45 research outputs found

    Disturbance Grassmann Kernels for Subspace-Based Learning

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    In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1

    Locality Preserving Projections for Grassmann manifold

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    Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional Grassmann manifold always involve with significantly high computational cost, which seriously limits the applicability of learning on Grassmann manifold in more wide areas. In this research, we propose an unsupervised dimensionality reduction algorithm on Grassmann manifold based on the Locality Preserving Projections (LPP) criterion. LPP is a commonly used dimensionality reduction algorithm for vector-valued data, aiming to preserve local structure of data in the dimension-reduced space. The strategy is to construct a mapping from higher dimensional Grassmann manifold into the one in a relative low-dimensional with more discriminative capability. The proposed method can be optimized as a basic eigenvalue problem. The performance of our proposed method is assessed on several classification and clustering tasks and the experimental results show its clear advantages over other Grassmann based algorithms.Comment: Accepted by IJCAI 201

    IME: Integrating Multi-curvature Shared and Specific Embedding for Temporal Knowledge Graph Completion

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    Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with various geometric structures interwoven. However, existing Temporal Knowledge Graph Completion (TKGC) methods either model TKGs in a single space or neglect the heterogeneity of different curvature spaces, thus constraining their capacity to capture these intricate geometric structures. In this paper, we propose a novel Integrating Multi-curvature shared and specific Embedding (IME) model for TKGC tasks. Concretely, IME models TKGs into multi-curvature spaces, including hyperspherical, hyperbolic, and Euclidean spaces. Subsequently, IME incorporates two key properties, namely space-shared property and space-specific property. The space-shared property facilitates the learning of commonalities across different curvature spaces and alleviates the spatial gap caused by the heterogeneous nature of multi-curvature spaces, while the space-specific property captures characteristic features. Meanwhile, IME proposes an Adjustable Multi-curvature Pooling (AMP) approach to effectively retain important information. Furthermore, IME innovatively designs similarity, difference, and structure loss functions to attain the stated objective. Experimental results clearly demonstrate the superior performance of IME over existing state-of-the-art TKGC models

    Tight Analysis of Decrypton Failure Probability of Kyber in Reality

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    Kyber is a candidate in the third round of the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography (PQC) Standardization. However, because of the protocol\u27s independence assumption, the bound on the decapsulation failure probability resulting from the original analysis is not tight. In this work, we give a rigorous mathematical analysis of the actual failure probability calculation, and provides the Kyber security estimation in reality rather than only in a statistical sense. Our analysis does not make independency assumptions on errors, and is with respect to concrete public keys in reality. Through sample test and experiments, we also illustrate the difference between the actual failure probability and the result given in the proposal of Kyber. The experiments show that, for Kyber-512 and 768, the failure probability resulting from the original paper is relatively conservative, but for Kyber-1024, the failure probability of some public keys is worse than claimed. This failure probability calculation for concrete public keys can also guide the selection of public keys in the actual application scenarios. What\u27s more, we measure the gap between the upper bound of the failure probability and the actual failure probability, then give a tight estimate. Our work can also re-evaluate the traditional 1−δ1-\delta correctness in the literature, which will help re-evaluate some candidates\u27 security in NIST post-quantum cryptographic standardization

    In-context Learning for Automated Driving Scenarios

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    One of the key challenges in current Reinforcement Learning (RL)-based Automated Driving (AD) agents is achieving flexible, precise, and human-like behavior cost-effectively. This paper introduces an innovative approach utilizing Large Language Models (LLMs) to intuitively and effectively optimize RL reward functions in a human-centric way. We developed a framework where instructions and dynamic environment descriptions are input into the LLM. The LLM then utilizes this information to assist in generating rewards, thereby steering the behavior of RL agents towards patterns that more closely resemble human driving. The experimental results demonstrate that this approach not only makes RL agents more anthropomorphic but also reaches better performance. Additionally, various strategies for reward-proxy and reward-shaping are investigated, revealing the significant impact of prompt design on shaping an AD vehicle's behavior. These findings offer a promising direction for the development of more advanced and human-like automated driving systems. Our experimental data and source code can be found here.Comment: 7 pages, 6 figures, 35 reference
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