Related papers: Dimensionality Reduction has Quantifiable Imperfec…
Despite the remarkable progresses made in deep-learning based depth map super-resolution (DSR), how to tackle real-world degradation in low-resolution (LR) depth maps remains a major challenge. Existing DSR model is generally trained and…
While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
The lower the distortion of an estimator, the more the distribution of its outputs generally deviates from the distribution of the signals it attempts to estimate. This phenomenon, known as the perception-distortion tradeoff, has captured…
We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely…
Dense vector retrieval is an important building block of modern machine learning systems, underlying applications ranging from semantic search to retrieval-augmented generation and knowledge-intensive reasoning. Beyond retrieving items that…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier,…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
Inspired by the success of generative image models, recent work on learned image compression increasingly focuses on better probabilistic models of the natural image distribution, leading to excellent image quality. This, however, comes at…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized…
We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems. Our technique represents the natural gradient direction as a…
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy the critical convexity inequality of…
Large-scale multi-session LiDAR mapping is crucial for various applications but still faces significant challenges in data redundancy, memory consumption, and efficiency. This paper presents MS-Mapping, a novel multi-session LiDAR mapping…
Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local…