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Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
Low dimensional embeddings that capture the main variations of interest in collections of data are important for many applications. One way to construct these embeddings is to acquire estimates of similarity from the crowd. However,…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Recent advancements in language representation learning primarily emphasize language modeling for deriving meaningful representations, often neglecting style-specific considerations. This study addresses this gap by creating generic,…
In this paper we sum up our works on multiscale programs, mainly simulations. We first start with describing what multiscaling is about, how it helps perceiving signal from a background noise in a ?ow of data for example, for a direct…
Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…
Machine learning models with inputs in a Euclidean space $\mathbb{R}^d$, when implemented on digital computers, generalize, and their generalization gap converges to $0$ at a rate of $c/N^{1/2}$ concerning the sample size $N$. However, the…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
Representation learning is a widely adopted framework for learning in data-scarce environments, aiming to extract common features from related tasks. While centralized approaches have been extensively studied, decentralized methods remain…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version. To this end, we consider respectively, two and three quartic oscillators as the unperturbed system, and…
This work combines algorithms based on word embeddings, dimensionality reduction, and clustering. The objective is to obtain topics from a set of unclassified texts. The algorithm to obtain the word embeddings is the BERT model, a neural…
Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction…
Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…
The rise of music large language models (LLMs) demands robust methods of evaluating output quality, especially in distinguishing high-quality compositions from "garbage music". Curiously, we observe that the standard cross-entropy loss -- a…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size…