Related papers: Geometry of Music Perception
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
Why depth yields a genuine computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional Gaussian setting, focusing on compositional target…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
Harmony in visual compositions is a concept that cannot be defined or easily expressed mathematically, even by humans. The goal of the research described in this paper was to find a numerical representation of artistic compositions with…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
We show that there is a fast algorithm that embeds hierarchical structures in three-dimensional Minkowski spacetime. The correlation of data ends up purely encoded in the causal structure. Our model relies solely on oriented token pairs --…
To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal…
Multi-pitch perception is investigated in a listening test using 30 recordings of musical sounds with two tones played simultaneously, except for two gong sounds with inharmonic overtone spectrum, judging roughness and separateness as the…
Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains…
It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of…
The relationship between perceptual loudness and physical attributes of sound is an important subject in both computer music and psychoacoustics. Early studies of "equal-loudness contour" can trace back to the 1920s and the measured…
From the work of Phong and Sturm in 2007, for a polarised projective manifold and an ample test configuration, one can associate the geodesic ray of plurisubharmonic metrics on the polarising line bundle using the solution of the…
Music Information Retrieval (MIR) is a collaborative scientific study that help to build innovative information research themes, novel frameworks, and developing connected delivery mechanisms in addition to making the world's massive…
Art has long played a profound role in shaping human emotion, cognition, and behavior. While visual arts such as painting and architecture have been studied through eye tracking, revealing distinct gaze patterns between experts and novices,…
The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…
Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with…
This paper is a survey and an analysis of different ways of using deep learning (deep artificial neural networks) to generate musical content. We propose a methodology based on five dimensions for our analysis: Objective - What musical…