Y.S. Kuo

Yu-Fen Huang, Nikki Moran, Simon Coleman et al.

In cross-modal music processing, translation between visual, auditory, and semantic content opens up new possibilities as well as challenges. The construction of such a transformative scheme depends upon a benchmark corpus with a comprehensive data infrastructure. In particular, the assembly of a large-scale cross-modal dataset presents major challenges. In this paper, we present the MOSA (Music mOtion with Semantic Annotation) dataset, which contains high quality 3-D motion capture data, aligned audio recordings, and note-by-note semantic annotations of pitch, beat, phrase, dynamic, articulation, and harmony for 742 professional music performances by 23 professional musicians, comprising more than 30 hours and 570 K notes of data. To our knowledge, this is the largest cross-modal music dataset with note-level annotations to date. To demonstrate the usage of the MOSA dataset, we present several innovative cross-modal music information retrieval (MIR) and musical content generation tasks, including the detection of beats, downbeats, phrase, and expressive contents from audio, video and motion data, and the generation of musicians' body motion from given music audio. The dataset and codes are available alongside this publication (https://github.com/yufenhuang/MOSA-Music-mOtion-and-Semantic-Annotation-dataset).

Yi-Shan Chu, Yueh-Cheng Kuo

We revisit the Universal Approximation Theorem(UAT) through the lens of the tropical geometry of neural networks and introduce a constructive, geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs). Tropical geometry shows that Rectified Linear Unit (ReLU) networks admit decision functions with a combinatorial structure often described as a tropical rational, namely a difference of tropical polynomials. Focusing on planar binary classification, we design purely sigmoidal MLPs that adhere to the finite-sum format of UAT: a finite linear combination of shifted and scaled sigmoids of affine functions. The resulting models yield decision boundaries that already align with prescribed shapes at initialization and can be refined by standard training if desired. This provides a practical bridge between the tropical perspective and smooth MLPs, enabling interpretable, shape-driven initialization without resorting to ReLU architectures. We focus on the construction and empirical demonstrations in two dimensions; theoretical analysis and higher-dimensional extensions are left for future work.