# Cross Domain Adaptation of Crowd Counting with Model-Agnostic Meta-Learning
## 4 Experiments
### Evaluation of the Density-Map Estimator Based on Dynamic-\(\beta\) MAML  
In this research, we used the synthetic data set GCC as the training set for meta-learning. Since GCC contains seven different weather scenes, we split these seven different scenes into different tasks. We fixed the feature extraction model parameters, and re-used the CSRNet feature-extracting function, or the component proposed in the previous section. The aim was to train the function \(g(\cdot)\) to generate density maps by meta-learning, and we trained the density-map estimator with tasks containing a training set and testing set.  
To evaluate the proposed dynamic-\(\beta\) MAML algorithm performance, we ran a series of training experiments to study the effect of meta-learning rate on density-estimator loss. As shown in Figure 6, for a fair comparison, we recorded the meta-learning rate \(\beta\) changes with the top 600 iterations. It was found that, no matter the initial value, under the influence of different hyperparameters \(\delta_{hyper}\) the meta-learning rate \(\beta\) will show different results in the learning process. From Figure 6, our proposed dynamic-\(\beta\) MAML algorithm shows faster convergence with the meta-learning rate, specifically for \(\
abla_{hyper}=1e-4\). We utilized the standard crowd-counting model trained in a supervised setting as the baseline [60]. When the training was complete, the model was evaluated directly on target scenes without adaption. Simultaneously, we chose FSCC [13] for the comparative analysis. FSCC is a state-of-the-art algorithm in few-shot adaptive crowd-counting scenarios. Table 1 shows the experimental results.  
From the table above, our proposed method can achieve MAE 16.13 and MSE 22.93 for 1-shot, and MAE 16.47 and MSE 23.48 for 5-shot. FSCC is state-of-the-art in few-shot crowd-counting problems. Our method exhibited better performance than FSCC.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Tasks** & **Method** & \multicolumn{2}{c}{**1-Shot (\(K=1\))**} & \multicolumn{2}{c}{**5-Shot (\(K=5\))**} \\  & & **MAE** & **MSE** & **MAE** & **MSE** \\ \hline \multirow{3}{*}{Scene1: Clear} & Baseline & 23.11 & 34.16 & 22.54 & 33.24 \\  & FSCC & 19.33 & 28.08 & 19.33 & 28.08 \\  & Ours & 18.34 & 26.48 & 18.34 & 26.48 \\  & Baseline & 21.99 & 32.35 & 21.81 & 32.06 \\  & FSCC & 17.12 & 24.52 & 17.37 & 24.92 \\  & Ours & 17.18 & 24.62 & 17.39 & 24.96 \\  & Baseline & 14.87 & 20.89 & 14.88 & 20.91 \\ Scene3: Rain & FSCC & 11.31 & 15.16 & 11.87 & 16.06 \\  & Ours & 11.32 & 15.17 & 11.91 & 16.12 \\  & Baseline & 32.00 & 48.45 & 32.13 & 48.66 \\ Scene4: Foggy & FSCC & 15.99 & 22.70 & 15.78 & 22.36 \\  & Ours & 15.71 & 22.25 & 15.99 & 22.70 \\  & Baseline & 39.56 & 60.59 & 39.13 & 59.90 \\ Scene5: Thunder & FSCC & 20.44 & 29.86 & 20.31 & 29.65 \\  & Ours & 19.23 & 27.91 & 20.01 & 29.17 \\  & Baseline & 19.44 & 28.25 & 19.72 & 28.70 \\ Scene6: Overcast & FSCC & 14.30 & 19.97 & 14.28 & 19.94 \\  & Ours & 14.22 & 19.85 & 14.65 & 20.54 \\  & Baseline & 24.52 & 36.43 & 24.37 & 36.19 \\ Scene7: Extra Sunny & FSCC & 17.49 & 25.11 & 17.47 & 25.08 \\  & Ours & 16.94 & 24.23 & 17.03 & 24.37 \\  & Baseline & 25.07 & 37.30 & 24.94 & 37.10 \\ Average & FSCC & 16.57 & 23.63 & 16.63 & 23.73 \\  & Ours & **16.13** & **22.93** & **16.47** & **23.48** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Verification of the proposed dynamic-\(\beta\) MAML algorithm with \(\delta_{hyper}=1\times 10^{-4}\) on dataset GCC by comparing with baseline and FSCC [13] method.  
Figure 6: (a) shows the meta-learning rate \(\beta\) with initial value \(\beta_{0}=1\times 10^{-6}\), (b) shows the meta-learning rate \(\beta\) with initial value \(\beta_{0}=1\times 10^{-3}\). (c) shows the loss with different values of hyper-parameter \(\delta_{hyper}\).