# Amortized Bayesian Meta-Learning with Accelerated Gradient Descent Steps
## 5 Conclusions  
We presented a novel meta-learning framework with fast training steps. To achieve efficient variational inference and provide uncertainty predictions, we adopted the amortized Bayesian method as a principled theory, together with a transductive scheme for constructing the variational posterior. To optimize the training process of meta-learner, we developed a synthetic inference network, which takes the output of the amortization network as input, and it produces the refined latent variables for meta-training. We also used a student-teacher network architecture as an online learning structure for cooperative training of the  
Figure 14: The comparison between the proposed model and the baseline (SGD) on the MINI-ImageNet dataset. Purely running the baseline network results in a slower convergence speed and worse accuracy performance at the same epochs, compared with the combined model using SIN.  
Figure 13: Sensitivity analysis on the accuracy factor of hyperparameter \(\xi\) in Algorithm 1 based 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 l} \hline \hline
**Method** & **Config** & **Acc (Sway-Ishot)** & **Epochs** & **Training Time** & **GPU Memory** & **Model Params** \\ \hline MAML [5] & supp-sz = 1, query-sz = 15 & 31.1\% & 20,000 & 1 h 45 min & 1.8 GB & 4.2 MB \\ \hline Versa [21] & supp-sz = 1, query-sz = 15 & 37.5\% & 20,000 & 2 h 15 min & 2.1 GB & 15.4 MB \\ \hline SIB [12] & supp-sz = 1, query-sz = 15 & 40.5\% & 20,000 & 3 h 21 min & 3.2 GB & 88.1 MB \\ \hline SIN (Ours) & supp-sz = 1, query-sz = 15 & **45.5** \% & 20,000 & **1 h 03 min** & 3.4 GB & 45.2 MB \\ \hline MAML [5] & supp-sz = 2, query-sz = 25 & 44.3\% & 35,000 & 3 h 03 min & 2.2 GB & 4.2 MB \\ \hline Versa [21] & supp-sz = 2, query-sz = 25 & 49.1\% & 35,000 & 3 h 55 min & 2.4 GB & 15.4 MB \\ \hline SIB [12] & supp-sz = 2, query-sz = 25 & 52.5\% & 35,000 & 5 h 49 min & 3.8 GB & 88.1 MB \\ \hline SIN (Ours) & supp-sz = 2, query-sz = 25 & **56.9**\% & 35,000 & **2 h 22 min** & 4.1 GB & 45.2 MB \\ \hline \hline \end{tabular}
\end{table}
Table 5: Details of training performance comparisons among different meta-learning approaches.  
synthetic inference network. The training process of the meta-network converges faster due to the proposed mechanism. The proposed method showed generalization and scalability on unseen samples, and it produced competitive/superior uncertainty estimations on few-shot learning tasks on two widely adopted 2D datasets with 30%\(\sim\)41% fewer training epochs compared with the state-of-the-art. It also improved learning accuracy by 3%\(\sim\)5% on unseen samples on the Mini-ImageNet dataset for classification tasks. These outcomes indicate that our method is effective for few-shot learning tasks, providing uncertainty predictions for the meta-learning model, together with flexibility and scalability, which means it is suitable for unseen cases through a fast learning process. In future work, we will consider optimizing the learning structure of the meta-learner, deriving more theoretical proof to propose the optimized bound for PAC-Bayesian meta-learning theories with hyper priors and posteriors.  
Conceptualization, Z.Z. and S.W.; Methodology, Z.Z. and X.L.; Software, Z.Z.; Validation, Z.Z.; Formal analysis, Z.Z.; Investigation, Z.Z.; Resources, Z.Z.; Data curation, Z.Z.; Writing--original draft, Z.Z.; Writing--review & editing, Z.Z. and X.L.; Visualization, Z.Z.; Supervision, X.L. and S.W.; Project administration, Z.Z.; Funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.