Occupancy prediction, aiming at predicting the occupancy status within voxelized 3D environment, is quickly gaining momentum within the autonomous driving community. Mainstream occupancy prediction works first discretize the 3D environment into voxels, then perform classification on such dense grids. However, inspection on sample data reveals that the vast majority of voxels is unoccupied.

In this section, we provide more details of model implementation and experiment setup for reproducibility of the experimental results. B.1 Details of Model Implementation B.1.1 Details of the Prediction Model The prediction model f is implemented with a graph neural network based model. Specifically, this prediction model includes the following components: Three layers of graph convolutional network (GCN) [34] with learnable node masks. The prediction model uses negative log likelihood loss. The representation dimension is set as 32. We use Adam optimizer, set the learning rate as 0.001, weight decay as 1e 5, the training epochs as 600, dropout rate as 0.1, and batch size as 500.

Counterfactual explanations promote explainability in machine learning models by answering the question "how should an input instance be perturbed to obtain a desired predicted label?". The comparison of this instance before and after perturbation can enhance human interpretation. Most existing studies on counterfactual explanations are limited in tabular data or image data. In this work, we study the problem of counterfactual explanation generation on graphs. A few studies have explored counterfactual explanations on graphs, but many challenges of this problem are still not well-addressed: 1) optimizing in the discrete and disorganized space of graphs; 2) generalizing on unseen graphs; and 3) maintaining the causality in the generated counterfactuals without prior knowledge of the causal model. To tackle these challenges, we propose a novel framework CLEAR which aims to generate counterfactual explanations on graphs for graph-level prediction models. Specifically, CLEAR leverages a graph variational autoencoder based mechanism to facilitate its optimization and generalization, and promotes causality by leveraging an auxiliary variable to better identify the underlying causal model.

Several benchmark multi-view datasets are adopted in our experiments. There are 948 news articles covering 416 different news stories. Among them, 169 news were reported in all three sources and each news was annotated with one of six topical labels: business, health, politics, entertainment, sport, and technology. MSRC is comprised of 240 images in eight classes. We select seven classes with each class containing 30 images.

In the supplementary, we first discuss the experimental details and hyperparameters in Section A. Next, we analyze the impact of different numbers of diffusion steps N on the replanning process in Section B, and further present the visualization in RLBench in Section C. Finally, we discuss how to compute the likelihood in Section D. In detail, our architecture comprises a temporal U-Net structure with six repeated residual networks. Each network consists of two temporal convolutions followed by GroupNorm [6], and a final Mish nonlinearity [4]. Additionally, We incorporate timestep and conditions embeddings, which are both 128-dimensional vectors produced by MLP, within each block. The probability ϵ of random actions is set to 0.03 in Stochastic Environments. The total number of diffusion steps, corresponding to the number of diffusion steps for Replan from scratch is set to 256 in Maze2D, 200 in Stochastic Environments, and 400 in RLBench.

We present a new approach for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularization on dual Kantorovich potentials. The main bottleneck of existing NOT solvers is associated with the procedure of finding a near-exact approximation of the conjugate operator (i.e., the c-transform), which is done either by optimizing over non-convex max-min objectives or by the computationally intensive fine-tuning of the initial approximated prediction. We resolve both issues by proposing a new theoretically justified loss in the form of expectile regularization which enforces binding conditions on the learning process of the dual potentials. Such a regularization provides the upper bound estimation over the distribution of possible conjugate potentials and makes the learning stable, completely eliminating the need for additional extensive fine-tuning. Proposed method, called Expectile-Regularized Neural Optimal Transport (ENOT), outperforms previous state-ofthe-art approaches in the established Wasserstein-2 benchmark tasks by a large margin (up to a 3-fold improvement in quality and up to a 10-fold improvement in runtime). Moreover, we showcase performance of ENOT for various cost functions in different tasks, such as image generation, demonstrating generalizability and robustness of the proposed algorithm.