In this section, we review some key results on the Wasserstein distance. Wpp Rπ(t,θi),Rρ(t,θi), (4) where the approximation comes from using Monte-Carlo integration by samplingθi uniformly in SD 1 [2]. M,M is the number of points used to approximate the integral. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. To do that, we first sortxms in an ascending order, such thatxi[m] xi[m+1], where i[m]istheindexofthesortedxms. Hamiltonian Monte Carlo (HMC)[24]isahighly-efficient MarkovChain Monte Carlo (MCMC) method used to generate samples from the posteriorw p(w|y).

The bottleneck introduced by the low-dimensional latent space is what characterizes the compression and representation learning capabilities ofautoencoders.

In this paper, we study the role of machine-learned predictions inofflineNP-hard problems. For offline problems, an algorithm has no information disadvantage compared to an optimal solution: thedisadvantage iscomputational.

The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision.

To this end, we propose a novel and effective approach, termed SOLOv2, following the principle of the SOLO method [32].

Byutilizingmodality dropout during pre-training, we demonstrate that a single fine-tuned model can achieve performance on par or better than the state-of-the-art modality-specific models.

Global information is essential for dense prediction problems, whose goal is to compute adiscrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressivemoving-average (ARMA) layer,anovelmodule with an adjustable receptive field controlled by the learnable autoregressive coefficients.