Local Critic Training of Deep Neural Networks

This paper proposes a novel approach to train deep neural networks by unlocking the layer-wise dependency of backpropagation training. The approach employs additional modules called local critic networks besides the main network model to be trained, which are used to obtain error gradients without complete feedforward and backward propagation processes. We propose a cascaded learning strategy for these local networks. In addition, the approach is also useful from multi-model perspectives, including structural optimization of neural networks, computationally efficient progressive inference, and ensemble classification for performance improvement. Experimental results show the effectiveness of the proposed approach and suggest guidelines for determining appropriate algorithm parameters

Music Popularity: Metrics, Characteristics, and Audio-Based Prediction

Understanding music popularity is important not only for the artists who create and perform music but also for the music-related industry. It has not been studied well how music popularity can be defined, what its characteristics are, and whether it can be predicted, which are addressed in this paper. We first define eight popularity metrics to cover multiple aspects of popularity. Then, the analysis of each popularity metric is conducted with long-term real-world chart data to deeply understand the characteristics of music popularity in the real world. We also build classification models for predicting popularity metrics using acoustic data. In particular, we focus on evaluating features describing music complexity together with other conventional acoustic features including MPEG-7 and Mel-frequency cepstral coefficient (MFCC) features. The results show that, although room still exists for improvement, it is feasible to predict the popularity metrics of a song significantly better than random chance based on its audio signal, particularly using both the complexity and MFCC features

On the twisted quadratic moment for Dirichlet L-functions

Given $c,$ a positive integer, we give an explicit formula and an asymptotic formula for $$\sum\chi(c)|L(1,\,\chi)|^{2},$$ where $\chi$ is the non-trivial Dirichlet character mod $f$ with $f>c.

Regularization Methods for Generative Adversarial Networks: An Overview of Recent Studies

Despite its short history, Generative Adversarial Network (GAN) has been extensively studied and used for various tasks, including its original purpose, i.e., synthetic sample generation. However, applying GAN to different data types with diverse neural network architectures has been hindered by its limitation in training, where the model easily diverges. Such a notorious training of GANs is well known and has been addressed in numerous studies. Consequently, in order to make the training of GAN stable, numerous regularization methods have been proposed in recent years. This paper reviews the regularization methods that have been recently introduced, most of which have been published in the last three years. Specifically, we focus on general methods that can be commonly used regardless of neural network architectures. To explore the latest research trends in the regularization for GANs, the methods are classified into several groups by their operation principles, and the differences between the methods are analyzed. Furthermore, to provide practical knowledge of using these methods, we investigate popular methods that have been frequently employed in state-of-the-art GANs. In addition, we discuss the limitations in existing methods and propose future research directions

Stationary Perturbation Theory with Spatially Well-separated Potentials

We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the respective centers of the two taken to be quite large. It is assumed that complete eigenfunctions of the local Hamiltonians (i.e., in the presence of $V_{1}(\vec{r})$ or $V_{2}(\vec{r})$ only) are available as inputs to our perturbation theory. If the two local Hamiltonians have degenerate bound-state energy levels, a systematic extension of the molecular orbital theory (or the tight-binding approximation) follows from our formalism. Our approach can be viewed as a systematic adaptation of the multiple scattering theory to the problem of bound states.Comment: 22 pages, no figures; uses revtex

Controllable Generative Adversarial Network

Recently introduced generative adversarial network (GAN) has been shown numerous promising results to generate realistic samples. The essential task of GAN is to control the features of samples generated from a random distribution. While the current GAN structures, such as conditional GAN, successfully generate samples with desired major features, they often fail to produce detailed features that bring specific differences among samples. To overcome this limitation, here we propose a controllable GAN (ControlGAN) structure. By separating a feature classifier from a discriminator, the generator of ControlGAN is designed to learn generating synthetic samples with the specific detailed features. Evaluated with multiple image datasets, ControlGAN shows a power to generate improved samples with well-controlled features. Furthermore, we demonstrate that ControlGAN can generate intermediate features and opposite features for interpolated and extrapolated input labels that are not used in the training process. It implies that ControlGAN can significantly contribute to the variety of generated samples.Comment: A fully revised version of this paper is published in IEEE Access. Please refer to https://doi.org/10.1109/ACCESS.2019.289910

Dyonic Instanton as Supertube between D4 Branes

We study dyonic instantons in (4+1) dimensional Yang-Mills theory. Especially we consider the most general two instanton solution given by the Jackiw-Nohl-Rebbi ansatz and find its dyonic version. By exploring the zeros of the Higgs field, we rederive the porism structure of triangles in this solution and also find the magnetic monopole string loop. This leads to the identification of dyonic instanton with the supertube inserted between D4 branes.Comment: 16 pages, 2 figures, JHEP styl

The Geometry of Dyonic Instantons in 5-dimensional Supergravity

We systematically construct and study smooth supersymmetric solutions in 5 dimensional N=1 Yang-Mills-Einstein supergravity. Our solution is based on the ADHM construction of (dyonic) multi-instantons in Yang-Mills theory, which extends to the gravity-coupled system. In a simple supergravity model obtained from N=2 theory, our solutions are regular ring-like configurations, which can also be interpreted as supertubes. By studying the SU(2) 2-instanton example in detail, we find that angular momentum is maximized, with fixed electric charge, for circular rings. This feature is qualitatively same as that of supertubes. Related to the existence of this upper bound of angular momentum, we also check the absence of closed timelike curves for the circular rings. Finally, in supergravity and gauge theory models with non-Abelian Chern-Simons terms, we point out that the solution in the symmetric phase carries electric charge which does not contribute to the energy. A possible explanation from the dynamics on the instanton moduli space is briefly discussed.Comment: 35 pages, no figure

Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences

We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and apply recent results for an infinite dimensional separable Banach space such as Lyapunov's convexity theorem and an exact Fatou's lemma to obtain the result.Comment: JEL Classification Numbers: C62, D51. Keywords: Separable Banach space, Saturated measure space, Price dependent preferences, Lyapunov's convexity theorem, Fatou's lemm

Quantum reservoir engineering through quadratic optomechanical interaction in the reversed dissipation regime

We explore the electromagnetic field coupled to a mechanical resonator via quadratic optomechanical interaction in the reversed dissipation regime where the mechanical damping rate is much larger than the cavity field dissipation rate. It is shown that in this regime, the cavity field effectively acquires an additional reservoir which is conditioned by the temperature of the mechanical bath as well as the mechanical damping rate. We analytically find the steady-state mean photon number and the critical temperature of the mechanical oscillator to cool or heat the coupled electromagnetic field. We also show that in the case of quadratic coupling, the temperature of the mechanical oscillator can be estimated in the quantum regime by observing the noise spectrum of the cavity field