Related papers: Learning Fricke signs from Maass form Coefficients

We introduce obfuscation testing, a novel methodology for validating whether large language models detect structural market patterns through causal reasoning rather than temporal association. Testing three dealer hedging constraint patterns…

We prove new explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures. In particular, we study $s$-sparse functions of the form $f(x) = \sum_{j=1}^s a_j e^{i \lambda_j x}$ for…

Despite the enormous success of artificial neural networks (ANNs) in many disciplines, the characterization of their computations and the origin of key properties such as generalization and robustness remain open questions. Recent…

Large Language Models (LLMs) have been observed to process non-human-readable text sequences, such as jailbreak prompts, often viewed as a bug for aligned LLMs. In this work, we present a systematic investigation challenging this…

In this paper, we propose a novel non-standard Local Fourier Analysis (LFA) variant for accurately predicting the multigrid convergence of problems with random and jumping coefficients. This LFA method is based on a specific basis of the…

We propose a method for estimating the Fisher score--the gradient of the log-likelihood with respect to model parameters--using score matching. By introducing a latent parameter model, we show that the Fisher score can be learned by…

Machine learning algorithms have recently been used to predict students' performance in an introductory physics class. The prediction model classified students as those likely to receive an A or B or students likely to receive a grade of C,…

Large language models are becoming the go-to solution for the ever-growing number of tasks. However, with growing capacity, models are prone to rely on spurious correlations stemming from biases and stereotypes present in the training data.…

A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for strongly-convex and smooth functions. Our analysis is much simpler in contrast to a similar…

Anomaly detection is important for industrial automation and part quality assurance, and while humans can easily detect anomalies in components given a few examples, designing a generic automated system that can perform at human or above…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…

The marginal likelihood, or Bayesian evidence, is a crucial quantity for Bayesian model comparison but its computation can be challenging for complex models, even in parameters space of moderate dimension. The learned harmonic mean…

Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm…

In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…

Despite their popularity, machine learning predictions are sensitive to potential unobserved predictors. This paper proposes a general algorithm that assesses how the omission of an unobserved variable with high explanatory power could…

We demonstrate that machine learning methods provide a powerful framework for modelling conditional asymmetric risk. Using a large cross-section of US stocks and a comprehensive set of firm characteristics, we show that allowing for…

The Fourier coefficients of a Maass form $\phi$ for SL$(n,\mathbb Z)$ are complex numbers $A_\phi(M)$, where $M=(m_1,m_2,\ldots,m_{n-1})$ and $m_1,m_2,\ldots ,m_{n-1}$ are nonzero integers. It is well known that coefficients of the form…