Related papers: Geometry-Aware Decoding with Wasserstein-Regulariz…

The quality of text generated by large language models depends critically on the decoding sampling strategy. While mainstream methods such as Top-$k$, Top-$p$, and Min-$p$ achieve a balance between diversity and accuracy through…

This paper presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast…

Many variants of Optimal Transport (OT) have been developed to address its heavy computation. Among them, notably, Sliced Wasserstein (SW) is widely used for application domains by projecting the OT problem onto one-dimensional lines, and…

Sampling-based decoding strategies have been widely adopted for Large Language Models (LLMs) in numerous applications, targeting a balance between diversity and quality via temperature tuning and tail truncation. Considering the strong…

Probabilistic language generators are theoretically modeled as discrete stochastic processes, yet standard decoding strategies (Top-k, Top-p) impose static truncation rules that fail to accommodate the dynamic information density of natural…

A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…

This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This…

We present a novel approach to selective model quantization that transcends the limitations of architecture-specific and size-dependent compression methods for Large Language Models (LLMs) using Entropy-Weighted Quantization (EWQ). By…

We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoising. Our framework represents each data point by a…

Alignment of large language models (LLMs) via SFT and RLHF/DPO typically ignores the global geometry of the representation space, relying instead on local token likelihoods or scalar scores. We view generation as tracing a semantic…

Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…

High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an…

Optimal Transport (OT) provides a useful geometric framework to estimate the permutation matrix under unsupervised cross-lingual word embedding (CLWE) models that pose the alignment task as a Wasserstein-Procrustes problem. However, linear…

Auto-encoders are among the most popular neural network architecture for dimension reduction. They are composed of two parts: the encoder which maps the model distribution to a latent manifold and the decoder which maps the latent manifold…

Decoding from large language models (LLMs) typically relies on fixed sampling hyperparameters (e.g., temperature, top-p), despite substantial variation in task difficulty and uncertainty across prompts and individual decoding steps. We…

This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…

Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally…

The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…