## 1 Introduction
### Literature Review  
Groove is influenced by multiple dimensions, making it difficult to directly define using a single or a few musical characteristics. It is both a musical phenomenon and a musical feature, shaped by a range of factors [3]. These include rhythmic features such as syncopation, microtiming, tempo, beat salience, and event density, as well as acoustic features like harmonic complexity and bass sounds [3]. Moreover, the groove experience can vary significantly depending on the musical style, highlighting its multidimensional nature [3]. Due to this complexity, previous studies often measure groove by evaluatingthe degree of sensorimotor coupling it induces, that is, the synchronization between music and movement. [PERSON] et al., for example, employed both behavioral and computational techniques to establish groove ratings based on this coupling [9]. Their research included the creation of a curated playlist with detailed groove ratings, which has been validated and extensively utilized in practical applications [10; 11; 12]. However, these ratings are typically obtained through physical measurements, which can be cumbersome and resource-intensive. Therefore, there is a pressing need for new methodologies that simplify the evaluation process while providing an objective assessment of groove without relying solely on intricate behavioral approaches. Based on music information retrieval (MIR) techniques, analyzing audio signals to extract acoustic features--which reflect musical elements such as rhythm, beat, and rhythmic structure--has been shown to effectively classify music [13; 14]. Therefore, investigating whether machine learning can accurately predict groove based on these acoustic features offers a promising approach to enhance our understanding and measurement of groove in music. Convolutional neural networks (CNNs) have been proposed and successfully applied across various domains, demonstrating particular strength in processing images, audio, and video [15]. A notable example is OpenL3, a pre-trained CNN widely used for tasks such as music genre recognition, instrument identification, and emotion detection [16]. Fractional-order convolutional neural networks (FOCNNs) extend traditional CNNs by incorporating principles of fractional calculus into the network architecture. Unlike standard CNNs that utilize integer-order derivatives, FOCNNs employ fractional-order derivatives, such as the Caputo derivative, to update the weights and biases of fully connected and convolutional layers [17; 18]. This approach has demonstrated higher accuracy in practical experiments [17; 19; 20]. In the context of groove classification, FOCNNs may offer a distinct advantage by enabling the model to capture subtle variations in rhythmic patterns and spectral features that are crucial to groove perception. This allows for a deeper understanding of the underlying acoustic features that define groove, making FOCNNs particularly well-suited for accurately classifying music into different groove levels. However, FOCNNs face challenges in practice, particularly in efficiently converging to an optimal solution when initial biases and weights are randomly selected [19]. This limitation necessitates the use of additional algorithms to optimize these parameters effectively. Evolutionary algorithms have played a pivotal role in optimizing neural network structures and weights [21]. For instance, genetic algorithms (GAs) and grammatical evolution have been employed to automatically design CNN topologies, achieving promising results even without data augmentation or preprocessing [22]. Additionally, methods like population extremum optimization (PEO) have shown success in dynamically updating biases and weights during CNN training [17]. Differential evolution (DE) stands out as a robust optimization algorithm, beginning with a randomly initialized population of potential solutions [23]. At each iteration, DE generates new candidate solutions by applying differential mutation and crossover operations.