# Non-Autoregressive Sparse Transformer Networks for Pedestrian Trajectory Prediction
## 4 Experiments
### Comparison with State-of-the-Arts  
We compare our proposed NaST with other models including Social GAN [7], Sophie [15], Social-BiGAT [18], SR-LSTM [8], Social-STGCNN [19], RSGB [64], STAR [27], GraphTCN [65], and SGCN [66]. The results evaluated by ADE and FDE metrics are shown in Table 1. Social GAN [7], Sophie [15], and Social-BIGAT [18] adopted Generative Adversarial Networks (GANs) to generalize trajectory prediction. Social GAN [7] improved over Social LSTM to generate multiple plausible trajectories. [PERSON] [15] introduced the social and physical attention mechanisms to an LSTM-based GAN model. Social-BiGAT [18] combined graph attention mechanism with GAN for prediction. SR-LSTM [8] computed social interactions by LSTM with pair-wise attention and motion gates. Social-STGCNN [19] modeled the interactions as a graph and proposed a kernel function to embed the social interactions between pedestrians within the adjacency matrix. STAR [27] constructed spatial and temporal transformers to capture social interactions among the crowd. SGCN [66] presented a Sparse Graph Convolution Network for pedestrian trajectory prediction. GraphTCN [65] was a CNN-based method which modeled the spatial interactions as social graphs and captured the spatio-temporal interactions with a modified temporal convolutional network.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **ETH** & **HOTEL** & **UNIV** & **ZARA1** & **ZARA2** & **AVG** \\ \hline Social GAN [7] & 0.87/1.62 & 0.67/1.37 & 0.76/1.52 & 0.35/0.68 & 0.42/0.84 & 0.61/1.21 \\ Sophie [15] & 0.70/1.43 & 0.76/1.67 & 0.54/1.24 & 0.30/0.63 & 0.38/0.78 & 0.51/1.15 \\ Social-BIGAT [18] & 0.69/1.29 & 0.49/1.01 & 0.55/1.32 & 0.30/0.62 & 0.36/0.75 & 0.48/1.00 \\ SR-LSTM [8] & 0.63/1.25 & 0.37/0.74 & 0.51/1.10 & 0.41/0.90 & 0.32/0.70 & 0.45/0.94 \\ Social-STGCNN [19] & 0.64/1.11 & 0.49/0.85 & 0.44/0.79 & 0.34/0.53 & 0.30/0.48 & 0.44/0.75 \\ RSBG w/o context [64] & 0.80/1.53 & 0.33/0.64 & 0.80/1.53 & 0.40/0.86 & 0.30/0.65 & 0.48/0.99 \\ STAR [27] & 0.36/0.65 & 0.17/0.36 & 0.31/0.62 & 0.26/0.55 & 0.22/0.46 & 0.26/0.53 \\ SGCN [66] & 0.63/1.03 & 0.32/0.55 & 0.37/0.70 & 0.37/0.70 & 0.25/0.45 & 0.37/0.65 \\ GraphTCN [65] & 0.59/1.12 & 0.27/0.52 & 0.42/0.87 & 0.30/0.62 & 0.23/0.48 & 0.36/0.72 \\ NaST (Ours) & 0.35/0.62 & 0.15/0.35 & 0.27/0.56 & 0.25/0.56 & 0.19/0.41 & **0.24/0.50** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison with some models on datasets ETH and UCY of ADE/FDE metrics (the lower numerical result is better).  
We observed that our method outperformed all the competitive methods on these benchmark datasets in terms of the average result of the ADE and FDE metrics. For the average ADE metric, our NaST surpassed the previous best method STAR [27] by 8%. For the average FDE metric, NaST is better than STAR [27] by a margin of 6%. In particular, the results showed that our model yielded better results than those dense methods such as Sophie [15], Social-STGCNN [19], and STAR [27], especially on the more complex datasets UNIV and ZARA2 containing dense crowd scenes. We speculated that the under-lying reason is that the dense methods construct superfluous social interactions, which interfere the trajectory prediction. Fortunately, the superfluous interaction is removed by the sparse transformer and focuses on the exact neighbors who are involved in the interaction. Furthermore, the non-autoregressive inference pattern could avoid accumulating errors and thus improve the efficiency of the model.