# Dual-Path Beat Tracking: Combining Temporal Convolutional Networks and Transformers in Parallel
## 5 Results and Discussions  
The results are presented across five benchmark datasets, Ballroom [34], Hainsworth [35], Harmonix [36], SMC [37], and GTZAN [38], using widely adopted metrics--F-Measure, CMLt (Continuity-based Measure with no tolerance), and AMLt (Accuracy-based Measure with loose tolerance). For further details, see [42]. For each dataset, the proposed model is compared with baseline models, including TCN [7], Beat This [12], SpecTNT-TCN [10], and Demixed DSA [8], summarized in Table 2.  
We include results from prior studies in the literature for reference, although it is important to note that these results are not directly comparable. Key differences in training methodologies and evaluation setups make direct comparisons challenging. Firstly, the training approach utilizes a combined dataset and eight-fold cross-validation, which means that the amount and variety of data used for training differ across various studies. Each study often utilizes a unique set of training data, which can significantly affect the results due to the diverse characteristics of music datasets. Additionally, the loss functions employed in previous studies vary, with some focusing on Binary Cross-Entropy, while others use different loss functions suited to their particular objectives, such as shift tolerance [12]. Likewise, data augmentation strategies differ, with some studies applying specific augmentations--such as time-stretching or pitch-shifting--to enhance model robustness, while others rely on source separation techniques to isolate certain elements like drums or bass before training [8]. Our approach, however, does not incorporate augmentation or source separation, which inherently makes our model's learning approach different. In our work, we opted not to use augmentation. This decision stems from the fact that our approach trains on full song sequences, unlike the models in comparison [7; 10; 12] that train on smaller sections due to memory and computational constraints or for faster convergence. Additionally, while various augmentation techniques, such as hop size variation, harmonic representations, masking, pitch and time tweaks, and demixing, have been explored in related works, their inclusion would have significantly increased training time and computational overhead, limiting practicality. Introducing augmentations would necessitate justifying and evaluating each augmentation method, adding further complexity. Although we acknowledge the potential benefits of augmentation, particularly for improving performance on unseen datasets, such \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Model** & **F-Measure** & **CMLt** & **AMLt** \\ \hline \multirow{6}{*}{Ballroom} & TCN & 0.933 & 0.864 & 0.881 \\  & Beat this & 0.975 & - & - \\  & SpecTNT-TCN & 0.962 & 0.939 & 0.967 \\  & Demixed DSA & 0.968 & 0.954 & 0.966 \\  & Ours & 0.961 & 0.937 & 0.962 \\ \hline \multirow{6}{*}{Hainsworth} & TCN & 0.874 & 0.755 & 0.795 \\  & Beat this & 0.919 & - & - \\  & SpecTNT-TCN & 0.877 & 0.862 & 0.915 \\  & Demixed DSA & 0.902 & 0.842 & 0.918 \\  & Ours & 0.883 & 0.916 & 0.906 \\ \hline \multirow{6}{*}{Harmonix} & TCN & - & - & - \\  & Beat this & 0.958 & - & - \\  & SpecTNT-TCN & 0.953 & 0.939 & 0.959 \\  & Demixed DSA & 0.954 & 0.905 & 0.957 \\  & Ours & 0.954 & 0.904 & 0.964 \\ \hline \multirow{6}{*}{SMC} & TCN & 0.543 & 0.315 & 0.432 \\  & Beat this & 0.627 & - & - \\  & SpecTNT-TCN & 0.605 & 0.514 & 0.663 \\  & Demixed DSA & 0.596 & 0.456 & 0.635 \\  & Ours & 0.582 & 0.455 & 0.618 \\ \hline \multirow{6}{*}{GTZAN *} & TCN & 0.843 & 0.695 & 0.715 \\  & Beat this & 0.891 & 0.798 & 0.898 \\ \cline{1-1}  & SpecTNT-TCN & 0.887 & 0.812 & 0.920 \\ \cline{1-1}  & Demixed DSA & 0.885 & 0.800 & 0.922 \\ \cline{1-1}  & Ours & 0.867 & 0.774 & 0.905 \\ \hline \hline \end{tabular}  
* indicates the dataset was not used by the authors of respective papers.  
\end{table} 
Table 2: Comparison of F-Measure, CMLt, and AMLt with other SOTA models. exploration is beyond the scope of this study.