The proof of the key lemma (Lemma 5), which establishes a connection between the margin operator and the robust margin operator, is presented in the main content. We still need to demonstrate that the properties in PAC-Bayes analysis hold for both the margin operator and the robust margin operator. The following proofs are adapted from the work of (Neyshabur et al., 2017b), with the steps being kept independent of the (robust) margin operator. We will begin by finishing the proofs of Lemma 6 and Lemma 7. Afterward, we will proceed to complete the proof of Theorem 1, which is our primary result. It is provided in (Neyshabur et al., 2017b), we Then we complete the proof of Lemma 6.1. By combining Lemma 6.1 and Lemma 5, we directly obtain Lemma 6.2.

Neural Information Processing Systems http://nips.cc/

Deep reinforcement learning (DRL) has led to a wide range of advances in sequential decision-making tasks. However, the complexity of neural network policies makes it difficult to understand and deploy with limited computational resources. Currently, employing compact symbolic expressions as symbolic policies is a promising strategy to obtain simple and interpretable policies. Previous symbolic policy methods usually involve complex training processes and pre-trained neural network policies, which are inefficient and limit the application of symbolic policies. In this paper, we propose an efficient gradient-based learning method named Efficient Symbolic Policy Learning (ESPL) that learns the symbolic policy from scratch in an end-to-end way.

However, it still lacks profound exploration targeted at 3DGS. Unlike its predecessor NeRF, 3DGS possesses two distinct features: 1) explicit 3D representation; and 2) real-time rendering speeds. These characteristics result in the 3DGS point cloud files being public and transparent, with each Gaussian point having a clear physical significance. Therefore, ensuring the security and fidelity of the original 3D scene while embedding information into the 3DGS point cloud files is an extremely challenging task. To solve the above-mentioned issue, we first propose a steganography framework for 3DGS, dubbed GS-Hider, which can embed 3D scenes and images into original GS point clouds in an invisible manner and accurately extract the hidden messages. Specifically, we design a coupled secured feature attribute to replace the original 3DGS's spherical harmonics coefficients and then use a scene decoder and a message decoder to disentangle the original RGB scene and the hidden message. Extensive experiments demonstrated that the proposed GS-Hider can effectively conceal multimodal messages without compromising rendering quality and possesses exceptional security, robustness, capacity, and flexibility. Our project is available at: https://xuanyuzhang21.

As black-box machine learning models grow in complexity and find applications in high-stakes scenarios, it is imperative to provide explanations for their predictions. Although Local Interpretable Model-agnostic Explanations (LIME) [22] is a widely adpoted method for understanding model behaviors, it is unstable with respect to random seeds [35, 24, 3] and exhibits low local fidelity (i.e., how well the explanation approximates the model's local behaviors) [21, 16]. Our study shows that this instability problem stems from small sample weights, leading to the dominance of regularization and slow convergence. Additionally, LIME's sampling neighborhood is non-local and biased towards the reference, resulting in poor local fidelity and sensitivity to reference choice.