## 4 Separation Mechanisms of Networks
### Proximity in Simultaneous Grouping  
For the human auditory system, the perception of two simultaneous tones is one classic simultaneous masking phenomenon, in which the just noticeable level of one sound (maskee) is raised by the presence of another sound (masker) [31]. It can be quantified by the masking amount (dB), which is the raised amount of the just noticeable level [32]. In this study, the masking amount of two pure tones is calculated by MPEG psychoacoustic model 1 [33]. The maximum value of masking amount occurs when the frequencies of two tones are in immediate proximity, and then the masking amount decreases as \(\Delta\)F increases. When the masking amount is reduced to 0 dB, there is no masking between masker and maskee. The corresponding \(\Delta\)F is regarded as the separable threshold and drawn by a white dashed curve in Figure 5. For the human auditory system, if \(\Delta\)F between two components lies under this curve, it will be affected by the masking effect and cannot be perceived as two sources. In contrast, the area above this curve is regarded as the separable range. This separable threshold indicates that the spectral analysis in the human auditory system follows the proximity principle and is good at low frequencies than higher frequencies. Results of simultaneous organization experiments for three different networks with three different window sizes are shown in Figure 5. SI-SDRi (dB) is the function of the frequency of tone A and \(\Delta\)F, where warmer color indicates a better separation. In general, all networks exhibit similar behavioral characteristics as human beings. When \(\Delta\)F between two tones is large, and tone A is at a lower frequency range (top left corner of each subgraph), components are more likely to be separated. The network separation relies on the frequency proximity of components. More importantly, the separable frequency range (the warmer area) decreases rapidly with frequency increases. The network separation ability at low frequencies is better than at high frequencies. It is highly consistent with the human auditory system, especially for ConvTasNet with a 32-sample window, DPRNN with a 4-sample window, and DPTNet with a 4-sample window. They learn the proximity principle with a similar effective range as humans. For the effective ranges, there are two slight differences worth our attention. One is that networks perform better than humans at low frequencies of 0.1 kHz to 0.2 kHz. The other one is at about 1 kHz, where components still can be separated by humans but cannot be separated by networks. Figure 4: The schematic spectrogram of the stimuli used in two experiments: (**a**) simultaneous organization experiments, where A and B indicate two concurrent tones with different frequency intervals (\(\Delta\)Fs). (**b**) sequential organization experiments, where alternating tones A and B indicate two tones with different frequency intervals (\(\Delta\)Fs) and tone repetition times (TRTs). Although similar auditory behavior characteristics are exhibited, the cues learned by networks with different parameters are slightly different. It has been established in Section 3 that the selection of parameters can affect network performance. The way and extent of parameters' impact on networks are explored in this experiment. The performance of separating these two simultaneous components with only different frequencies indicates the network frequency resolution. Results show that regardless of network structures, as the window length increases, the frequency selectivity ability of the network decreases. It indicates that the networks with smaller temporal windows have better time resolution and higher frequency resolution. It is the opposite of traditional time-frequency analysis (such as STFT), in which a high spectral resolution requires a long temporal window, resulting in lower temporal resolution.