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This paper proposes an approach to the joint modeling of the short-time Fourier transform magnitude and phase spectrograms with a deep generative model. We assume that the magnitude follows a Gaussian distribution and the phase follows a…

Diffusion model, as a new generative model which is very popular in image generation and audio synthesis, is rarely used in speech enhancement. In this paper, we use the diffusion model as a module for stochastic refinement. We propose…

Large Language Models (LLMs) trained for average correctness often exhibit mode collapse, producing narrow decision behaviors on tasks where multiple responses may be reasonable. This limitation is particularly problematic in ordinal…

In this note we establish hypocoercivity and exponential relaxation to the Maxwellian for a class of kinetic Fokker-Planck-Alignment equations arising in the studies of collective behavior. Unlike previously known results in this direction…

Many advances in Natural Language Processing have been based upon more expressive models for how inputs interact with the context in which they occur. Recurrent networks, which have enjoyed a modicum of success, still lack the…

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability…

In deep learning research, many melody extraction models rely on redesigning neural network architectures to improve performance. In this paper, we propose an input feature modification and a training objective modification based on two…

We have studied the synchronization in finite $N$-unit FitzHugh-Nagumo neuron ensembles subjected to additive and multiplicative noises, by using the augmented moment method (AMM) which is reformulated with the use of the Fokker-Planck…

Recent developments in speech synthesis have produced systems capable of outcome intelligible speech, but now researchers strive to create models that more accurately mimic human voices. One such development is the incorporation of multiple…

This paper proposes a hierarchical generative model with a multi-grained latent variable to synthesize expressive speech. In recent years, fine-grained latent variables are introduced into the text-to-speech synthesis that enable the fine…

We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and…

In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…

Recently, neural approaches to coherence modeling have achieved state-of-the-art results in several evaluation tasks. However, we show that most of these models often fail on harder tasks with more realistic application scenarios. In…

A simple model of language evolution, proposed in \cite{K_N}, is characterized by a pay-off in communicative function, and by an error in learning, that measures the accuracy in language acquisition. In the mean field approximation, this…

Many classical examples of models of self-organized dynamics, including the Cucker-Smale, Motsch-Tadmor, multi-species, and several others, include an alignment force that is based upon density-weighted averaging protocol. Those protocols…

Recent research has revealed that neural language models at scale suffer from poor temporal generalization capability, i.e., the language model pre-trained on static data from past years performs worse over time on emerging data. Existing…

We present a method for audio denoising that combines processing done in both the time domain and the time-frequency domain. Given a noisy audio clip, the method trains a deep neural network to fit this signal. Since the fitting is only…

The recent emergence of machine-learning based generative models for speech suggests a significant reduction in bit rate for speech codecs is possible. However, the performance of generative models deteriorates significantly with the…

This work is concerned with stochastic consensus conditions of multi-agent systems with both time-delays and measurement noises. For the case of additive noises, we develop some necessary conditions and sufficient conditions for stochastic…

Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…