Related papers: Learning Fricke signs from Maass form Coefficients

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…

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Families of DFAs (FDFAs) are a computational model recognizing $\omega$-regular languages. They were introduced in the quest of finding a Myhill-Nerode theorem for $\omega$-regular languages, and obtaining learning algorithms. FDFAs have…

Bayesian inference allows the transparent communication of uncertainty in material flow analyses (MFAs), and a systematic update of uncertainty as new data become available. However, the method is undermined by the difficultly of defining…

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In the era of large language models (LLMs), detecting pretraining data has been increasingly important due to concerns about fair evaluation and ethical risks. Current methods differentiate members and non-members by designing scoring…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

As an essential characteristics of fractional calculus, the memory effect is served as one of key factors to deal with diverse practical issues, thus has been received extensive attention since it was born. By combining the fractional…

Machine learning algorithms have recently been used to classify students as those likely to receive an A or B or students likely to receive a C, D, or F in a physics class. The performance metrics used in that study become unreliable when…

Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention.…

In this paper, we study the vanishing order of rational $L$-functions from a data scientific perspective. Each $L$-function is represented in our data by finitely many Dirichlet coefficients, the normalisation of which depends on the…

Let $f$ be a normalized primitive Hecke eigen cusp form of even integral weight $k$ for the full modular group $SL(2,\mathbb{Z})$. For integers $j \geq 2$, let $\lambda_{sym^j f}(m)$ denote the $m$th Fourier coefficient of the $j$th…

Always-on spoken language interfaces, e.g. personal digital assistants, rely on a wake word to start processing spoken input. We present novel methods to train a hybrid DNN/HMM wake word detection system from partially labeled training…

Learning to predict masked tokens in a sequence has been shown to be a helpful pretraining objective for powerful language models such as PaLM2. After training, such masked language models (MLMs) can provide distributions of tokens in the…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase…

In this paper, we study non-trivial upper bounds for the sum $\sum \limits_{n \in S} |\lambda_f(n)|$ where $f$ is a normalized Maass eigencusp form for the full modular group, $\lambda_f(n)$ is the $n$th normalized Fourier coefficient of…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…