testing. Each object contains 36 views spaced every 10 degrees in the azimuth rotation. We designed the structure of the feature network \(f(\cdot)\) and the amortization network \(\phi(\cdot)\), as displayed in Table 3. Since the size of the input image is \(32\times 32\) with one channel, a simple convolution network is formed for feature extraction. Then, we used an MLP neural network with two hidden dense layers and an fc layer as the structure of \(\phi\). The structure of the SIN network is shown in Figure 4. We trained our network with a batch size of 16, a learning rate of 0.003 in 1k epochs, and a task number of 12 with 5 shots per category. For the comparison experiment, we evaluated Versa [7] with the conditional \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Method** & **Backbone** & **1-Shot** & **5-Shot** & **Epochs** \\ \hline Matching Nets [15] & Conv-4-64 & 44.2\% & 57\% & 30,000 \\ MAML [5] & Conv-4-64 & 48.7 \(\pm\) 1.8\% & 63.1 \(\pm\) 0.9\% & 60,000 \\ Meta-SGD [31] & Conv-4-64 & 50.5 \(\pm\) 1.8\% & 64.0 \(\pm\) 0.9\% & 50,000 \\ Prototypical-Nets [16] & Conv-4-64 & 46.6 \(\pm\) 0.8\% & 65.7 \(\pm\) 0.7\% & 40,000 \\ Versa [21] & Conv-5-64 & 53.4 \(\pm\) 1.8\% & 67.3 \(\pm\) 0.8\% & 60,000 \\ SIB [12] & Conv4-4-64 & 56.0 \(\pm\) 0.6\% & 70.7 \(\pm\) 0.4\% & 50,000 \\ \hline SIN (Ours) & Conv4-4-64 & **57.9 \(\pm\) 0.7\%** & **71.3 \(\pm\) 0.6\%** & **35,000** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average classification accuracies on the Mini-ImageNet dataset among different methods (five-way one-/five-shot). Figure 10: Accuracy performances for unseen samples among state-of-the-art meta-learning methods, with the increasing number of training epochs on the Mini-ImageNet dataset (image classification tasks). (**a**) One-shot learning. (**b**) Five-shot learning. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Method** & **Backbone** & **1-Shot** & **5-Shot** & **Epochs** \\ \hline Matching Nets [15] & Conv-4-64 & 97.3\% & 98.6\% & 30,000 \\ MAML [5] & Conv-4-64 & 98.7 \(\pm\) 0.4\% & 99.8 \(\pm\) 0.9\% & 60,000 \\ Meta-SGD [31] & Conv-4-64 & 99.53 \(\pm\) 0.2\% & 99.7 \(\pm\) 0.1\% & 50,000 \\ Prototypical-Nets [16] & Conv-4-64 & 97.4 & 99.3 & 40,000 \\ Versa [21] & Conv-5-64 & 98.7 \(\pm\) 0.2\% & 99.5 \(\pm\) 0.1\% & 60,000 \\ SIB [12] & Conv-4-4-64 & 99.4 \(\pm\) 0.1\% & 99.7 \(\pm\) 0.1\% & 50,000 \\ \hline \hline SIN (Ours) & Conv4-4-64 & **99.5 \(\pm\) 0.1\%** & **99.8 \(\pm\) 0.1\%** & **35,000** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average classification accuracies on the Omniglot dataset among different methods (five-way one-/five-shot). variational autoencoder (C-VAE) model [33]. The network structure of Versa was designed by referring to the author's paper, with specific training parameters; the C-VAE network was trained in batch mode, at once, on all 12 category objects. Note that all the models were trained to reconstruct the view from a single orientation; the rest were treated as unseen samples. Figure 12 shows the reconstruction results of unseen objects from these test samples, varying in azimuth orientations. It can be seen that all of the algorithms are able to capture the orientations of the objects among the generated images; both Versa and SIN provided much more details, while SIN produced images that were visually sharper than Versa. Objects generated from Versa provided smooth details whereas SIN occasionally generated particle noises as reconstruction errors.