Efficiently sampling from un-normalized target distributions is a fundamental problem in scientific computing and machine learning. Traditional approaches such as Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples from such distributions but suffer from computational inefficiency, particularly when dealing with high-dimensional targets, as they require numerous iterations to generate a batch of samples. In this paper, we introduce an efficient and scalable neural implicit sampler that overcomes these limitations. The implicit sampler can generate large batches of samples with low computational costs by leveraging a neural transformation that directly maps easily sampled latent vectors to target samples without the need for iterative procedures. To train the neural implicit samplers, we introduce two novel methods: the KL training method and the Fisher training method.

We propose embodied scene-aware human pose estimation where we estimate 3D poses based on a simulated agent's proprioception and scene awareness, along with external third-person observations. Unlike prior methods that often resort to multistage optimization, non-causal inference, and complex contact modeling to estimate human pose and human scene interactions, our method is one-stage, causal, and recovers global 3D human poses in a simulated environment. Since 2D third-person observations are coupled with the camera pose, we propose to disentangle the camera pose and use a multi-step projection gradient defined in the global coordinate frame as the movement cue for our embodied agent. Leveraging a physics simulation and prescanned scenes (e.g., 3D mesh), we simulate our agent in everyday environments (library, office, bedroom, etc.) and equip our agent with environmental sensors to intelligently navigate and interact with the geometries of the scene. Our method also relies only on 2D keypoints and can be trained on synthetic datasets derived from popular human motion databases. To evaluate, we use the popular H36M and PROX datasets and achieve high quality pose estimation on the challenging PROX dataset without ever using PROX motion sequences for training. Code and videos are available on the project page.

The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured outputs like sets, images, language, etc.

Meta-learning approaches enable machine learning systems to adapt to new tasks given few examples by leveraging knowledge from related tasks. However, a large number of meta-training tasks are still required for generalization to unseen tasks during meta-testing, which introduces a critical bottleneck for real-world problems that come with only few tasks, due to various reasons including the difficulty and cost of constructing tasks. Recently, several task augmentation methods have been proposed to tackle this issue using domain-specific knowledge to design augmentation techniques to densify the meta-training task distribution.

We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points without replacement leads to faster convergence compared to sampling with replacement. For the smooth and strongly convex-strongly concave setting, we consider gradient descent ascent and the proximal point method, and present a unified analysis of two popular without-replacement sampling strategies, namely Random Reshuffling (RR), which shuffles the data every epoch, and Single Shuffling or Shuffle Once (SO), which shuffles only at the beginning. We obtain tight convergence rates for RR and SO and demonstrate that these strategies lead to faster convergence than uniform sampling. Moving beyond convexity, we obtain similar results for smooth nonconvex-nonconcave objectives satisfying a two-sided Polyak-Łojasiewicz inequality. Finally, we demonstrate that our techniques are general enough to analyze the effect of data-ordering attacks, where an adversary manipulates the order in which data points are supplied to the optimizer. Our analysis also recovers tight rates for the incremental gradient method, where the data points are not shuffled at all.