Which allows to conclude that the sigmoid corresponds to the Heaviside function perturbed with a logistic noise. As introduced in the paper, control variates methods can be used to reduce the noise of the Monte-Carlo estimators of the Jacobian of a perturbed renderer, without inducing any extra-computation. Proposition 5. Jacobian of perturbed renderers can be written as: J We adapt the previous proof to the case of a Cauchy distribution for the noise. Z 1 (67) remains valid. Z 1 (73) 17 Figure 9: Pose optimization with an initial guess uniformly sampled on the rotation space.

All coordinates will be modeled by independent Gumbel distributions, and thus it is enough to calculate the expected side-length of a box as the expected volume will simply be the product of the expected side-lengths. To properly restrict the Gumbel distributions to[0,1], we can either formcensoredortruncated distributions. Thetruncateddistribution,ontheotherhand,multipliesthe densities with the indicator function for[0,1]and renormalizes them to integrate to 1. The higher the temperature of the boxes, the more the true integral will tend to provide larger conditional probabilities. Monte Carlo experiments support this conclusion.

Retrieval-augmented generation (RAG) mitigates the hallucination problem in large language models (LLMs) and has proven effective for personalized usages. However, delivering private retrieved documents directly to LLMs introduces vulnerability to membership inference attacks (MIAs), which try to determine whether the target data point exists in the private external database or not. Based on the insight that MIA queries typically exhibit high similarity to only one target document, we introduce a novel similarity-based MIA detection framework designed for the RAG system. With the proposed method, we show that a simple detect-and-hide strategy can successfully obfuscate attackers, maintain data utility, and remain system-agnostic against MIA. We experimentally prove its detection and defense against various state-of-the-art MIA methods and its adaptability to existing RAG systems.

Small subsets of data with disproportionate influence on model outcomes can have dramatic impacts on conclusions, with a few data points sometimes overturning key findings. While recent work has developed methods to identify these most influential sets, no formal theory exists to determine when their influence reflects genuine problems rather than natural sampling variation. We address this gap by developing a principled framework for assessing the statistical significance of most influential sets. Our theoretical results characterize the extreme value distributions of maximal influence and enable rigorous hypothesis tests for excessive influence, replacing current ad-hoc sensitivity checks. We demonstrate the practical value of our approach through applications across economics, biology, and machine learning benchmarks.

The actor losses used in DoubleGum, SAC, and DDPG are all derived from the same principle. SAC (Haarnoja et al., 2018a,b) has a policy with learned variance and state-independent Section B.1 shows this for the actor losses of DoubleGum, SAC, and DDPG. We now relate the critic losses to each other, starting from the most general case, DoubleGum. The SAC noise model is derived from Equation 16 in three ways. In continuous control, Fujimoto et al. (2018) introduced Twin Networks, a method that improved Follow-up work selects a quantile estimate from an ensemble (Kuznetsov et al., 2020; Chen et al., 2021; Ball et al., 2023), which we demonstrate is Moskovitz et al. (2021) and Ball et al. (2023) showed that the appropriate Garg et al. (2023) present a method of estimating its value using Gumbel regression.