SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 10: Long-term forecasting results comparison with different lookback window lengths  $L \in \{96, 192, 336\}$ . The prediction lengths are as  $\tau \in \{96, 192, 336, 720\}$ . The best results are in **bold** and the second best results are **underlined**.
Models Metrics	FreTS	PatchTST	LTSF-Linear	FEDformer	Autoformer	Informer	Reformer
MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE
96	96	0.037	0.051	0.039	0.052	0.038	0.052	0.050	0.067	0.050	0.066	0.066	0.084	0.126	0.146
192	0.050	0.067	0.055	0.074	0.053	0.069	0.064	0.082	0.063	0.083	0.068	0.088	0.147	0.169
336	0.062	0.082	0.071	0.093	0.064	0.085	0.080	0.105	0.075	0.101	0.093	0.127	0.157	0.189
720	0.088	0.110	0.132	0.166	0.092	0.116	0.151	0.183	0.150	0.181	0.117	0.170	0.166	0.201
192	96	0.036	0.050	0.037	0.051	0.038	0.051	0.067	0.086	0.066	0.085	0.109	0.131	0.123	0.143
192	0.051	0.068	0.052	0.070	0.053	0.070	0.080	0.101	0.080	0.102	0.144	0.172	0.139	0.161
336	0.066	0.087	0.072	0.097	0.073	0.096	0.093	0.122	0.099	0.129	0.141	0.177	0.155	0.181
720	0.088	0.110	0.099	0.128	0.098	0.122	0.190	0.222	0.191	0.224	0.173	0.210	0.159	0.193
336	96	0.038	0.052	0.039	0.053	0.040	0.055	0.088	0.113	0.088	0.110	0.137	0.169	0.128	0.148
192	0.053	0.070	0.055	0.071	0.055	0.072	0.103	0.133	0.104	0.133	0.161	0.195	0.138	0.159
336	0.071	0.092	0.074	0.099	0.077	0.100	0.123	0.155	0.127	0.159	0.156	0.193	0.156	0.179
720	0.082	0.108	0.100	0.129	0.087	0.110	0.210	0.242	0.211	0.244	0.173	0.210	0.168	0.205
the weight coefficients of the real or imaginary part exhibit energy aggregation characteristics (clear diagonal patterns) which can facilitate frequency-domain MLPs in learning the significant features.
(a)  $\mathcal{W}_r$  under I/O=48/192
(b)  $\mathcal{W}_r$  under I/O=48/336
(c)  $\mathcal{W}_r$  under I/O=72/336
(d)  $\mathcal{W}_i$  under I/O=48/192
(e)  $\mathcal{W}_i$  under I/O=48/336
(f)  $\mathcal{W}_i$  under I/O=72/336
Figure 7: The visualizations of the weights  $\mathcal{W}$  in the frequency temporal learner on the Traffic dataset. 'I/O' denotes lookback window sizes/prediction lengths.  $\mathcal{W}_r$  and  $\mathcal{W}_i$  are the real and imaginary parts of  $\mathcal{W}$ , respectively.
G.2 Weight Visualizations for Global View
To verify the characteristics of a global view of learning in the frequency domain, we perform additional experiments on the Traffic and Electricity datasets and compare the weights learned on the input in the time domain with those learned on the input frequency spectrum. The results are presented in Figures 9 and 10. The left side of the figures displays the weights learned on the input in the time domain, while the right side shows those learned on the real part of the input frequency spectrum. From the figures, we can observe that the patterns learned on the input frequency spectrum exhibit more obvious periodic patterns compared to the time domain. This is attributed to the global view characteristics of the frequency domain. Furthermore, we visualize the predictions of FreTS on
(a)  $\mathcal{W}_r$  under I/O=96/96
(b)  $\mathcal{W}_r$  under I/O=96/336
(c)  $\mathcal{W}_r$  under I/O=96/720
(d)  $\mathcal{W}_i$  under I/O=96/96
(e)  $\mathcal{W}_i$  under I/O=96/336
(f)  $\mathcal{W}_i$  under I/O=96/720
Figure 8: The visualizations of the weights  $\mathcal{W}$  in the frequency temporal learner on the Electricity dataset. 'I/O' denotes lookback window sizes/prediction lengths.  $\mathcal{W}_r$  and  $\mathcal{W}_i$  are the real and imaginary parts of  $\mathcal{W}$ , respectively.
the Traffic and Electricity datasets, as depicted in Figures 11 and 12, which show that FreTS exhibit a good ability to fit cyclic patterns. In summary, these results demonstrate that FreTS has a strong capability to capture the global periodic patterns, which benefits from the global view characteristics of the frequency domain.
(a) Learned on the input
Figure 9: Visualization of the weights  $(L \times \tau)$  on the Traffic dataset with lookback window size of 72 and prediction length of 336.
(b) Learned on the frequency spectrum
(a) Learned on the input
(b) Learned on the frequency spectrum
Figure 10: Visualization of the weights  $(L \times \tau)$  on the Electricity dataset with lookback window size of 96 and prediction length of 96.
(a)  $\mathrm{I} / \mathrm{O} = 48 / 48$
(b)  $\mathrm{I} / \mathrm{O} = 48 / 96$
(c)  $\mathrm{I} / \mathrm{O} = 48 / 192$
Figure 11: Visualizations of predictions (forecast vs. actual) on the Traffic dataset. 'I/O' denotes lookback window sizes/prediction lengths.
(d)  $\mathrm{I} / \mathrm{O} = 48 / 336$
(a)  $1 / 0 = 96 / 96$
(b)  $\mathrm{I} / \mathrm{O} = 96 / 192$
(c)  $\mathrm{I} / \mathrm{O} = 96 / 336$
(d)  $\mathrm{I} / \mathrm{O} = 96 / 720$
Figure 12: Visualizations of predictions (forecast vs. actual) on the Electricity dataset. 'I/O' denotes lookback window sizes/prediction lengths.