Artificial Neural Networks Solve Musical Problems With Fourier Phase Spaces

Abstract

How does the brain represent musical properties? Even with our growing understanding of the cognitive neuroscience of music, the answer to this question remains unclear. One method for conceiving possible representations is to use artificial neural networks, which can provide biologically plausible models of cognition. One could train networks to solve musical problems, and then study how these networks encode musical properties. However, researchers rarely examine network structure in detail because networks are difficult to interpret, and because many assume that networks capture informal or subsymbolic properties. Here we report very high correlations between network connection weights and discrete Fourier phase spaces used to represent musical sets. This is remarkable because there is no clear mathematical relationship between network learning rules and discrete Fourier analysis. That networks discover Fourier phase spaces indicates that these spaces have an important role to play outside of formal music theory. Finding phase spaces in networks raises the strong possibility that Fourier components are possible codes for musical cognition.

[Retracted] Pop Music Trend and Image Analysis Based on Big Data Technology

“…Dawson et al stated that people could train the networks to solve musical problems and study how these networks encode musical properties. They also reported very high correlations between the network connection weights and discrete Fourier phase spaces used to represent the musical sets [ 13 ]. Dorfler et al posed the question of whether replacing it by applying adaptive or learned filters directly to the raw data can improve learning success.…”

Application of local fully Convolutional Neural Network combined with YOLO v5 algorithm in small target detection of remote sensing image

“…Besides, it can complete data integration by establishing the connections between data through analyzing and processing a large amount of data information. Therefore, DL is gradually completing the target detection in the most efficient technical way in the field of AI [2,3]. For a long time, technicians from all walks of life have tried to simulate the complex process of remote sensing image interpretation by remote sensing experts through the method of computer interpretation to the greatest extent.…”

What Is Cognitive Psychology?

“…Some researchers argue that failing to understand network structure limits networks' ability to contribute new cognitive theories (McCloskey, 1991;Seidenberg, 1993). However, various techniques do exist for understanding how networks operate (Berkeley et al, 1995;Dawson, 2018;Dawson et al 2020;Hanson & Burr, 1990). Importantly, when we use such techniques to interpret networks, the distinction between networks and rule-based models becomes less clear.…”

“…Most researchers who conduct such research assume that networks capture musical properties that we cannot express using formal rules (Bharucha, 1999). However, when we interpret the internal structures of musical networks, we discover many formal musical properties (Dawson, 2018;Dawson et al, 2020).…”