## 3 Results
### Decoder Analysis  
For Dataset 1, we evaluated how well our decoders produced joystick trajectories, using the correlation coefficient between actual trajectories and decoded trajectories as a metric of model accuracy. Using two-tailed \(t\)-tests, we found that both SLSTM models perform significantly better (\(p<5\times 10^{-3}\)) than all other decoders. However, the two SLSTM models did not perform significantly differently when compared to one another (\(p=0.122\)). When we compared the LSTM model with the spiking neural networks without (S)LSTM layers, they all performed similarly (\(p>0.2\)). However, all performed much better than the unscented Kalman filter (\(p<5\times 10^{-4}\)). The coefficient of determination was then used to analyze the decoding performance. This metric also accounts for absolute errors in the decoded value. For Dataset 1, when using a two-tailed \(t\)-test, we again found that the swSNN-SLSTM and memSNN-SLSTM were statistically similar (\(p=0.59\)), while outperforming (\(p<0.01\)) all other decoders. Again, the non-SLSTM layer spiking neural networks and the LSTM neural network performed similarly (\(p>0.34\)), but significantly outperformed the Kalman filter (\(p<1\times 10^{-5}\)). Figure 2 shows plots of eight successful trials from Dataset 1, decoded by each of the six decoding algorithms used. swSNN-SLSTM and memSNN-SLSTM displayed a comparable performance, with the decoded trajectories closely matching the ground truth, which is the actual joystick position. However, those decoded using swSNN-SLSTM overshoot by a small amount, while memSNN-SLSTM varies, both overshooting and undershooting. We can also see that swSNN, memSNN, and the LSTM decoder display a worse tracking of  
decoder performance. We can also clearly see that the main problem with the UKF5 Kalman filter is that it frequently overshot and undershot when the ground truth encountered a sudden change. Figure 2: Top: Two-dimensional joystick cursor positions from Dataset 1. Dashed lines indicate real trajectories, and whole lines indicate decoded trajectories. Each color represents one successful trial (which has one real trajectory and one decoded trajectory). The decoders used are: (**A**) swSNN-SLSTM; (**B**) memSNN-SLSTM; (**C**) swSNN; (**D**) memSNN; (**E**) LSTM; (**F**) UKF5. Bottom: joystick trajectories of decoders in one representative successful trial, separated into x and y dimensions. (**G,J**) show swSNN-SLSTM and memSNN-SLSTM for x and y, respectively; (**H,K**) show swSNN and memSNN for x and y, respectively; and (**L,L**) show LSTM and UKF5 for x and y, respectively. When we looked at the actual joystick trajectories for Dataset 1, we noticed specific issues with some of the decoders. For the spike-weighted SNNs, we observed that swSNN displayed oscillatory behavior when the joystick position remained at 0. However, this issue was reduced for the swSNN-SLSTM decoder. The membrane-based SNN, memSNN, did not have large changes in its gradient when rising or falling. However, it did not fall to 0 when the joystick was at rest. memSNN-SLSTM also did not fall to 0 as cleanly as swSNN-SLSTM; however, it improved when compared to memSNN. On the other hand, the LSTM model was able to settle at 0, but showed a worse tracking of peaks and troughs in joystick movements. We can also quantify model performance by looking at the correlation coefficients and coefficients of determination for the decoded position variables (Figure 3). Using two-tailed \(t\)-tests, we can see that swSNN-SLSTM outperforms all other decoders (\(p<5\times 10^{-5}\)). We also found that memSNN-SLSTM, and LSTM performed statistically similarly (\(p=0.50\)); however, they also outperformed the SNN models and UKF5 (\(p<0.01\)). swSNN's performance was statistically similar to both memSNN and the Kalman filter (\(p>0.05\)).