Related papers: Learning Fricke signs from Maass form Coefficients

Harmonic weak Maass forms of half-integral weight are the subject of many recent works. They are closely related to Ramanujan's mock theta functions, their theta lifts give rise to Arakelov Green functions, and their coefficients are often…

We present a Fourier-based machine learning technique that characterizes and detects facial emotions. The main challenging task in the development of machine learning (ML) models for classifying facial emotions is the detection of accurate…

We study the signs of the Fourier coefficients of a newform. Let $f$ be a normalized newform of weight $k$ for $\Gamma_0(N)$. Let $a_f(n)$ be the $n$th Fourier coefficient of $f$. For any fixed positive integer $m$, we study the…

While fine-tuning LLMs on NLI corpora improves their inferential performance, the underlying mechanisms driving this improvement remain largely opaque. In this work, we conduct a series of experiments to investigate what LLMs actually learn…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

Random forest (RF) regression model is used to predict the lattice constant, magnetic moment and formation energies of full Heusler alloys, half Heusler alloys, inverse Heusler alloys and quaternary Heusler alloys based on existing as well…

This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide…

Large Language Models (LLMs) have emerged as dominant foundational models in modern NLP. However, the understanding of their prediction processes and internal mechanisms, such as feed-forward networks (FFN) and multi-head self-attention…

Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…

Large Language Models (LLMs) can acquire unintended biases from seemingly benign training data even without explicit cues or malicious content. Existing methods struggle to detect such risks before fine-tuning, making post hoc evaluation…

We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…

In this article, we establish an average behaviour of the normalised Fourier coefficients of the Hecke eigenforms supported at the integers represented by any primitive integral positive definite binary quadratic form of fixed discriminant…

We introduce a novel statistic to probe the statistics of phases of Fourier modes in two-dimensions (2D) for weak lensing convergence field $\kappa$. This statistic contains completely independent information compared to that contained in…

Individual events at high-energy colliders like the LHC can be represented by a sequence of measurements, or 'point patterns' in an observable space. Starting from this data representation, we build a simple Bayesian probabilistic model for…

Machine learning models are vulnerable to membership inference attack, which can be used to determine whether a given sample appears in the training data. Most existing methods assume the attacker has full access to the features of the…

Word frequency is a strong predictor in most lexical processing tasks. Thus, any model of word recognition needs to account for how word frequency effects arise. The Discriminative Lexicon Model (DLM; Baayen et al., 2018a, 2019) models…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…