Yusuke Imai

Tomoyuki Kubota, Yusuke Imai, Sumito Tsunegi et al.

A physical neural network (PNN) has both the strong potential to solve machine learning tasks and intrinsic physical properties, such as high-speed computation and energy efficiency. Reservoir computing (RC) is an excellent framework for implementing an information processing system with a dynamical system by attaching a trained readout, thus accelerating the wide use of unconventional materials for a PNN. However, RC requires the dynamics to reproducibly respond to input sequence, which limits the type of substance available for building information processors. Here we propose a novel framework called generalized reservoir computing (GRC) by turning this requirement on its head, making conventional RC a special case. Using substances that do not respond the same to identical inputs (e.g., a real spin-torque oscillator), we propose mechanisms aimed at obtaining a reliable output and show that processed inputs in the unconventional substance are retrievable. Finally, we demonstrate that, based on our framework, spatiotemporal chaos, which is thought to be unusable as a computational resource, can be used to emulate complex nonlinear dynamics, including large scale spatiotemporal chaos. Overall, our framework removes the limitation to building an information processing device and opens a path to constructing a computational system using a wider variety of physical dynamics.

Yusuke Imai

Raga is a central musical concept in South Asia, especially India, and we investigate connections between Western classical music and Melakarta raga that is a raga in Karnatak (south Indian) classical music, through musical icosahedron. In our previous study, we introduced some kinds of musical icosahedra connecting various musical concepts in Western music: chromatic/whole tone musical icosahedra, Pythagorean/whole tone musical icosahedra, and exceptional musical icosahedra. In this paper, first, we introduce kinds of musical icosahedra that connect the above musical icosahedra through two kinds of permutations of 12 tones: inter-permutations and intra-permutations, and we call them intermediate musical icosahedra. Next, we define a neighboring number as a number of pairs of neighboring two tones in a given scale that neighbor each other on a given musical icosahedron, and we also define a musical invariant as a linear combination of the neighboring numbers. We find there exists a pair of a musical invariant and scales that is constant for some musical icosahedra and analyze their mathematical structure. Last, we define an extension of a given scale by the inter-permutations of a given musical icosahedron: the permutation-extension. Then, we show that the permutation-extension of the C major scale by Melakarta raga musical icosahedra that are four of the intermediate musical icosahedra from the type 1 chromatic/whole tone musical icosahedron to the type 1' Pythagorean/whole tone musical icosahedron, is a set of all the scales included in Melakarta raga. There exists a musical invariant that is constant for all the musical icosahedra corresponding to the scales of Melakarta raga, and we obtained a diagram representation of those scales characterizing the musical invariant.

Yusuke Imai

We propose a new way of analyzing musical pieces by using the exceptional musical icosahedra where all the major/minor triads are represented by golden triangles or golden gnomons. First, we introduce a concept of the golden neighborhood that characterizes golden triangles/gnomons that neighbor a given golden triangle or gnomon. Then, we investigate a relation between the exceptional musical icosahedra and the neo-Riemannian theory, and find that the golden neighborhoods and the icosahedron symmetry relate any major/minor triad with any major/minor triad. Second, we show how the exceptional musical icosahedra are applied to analyzing harmonies constructed by four or more tones. We introduce two concepts, golden decomposition and golden singular. The golden decomposition is a decomposition of a given harmony into the minimum number of harmonies constructing the given harmony and represented by the golden figure (a golden triangle, a golden gnomon, or a golden rectangle). A harmony is golden singular if and only if the harmony does not have golden decompositions. We show results of the golden analysis (analysis by the golden decomposition) of the tertian seventh chords and the mystic chord. While the dominant seventh chord is the only tertian seventh chord that is golden singular in the type 1[star] and the type 4[star] exceptional musical icosahedron, the half-diminished seventh chord is the only tertian seventh chord that is golden singular in the type 2 [star] and the type 3[star] exceptional musical icosahedron. Last, we apply the golden analysis to the famous prelude in C major composed by Johann Sebastian Bach (BWV 846). We found 7 combinations of the golden figures on the type 2 [star] or the type 3 [star] exceptional musical icosahedron dually represent all the measures of the BWV 846.