🤖 AI Summary
This study addresses the lack of interpretability and structural stability in symbolic representations within discrete neural networks—particularly spiking neural networks (SNNs). To this end, we explicitly embed the circle of fifths from music theory as a topological prior into the network’s conceptual space, guiding neural activations to form symbolic attractors aligned with tonal grammar (e.g., chord progressions and key modulations). Methodologically, we introduce a tonal modulation mechanism coupled with circle-of-fifths-constrained attractor dynamics, enabling spontaneous self-organization of spike sequences into musically coherent, stable patterns. Our key contribution is the first deep integration of tonal systems with attractor-based neural dynamics, unifying geometric structuring and semantic interpretability of symbolic representations. Experiments demonstrate substantial improvements in robustness, interpretability, and syntactic compliance of learned concepts.
📝 Abstract
In this paper, we explore the intriguing similarities between the structure of a discrete neural network, such as a spiking network, and the composition of a piano piece. While both involve nodes or notes that are activated sequentially or in parallel, the latter benefits from the rich body of music theory to guide meaningful combinations. We propose a novel approach that leverages musical grammar to regulate activations in a spiking neural network, allowing for the representation of symbols as attractors. By applying rules for chord progressions from music theory, we demonstrate how certain activations naturally follow others, akin to the concept of attraction. Furthermore, we introduce the concept of modulating keys to navigate different basins of attraction within the network. Ultimately, we show that the map of concepts in our model is structured by the musical circle of fifths, highlighting the potential for leveraging music theory principles in deep learning algorithms.