相关论文: Quantized Wasserstein Procrustes Alignment of Word…

Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

The Burrows-Wheeler Transform (BWT) is a string transformation technique widely used in areas such as bioinformatics and file compression. Many applications combine a run-length encoding (RLE) with the BWT in a way which preserves the…

In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…

Computing the empirical Wasserstein distance in the Wasserstein-distance-based independence test is an optimal transport (OT) problem with a special structure. This observation inspires us to study a special type of OT problem and propose a…

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves this problem…

Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…

Robustness studies of black-box models is recognized as a necessary task for numerical models based on structural equations and predictive models learned from data. These studies must assess the model's robustness to possible…

Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…

Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…

In this paper, we revisit math word problems~(MWPs) from the cross-lingual and multilingual perspective. We construct our MWP solvers over pretrained multilingual language models using sequence-to-sequence model with copy mechanism. We…

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and representational capacity. While existing ultra-low-bit…

This thesis examines self-attention training through the lens of Optimal Transport (OT) and develops an OT-based alternative for tabular classification. The study tracks intermediate projections of the self-attention layer during training…

Post-training quantization has emerged as the most widely used strategy for deploying large language models at low precision. Still, current methods show perplexity degradation at bit-widths less than or equal to 4, partly because…

The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…

We propose a novel Wasserstein method with a distillation mechanism, yielding joint learning of word embeddings and topics. The proposed method is based on the fact that the Euclidean distance between word embeddings may be employed as the…

We propose a quantum data fitting algorithm for non-sparse matrices, which is based on the Quantum Singular Value Estimation (QSVE) subroutine and a novel efficient method for recovering the signs of eigenvalues. Our algorithm generalizes…

We present a protocol for error characterization and its experimental implementation with 4 qubits in liquid state NMR. The method is designed to retrieve information about spatial correlations and scales as $O(n^w)$, where $w$ is the…

We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al,…

Due to the mismatch of statistical distributions of acoustic speech between training and testing sets, the performance of spoken language identification (SLID) could be drastically degraded. In this paper, we propose an unsupervised neural…