Capturing and maintaining geometric interactions among different body parts is crucial for successful motion retargeting in skinned characters. Existing approaches often overlook body geometries or add a geometry correction stage after skeletal motion retargeting.

Free ChatGPT users will have to wait a while longer to be able to use its built-in image generation capability. OpenAI has just launched a feature that will allow users to generate images directly inside of ChatGPT, and it was supposed to roll out to all Plus, Pro, Team and Free users. But according to company CEO Sam Altman, it has been way more popular than OpenAI had expected even though they already had high expectations to begin with. As such, its rollout to the free tier is "unfortunately going to be delayed for a while." People have been posting ChatGPT's output all over social media.

Recent advances in 4D generation mainly focus on generating 4D content by distilling pre-trained text or single-view image-conditioned models. It is inconvenient for them to take advantage of various off-the-shelf 3D assets with multi-view attributes, and their results suffer from spatiotemporal inconsistency owing to the inherent ambiguity in the supervision signals.

Simulating large scenes with many rigid objects is crucial for a variety of applications, such as robotics, engineering, film and video games. Rigid interactions are notoriously hard to model: small changes to the initial state or the simulation parameters can lead to large changes in the final state. Recently, learned simulators based on graph networks (GNNs) were developed as an alternative to hand-designed simulators like MuJoCo [36] and PyBullet [13]. They are able to accurately capture dynamics of real objects directly from real-world observations. However, current state-of-the-art learned simulators operate on meshes and scale poorly to scenes with many objects or detailed shapes.

In this section, we provide further details for our data modeling. Our diffusion model generates full environment transitions i.e., a concatenation of states, actions, rewards, next states, and terminals where they are present. For the purposes of modeling, we normalize each continuous dimension (non-terminal) to have 0 mean and 1 std. We visualize the marginal distributions over the state, action, and reward dimensions on the standard halfcheetah medium-replay dataset in Figure 8 and observe that the synthetic samples accurately match the high-level statistics of the original dataset. We note the difficulties of appropriately modeling the terminal variable which is a binary variable compared to the rest of the dimensions which are continuous for the environments we investigate.

Gradient-based algorithms have shown great promise in solving large (two-player) zero-sum games. However, their success has been mostly confined to the lowprecision regime since the number of iterations grows polynomially in 1/ϵ, where ϵ > 0 is the duality gap. While it has been well-documented that linear convergence--an iteration complexity scaling as log(1/ϵ)--can be attained even with gradient-based algorithms, that comes at the cost of introducing a dependency on certain condition number-like quantities which can be exponentially large in the description of the game. To address this shortcoming, we examine the iteration complexity of several gradient-based algorithms in the celebrated framework of smoothed analysis, and we show that they have polynomial smoothed complexity, in that their number of iterations grows as a polynomial in the dimensions of the game, log(1/ϵ), and 1/σ, where σ measures the magnitude of the smoothing perturbation. Our result applies to optimistic gradient and extra-gradient descent/ascent, as well as a certain iterative variant of Nesterov's smoothing technique. From a technical standpoint, the proof proceeds by characterizing and performing a smoothed analysis of a certain error bound, the key ingredient driving linear convergence in zero-sum games. En route, our characterization also makes a natural connection between the convergence rate of such algorithms and perturbation-stability properties of the equilibrium, which is of interest beyond the model of smoothed complexity.