A.1 Estimating Test Robust Accuracy Instead of estimating the robust generalization gap, one might expect the analysis on the relationship between test robust accuracy and the measures. In this regard, we investigate the correlation between the measures and the test robust accuracy 1 E(w; ϵ, D) on the test dataset D instead of the robust generalization gap g(w). Figure 1 illustrates the difference in total τ when the robust generalization gap and the test robust accuracy are used as the target variable for correlation analysis. Figure 6: Comparison of the total τ when the robust generalization g(w) (yellow) and the test robust accuracy 1 E(w; ϵ, D) (blue) are used as the target variables for correlation analysis. Although we observe some different behavior of measures, we find that estimating the test robust accuracy can be more challenging.

Developed by a team of scientists at Seoul National University and Gachon University in South Korea, PB, or the Particle-armored liquid roBot, is designed to behave the way cells do, and imitate biological forms and functions. The morphing bot can ooze around tiny pillars, skim across water to reach a dry surface without bursting, merge with another PB, and swallow a glass bead, all without compromising structural integrity. The robot is still in the research stages, but the promising results so far raise hopes that PB could potentially help advance drug delivery and even tumor cell destruction in the future.

Given a graph with textual attributes, we enable users to'chat with their graph': that is, to ask questions about the graph using a conversational interface. In response to a user's questions, our method provides textual replies and highlights the relevant parts of the graph. While existing works integrate large language models (LLMs) and graph neural networks (GNNs) in various ways, they mostly focus on either conventional graph tasks (such as node, edge, and graph classification), or on answering simple graph queries on small or synthetic graphs. In contrast, we develop a flexible question-answering framework targeting real-world textual graphs, applicable to multiple applications including scene graph understanding, common sense reasoning, and knowledge graph reasoning. Toward this goal, we first develop a Graph Question Answering (GraphQA) benchmark with data collected from different tasks. Then, we propose our G-Retriever method, introducing the first retrievalaugmented generation (RAG) approach for general textual graphs, which can be fine-tuned to enhance graph understanding via soft prompting. To resist hallucination and to allow for textual graphs that greatly exceed the LLM's context window size, G-Retriever performs RAG over a graph by formulating this task as a Prize-Collecting Steiner Tree optimization problem. Empirical evaluations show that our method outperforms baselines on textual graph tasks from multiple domains, scales well with larger graph sizes, and mitigates hallucination.

We compare our method with four competing methods in Table 1 of the main paper. Below, we provide more details about how we obtain the scores on Structured3D [6] for each method. Floor-SP [1] extracts geometry primitives from density maps using deep neural networks and optimizes the floorplan graph structure with room-wise coordinate descent. We use the evaluation score reported by [5]. MonteFloor [3] applies MCTS to select room proposals that maximize an objective function combining the density map predicted by a deep network and regularization terms on the room shapes.

Mutual information (MI) is a general measure of statistical dependence with widespread application across the sciences. However, estimating MI between multidimensional variables is challenging because the number of samples necessary to converge to an accurate estimate scales unfavorably with dimensionality. In practice, existing techniques can reliably estimate MI in up to tens of dimensions, but fail in higher dimensions, where sufficient sample sizes are infeasible. Here, we explore the idea that underlying low-dimensional structure in high-dimensional data can be exploited to faithfully approximate MI in high-dimensional settings with realistic sample sizes. We develop a method that we call latent MI (LMI) approximation, which applies a nonparametric MI estimator to low-dimensional representations learned by a simple, theoretically-motivated model architecture.

Cascading bandits is a natural and popular model that frames the task of learning to rank from Bernoulli click feedback in a bandit setting. For the case of unstructured rewards, we prove matching upper and lower bounds for the problem-independent (i.e., gap-free) regret, both of which strictly improve the best known. A key observation is that the hard instances of this problem are those with small mean rewards, i.e., the small click-through rates that are most relevant in practice. Based on this, and the fact that small mean implies small variance for Bernoullis, our key technical result shows that variance-aware confidence sets derived from the Bernstein and Chernoff bounds lead to optimal algorithms (up to log terms), whereas Hoeffding-based algorithms suffer order-wise suboptimal regret. This sharply contrasts with the standard (non-cascading) bandit setting, where the variance-aware algorithms only improve constants. In light of this and as an additional contribution, we propose a variance-aware algorithm for the structured case of linear rewards and show its regret strictly improves the state-of-the-art.

This paper focuses on improving the reconstruction of 2D floorplans from unstructured 3D point clouds. We identify opportunities for enhancement over the existing methods in three main areas: semantic quality, efficient representation, and local geometric details. To address these, we presents SLIBO-Net, an innovative approach to reconstructing 2D floorplans from unstructured 3D point clouds. We propose a novel transformer-based architecture that employs an efficient floorplan representation, providing improved room shape supervision and allowing for manageable token numbers. By incorporating geometric priors as a regularization mechanism and post-processing step, we enhance the capture of local geometric details. We also propose a scale-independent evaluation metric, correcting the discrepancy in error treatment between varying floorplan sizes. Our approach notably achieves a new state-of-the-art on the Structured3D dataset. The resultant floorplans exhibit enhanced semantic plausibility, substantially improving the overall quality and realism of the reconstructions.

The key challenge of multi-view indoor 3D object detection is to infer accurate geometry information from images for precise 3D detection. Previous method relies on NeRF for geometry reasoning. However, the geometry extracted from NeRF is generally inaccurate, which leads to sub-optimal detection performance. In this paper, we propose MVSDet which utilizes plane sweep for geometry-aware 3D object detection. To circumvent the requirement for a large number of depth planes for accurate depth prediction, we design a probabilistic sampling and soft weighting mechanism to decide the placement of pixel features on the 3D volume. We select multiple locations that score top in the probability volume for each pixel and use their probability score to indicate the confidence. We further apply recent pixel-aligned Gaussian Splatting to regularize depth prediction and improve detection performance with little computation overhead. Extensive experiments on ScanNet and ARKitScenes datasets are conducted to show the superiority of our model.

We propose a new algorithm for model-based distributional reinforcement learning (RL), and prove that it is minimax-optimal for approximating return distributions in the generative model regime (up to logarithmic factors), the first result of this kind for any distributional RL algorithm. Our analysis also provides new theoretical perspectives on categorical approaches to distributional RL, as well as introducing a new distributional Bellman equation, the stochastic categorical CDF Bellman equation, which we expect to be of independent interest. Finally, we provide an experimental study comparing a variety of model-based distributional RL algorithms, with several key takeaways for practitioners.