# Dual-Path Beat Tracking: Combining Temporal Convolutional Networks and Transformers in Parallel
## 2 Background  
Early techniques primarily relied on extracting fundamental audio features like note onsets, pitch, and duration, followed by periodicity detection to estimate beat times. These traditional methods, pioneered by researchers like [PERSON] [14] and [PERSON] [15], used amplitude peaks or manual parameter tuning to detect rhythms but struggled to generalize across musical genres and required labor-intensive adjustments. As music styles and rhythmic structures became increasingly diverse, machine learning methods gained prominence. These approaches improved generalization by training on larger datasets and embedding probabilistic elements into the beat-tracking process. [PERSON] et al. [16] developed a beat-tracking system to process music played on ensembles of different instruments. However, their system was mostly limited to rock/pop music, where drums were the primary driving factor for beat positions, since bass drum appears on strong beats and snare drum appears on weak beats. It selected the best hypothesis by examining multiple hypotheses in parallel and making assumptions about tempo and time signatures. [PERSON]'s [17] psychoacoustic approach used frequency bands to detect beats, while [PERSON] and [PERSON] [18] introduced probabilistic models that used Bayesian frameworks to model beats as dynamic systems. These probabilistic models accounted for tempo variations and rhythmic irregularities, improving reliability in more complex musical contexts. [PERSON] and [PERSON] [19] further advanced the field by using Fourier transform-based analyses to detect onsets, followed by probabilistic tracking of metrical structures (tatum, tactus, and measure), achieving robustness across different genres and tempos. Most of the deep learning approaches to beat or downbeat tracking follow the pipeline shown in Figure 1.  
In this pipeline, audio input can be used directly in its waveform form or transformed into a more suitable representation, such as a spectrogram, cepstrum, or a hybrid representation. Trainable harmonic filters or similar techniques can then be applied to convert the input into a harmonic representation, enhancing feature extraction. At this stage, features may be handcrafted, or alternatively, a DNN model can be used to automatically learn features from the audio. After feature learning, the DNN outputs an activation, representing the probability that each frame contains a beat, downbeat, or non-beat. For post-processing, a probabilistic graphical model is applied to the DNN-derived likelihoods, enabling musical consistency constraints to be enforced during inference. This post-processing may involve models such as a Bar Pointer model, Hidden Markov Model (HMM), Dynamic Bayesian Network (DBN), Conditional Random Field (CRF), or particle filtering [1; 20; 21; 22]. The adoption of deep learning marked a transformative era in beat tracking, beginning with Recurrent Neural Networks (RNNs) and later Convolutional Neural Networks (CNNs). RNNs with long short-term memory (LSTM) units, introduced by [PERSON] and [PERSON] [23], became some of the first data-driven models for beat tracking. These models could adapt to various musical styles by learning directly from data and transforming audio signals into beat activations, laying the groundwork for style-specific beat-tracking systems. However, RNNs were computationally intensive and often required complex post-processing, with post-processing such as Dynamic Bayesian Networks (DBNs) to achieve rhythmic consistency [24] or combined with convolutional networks with particle filtering in post-processing [25; 26]. Figure 1: General pipeline for beat tracking using deep neural networks. Each stage in this progression, from handcrafted methods to advanced neural networks, has contributed to more accurate, adaptable beat-tracking systems. Deep learning models now achieve good accuracy on many benchmarks, yet the continued refinement of these hybrid architectures and post-processing techniques suggests ongoing potential for further improvements.