KV cache stores key and value states from previous tokens to avoid re-computation, yet it demands substantial storage space, especially for long sequences. Adaptive KV cache compression seeks to discern the saliency of tokens, preserving vital information while aggressively compressing those of less importance.

In multi-agent coverage control problems, agents navigate their environment to reach locations that maximize the coverage of some density. In practice, the density is rarely known a priori, further complicating the original NP-hard problem.

Latent Bayesian optimization (LBO) approaches have successfully adopted Bayesian optimization over a continuous latent space by employing an encoderdecoder architecture to address the challenge of optimization in a high dimensional or discrete input space. LBO learns a surrogate model to approximate the black-box objective function in the latent space. However, we observed that most LBO methods suffer from the'misalignment problem', which is induced by the reconstruction error of the encoder-decoder architecture. It hinders learning an accurate surrogate model and generating high-quality solutions. In addition, several trust region-based LBO methods select the anchor, the center of the trust region, based solely on the objective function value without considering the trust region's potential to enhance the optimization process.

We give a faster algorithm for computing an approximate John ellipsoid around points in dimensions. The best known prior algorithms are based on repeatedly computing the leverage scores of the points and reweighting them by these scores [CCLY19]. We show that this algorithm can be substantially sped up by delaying the computation of high accuracy leverage scores by using sampling, and then later computing multiple batches of high accuracy leverage scores via fast rectangular matrix multiplication. We also give low-space streaming algorithms for John ellipsoids using similar ideas.

In this paper, we propose a sequence-to-set method that can transform any sequence generative model based on maximum likelihood to a set generative model where we can evaluate the utility/probability of any set. An efficient importance sampling algorithm is devised to tackle the computational challenge of learning our sequenceto-set model. We present GRU2Set, which is an instance of our sequence-to-set method and employs the famous GRU model as the sequence generative model. To further obtain permutation invariant representation of sets, we devise the SetNN model which is also an instance of the sequence-to-set model. A direct application of our models is to learn an order/set distribution from a collection of e-commerce orders, which is an essential step in many important operational decisions such as inventory arrangement for fast delivery.

In this paper, we propose a sequence-to-set method that can transform any sequence generative model based on maximum likelihood to a set generative model where we can evaluate the utility/probability of any set. An efficient importance sampling algorithm is devised to tackle the computational challenge of learning our sequenceto-set model. We present GRU2Set, which is an instance of our sequence-to-set method and employs the famous GRU model as the sequence generative model. To further obtain permutation invariant representation of sets, we devise the SetNN model which is also an instance of the sequence-to-set model. A direct application of our models is to learn an order/set distribution from a collection of e-commerce orders, which is an essential step in many important operational decisions such as inventory arrangement for fast delivery.

Graph Neural Networks (GNNs), a type of neural network that can learn from graph-structured data through neighborhood information aggregation, have shown superior performance in various downstream tasks. However, as the number of layers increases, node representations become indistinguishable, which is known as over-smoothing. To address this issue, many residual methods have emerged. In this paper, we focus on the over-smoothing issue and related residual methods. Firstly, we revisit over-smoothing from the perspective of overlapping neighborhood subgraphs, and based on this, we explain how residual methods can alleviate over-smoothing by integrating multiple orders neighborhood subgraphs to avoid the indistinguishability of the single high-order neighborhood subgraphs. Additionally, we reveal the drawbacks of previous residual methods, such as the lack of node adaptability and severe loss of high-order neighborhood subgraph information, and propose a Posterior-Sampling-based, Node-Adaptive Residual module (PSNR). We theoretically demonstrate that PSNR can alleviate the drawbacks of previous residual methods. Furthermore, extensive experiments verify the superiority of the PSNR module in fully observed node classification and missing feature scenarios.

Self-supervised learning aims to learn good representations with unlabeled data. Recent works have shown that larger models benefit more from self-supervised learning than smaller models. As a result, the gap between supervised and selfsupervised learning has been greatly reduced for larger models. In this work, instead of designing a new pseudo task for self-supervised learning, we develop a model compression method to compress an already learned, deep self-supervised model (teacher) to a smaller one (student). We train the student model so that it mimics the relative similarity between the datapoints in the teacher's embedding space. For AlexNet, our method outperforms all previous methods including the fully supervised model on ImageNet linear evaluation (59.0%

Although 3D point cloud recognition has achieved substantial progress on standard benchmarks, the typical models are vulnerable to point cloud corruptions, leading to security threats in real-world applications. To improve the corruption robustness, various data augmentation methods have been studied, but they are mainly limited to the spatial domain. As the point cloud has low information density and significant spatial redundancy, it is challenging to analyze the effects of corruptions. In this paper, we focus on the frequency domain to observe the underlying structure of point clouds and their corruptions. Through graph Fourier transform (GFT), we observe a correlation between the corruption robustness of point cloud recognition models and their sensitivity to different frequency bands, which is measured by the GFT spectrum of the model's Jacobian matrix. To reduce the sensitivity and improve the corruption robustness, we propose Frequency Adversarial Training (FAT) that adopts frequency-domain adversarial examples as data augmentation to train robust point cloud recognition models against corruptions. Theoretically, we provide a guarantee of FAT on its out-of-distribution generalization performance. Empirically, we conducted extensive experiments with various network architectures to validate the effectiveness of FAT, which achieves the new state-of-the-art results.

A.1 Proof of Proposition 1 Proposition 1 in the paper is for the case that p Given the marginal distributions p and q, we say that the transport plan π Π(p, q) preserves the matching of a keypoint pair with index (i, j) K, if π satisfies one of the following conditions: 1. The left part of Fig. A-1 illustrates these conditions. Then, the transport plan π = M π with π Π(p, q; M) preserves the matching of keypoint pairs with index in K. For the other points (corresponding to the last three cases in Eq. (A-1)), we set M Proof: For any (i, j) K, we next prove that π preserves the matching of keypoint pair (i, j). This means that π preserves the matching of keypoint pairs with index in K. A.2 Linear Programming for Solving KPG-RL We cast the matrix G (resp.