Triplet sampling was implemented based on the temporal vicinity of samples. Since the input is sequential, for each sample (called anchor) in the sequence, we consider a small and a large temporal window with predefined fixed widths. These two temporal windows are centered at the timestamp of the anchor. Any sample inside the smaller temporal window can be considered as a positive sample and any sample outside the small window but inside the large window can be considered as a negative sample. The widths of the temporal windows roughly depend on the speed of the observer in the environment.

Vision-language pre-training methods, e.g., CLIP, demonstrate an impressive zero-shot performance on visual categorizations with the class proxy from the text embedding of the class name.

Remarkably, we find that this causality condition provides a natural framework to parameterize the cost function that is learned by the discriminator as arobust (worst-case) distance, and anideal mechanism for learning time dependent data distributions.

This paper introduces anew onlineestimator ofentropy-regularized OTdistances between twosucharbitrary distributions.

The Sinkhorn distance, a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, rendering them prohibitively expensive on massive data sets. In this work, we show that this challenge is surprisingly easy to circumvent: combining two simple techniques--the Nyström method and Sinkhorn scaling--provably yields an accurate approximation of the Sinkhorn distance with significantly lower time and memory requirements than other approaches. We prove our results via new, explicit analyses of the Nyström method and of the stability properties of Sinkhorn scaling. We validate our claims experimentally by showing that our approach easily computes Sinkhorn distances on data sets hundreds of times larger than can be handled by other techniques.

Recently, there has been significant progress in learning-based diffusion samplers, which aim to sample from a given unnormalized density. Many of these approaches formulate the sampling task as a stochastic optimal control (SOC) problem using a canonical uninformative reference process, which limits their ability to efficiently guide trajectories toward the target distribution. In this work, we propose the Non-Equilibrium Annealed Adjoint Sampler (NAAS), a novel SOC-based diffusion framework that employs annealed reference dynamics as a non-stationary base SDE. This annealing structure provides a natural progression toward the target distribution and generates informative reference trajectories, thereby enhancing the stability and efficiency of learning the control. Owing to our SOC formulation, our framework can incorporate a variety of SOC solvers, thereby offering high flexibility in algorithmic design. As one instantiation, we employ a lean adjoint system inspired by adjoint matching, enabling efficient and scalable training. We demonstrate the effectiveness of NAAS across a range of tasks, including sampling from classical energy landscapes and molecular Boltzmann distributions.

Point cloud registration is a crucial task in 3D computer vision that involves aligning a pair of partially overlapped point clouds to create a unified scene representation.