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Generative adversarial network (GAN) based vocoders have achieved significant attention in speech synthesis with high quality and fast inference speed. However, there still exist many noticeable spectral artifacts, resulting in the quality decline of synthesized speech. In this work, we adopt a novel GAN-based vocoder designed for few artifacts and high fidelity, called FA-GAN. To suppress the aliasing artifacts caused by non-ideal upsampling layers in high-frequency components, we introduce the anti-aliased twin deconvolution module in the generator. To alleviate blurring artifacts and enrich the reconstruction of spectral details, we propose a novel fine-grained multi-resolution real and imaginary loss to assist in the modeling of phase information. Experimental results reveal that FA-GAN outperforms the compared approaches in promoting audio quality and alleviating spectral artifacts, and exhibits superior performance when applied to unseen speaker scenarios.

Voice conversion (VC), as a voice style transfer technology, is becoming increasingly prevalent while raising serious concerns about its illegal use. Proactively tracing the origins of VC-generated speeches, i.e., speaker traceability, can prevent the misuse of VC, but unfortunately has not been extensively studied. In this paper, we are the first to investigate the speaker traceability for VC and propose a traceable VC framework named VoxTracer. Our VoxTracer is similar to but beyond the paradigm of audio watermarking. We first use unique speaker embedding to represent speaker identity. Then we design a VAE-Glow structure, in which the hiding process imperceptibly integrates the source speaker identity into the VC, and the tracing process accurately recovers the source speaker identity and even the source speech in spite of severe speech quality degradation. To address the speech mismatch between the hiding and tracing processes affected by different distortions, we also adopt an asynchronous training strategy to optimize the VAE-Glow models. The VoxTracer is versatile enough to be applied to arbitrary VC methods and popular audio coding standards. Extensive experiments demonstrate that the VoxTracer achieves not only high imperceptibility in hiding, but also nearly 100% tracing accuracy against various types of audio lossy compressions (AAC, MP3, Opus and SILK) with a broad range of bitrates (16 kbps - 128 kbps) even in a very short time duration (0.74s). Our speech demo is available at https://anonymous.4open.science/w/DEMOofVoxTracer., Comment: has been accepted by ACM MM 2023

The study of Frobenius endomorphism provides numerous information about its corresponding Abelian variety. To understand the action of the Frobenius endomorphism, one may be interested in its eigenvalues. According to Weil's third conjecture ("Riemann hypothesis over finite fields"), they all have absolute value less than or equal to $2g\sqrt{p}$. Thus, the eigenvalues of the Frobenius endomorphism all belong to the same compact subset of the complex plane, and are roots of the same monic polynomial with integer coefficients (the characteristic polynomial of the Frobenius endomorphism). Such complex numbers are called algebraic integers "totally" in a compact subset, which means algebraic integers all conjugates of which belong to a same given compact subset of the complex plane. The study of such algebraic integers helps to understand the eigenvalues of the Frobenius endomorphism, especially their distribution. In this paper, we will study the following question : under which conditions a compact subset of the complex plane has a finite or infinite number of algebraic integers "totally" in it ? The problem can be studied in light of the notion of capacity of a compact subset, which comes from potential theory. In this paper, we will present the theory of capacity and some theorems (Fekete, Szeg\"o, Robinson) derived from it that partially answer the question: in the case of a union of real segments, when the capacity is smaller (resp. larger) than 1, it contains a finite (resp. infinite) number of algebraic integers totally in it. For instance, for real line segments, the limit length is 4. This paper is written as part of a collective project conducted in \'Ecole Polytechnique (France). It is aimed towards undergraduate audience in mathematics, with basic knowledge in algebra, topology, analysis, and dwells into a modern topic of research., Comment: 76 pages. The paper is also available in French : arXiv:1908.07569.pdf