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We consider various asymptotic scaling limits $N\to\infty$ for the $2N$ complex eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble. These are known to be integrable, forming Pfaffian point…

This paper is concerned with the study of properties of the exact solution of the fundamental integrable $G_2$ vertex model. The model $R$-matrix and respective spin chain are presented in terms of the basis generators of the $G_2$ Lie…

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical…

Accurate uncertainty quantification is crucial for the safe deployment of machine learning models, and prior research has demonstrated improvements in the calibration of modern language models (LMs). We study in-context learning (ICL), a…

We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…

Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on…

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for…

The variational optimization of high-dimensional neural network models, such as those used in neural quantum states (NQS), presents a significant challenge in machine intelligence. Conventional first-order stochastic methods (e.g., Adam)…

Large language models (LLMs) have demonstrated emergent in-context learning (ICL) capabilities across a range of tasks, including zero-shot time-series forecasting. We show that text-trained foundation models can accurately extrapolate…

Quantum error correction allows inherently noisy quantum devices to emulate an ideal quantum computer with reasonable resource overhead. As a crucial component, decoding architectures have received significant attention recently. In this…

Imbalanced datasets are a fundamental issue in industrial condition monitoring and fault classification pipelines, causing classical machine learning models to overfit the majority classes while failing to learn the minority fault patterns.…

We study in-context learning (ICL) of linear regression in a deep linear self-attention model, characterizing how performance depends on various computational and statistical resources (width, depth, number of training steps, batch size and…

We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…

Large Language Models (LLMs) exhibit impressive performance across various tasks, but deploying them for inference poses challenges. Their high resource demands often necessitate complex, costly multi-GPU pipelines, or the use of smaller,…

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on…

Inferring the coupling of different atmospheric layers requires observing spectral lines sensitive to the atmospheric parameters, particularly the magnetic field vector, at various heights. The best way to tackle this goal is to perform…

Consider a linear quadratic regulator (LQR) problem being solved in a model-free manner using the policy gradient approach. If the gradient of the quadratic cost is being transmitted across a rate-limited channel, both the convergence and…

The relative smoothing rates of various gauge field smoothing algorithms are investigated on ${\cal O}(a^2)$-improved $\suthree$ Yang--Mills gauge field configurations. In particular, an ${\cal O}(a^2)$-improved version of APE smearing is…

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the…