In this part, we state the orthogonal decomposition Property, motivate its importance with a pedagogical example, and finally prove Proposition 1, which enables the decomposition property in the context of HSIC attribution method. A.1 Orthogonal Decomposition Property Let x = {x1,..., xn}2Xn be a set of n univariate random input variables. For any subset A = {l1,...,l |A|} { 1,...,n}, we denote xA =( xl1,..., xl|A|) the vector of input variables with indices in A. Let y the random output variable defined by y = f(x), F the RKHS defined by the kernel kA: X|A|! R and G the RKHS defined by the kernel l: Y! R. In [11], the author shows that for any choice of kernel l, if we respect some constraints on the kernel kA, we can construct indices HSIC (xA,y) that satisfy the following decomposition property. The constraints on the kernel kA are detailed in the main document and in the last section of this appendix.

This paper presents a new efficient black-box attribution method built on HilbertSchmidt Independence Criterion (HSIC). Based on Reproducing Kernel Hilbert Spaces (RKHS), HSIC measures the dependence between regions of an input image and the output of a model using the kernel embedding of their distributions. It thus provides explanations enriched by RKHS representation capabilities. HSIC can be estimated very efficiently, significantly reducing the computational cost compared to other black-box attribution methods. Our experiments show that HSIC is up to 8 times faster than the previous best black-box attribution methods while being as faithful. Indeed, we improve or match the state-of-the-art of both black-box and white-box attribution methods for several fidelity metrics on Imagenet with various recent model architectures. Importantly, we show that these advances can be transposed to efficiently and faithfully explain object detection models such as YOLOv4. Finally, we extend the traditional attribution methods by proposing a new kernel enabling an ANOVA-like orthogonal decomposition of importance scores based on HSIC, allowing us to evaluate not only the importance of each image patch but also the importance of their pairwise interactions.

Because a diffusion model shares parameters for all diffusion steps, the noise schedule (parametrized by 1:T) is an important hyperparameter that determines how much weight we assign to each denoising problem. We find that standard noise schedules for continuous diffusions are not robust for text data. We hypothesize that the discrete nature of text and the rounding step make the model insensitive to noise near t =0 . Concretely, adding small amount of Gaussian noise to a word embedding is unlikely to change its nearest neighbor in the embedding space, making denoising an easy task near t =0 . To address this, we introduce a new sqrt noise schedule that is better suited for text, shown in Figure 5 defined by t =1 p t/T +s, where s is a small constant that corresponds to the starting noise level11. Compared to standard linear and cosine schedules, our sqrt schedule starts with a higher noise level and increase noise rapidly for the first 50 steps. Then sqrt slows down injecting noise to avoid spending much steps in the high-noise problems, which may be too difficult to solve well. The hyperparameters that are specific to Diffusion-LM include the number of diffusion steps, the architecture of the Diffusion-LM, the embedding dimension, and the noise schedule, . We set the diffusion steps to be 2000, the architecture to be BERT-base [7], and the sequence length to be 64. For the embedding dimensions, we select from d 2{ 16,64,128,256} and select d = 16for the E2E dataset and d = 128for ROCStories. For the noise schedule, we design the sqrt schedule (Appendix A) that is more robust to different parametrizations and embedding dimensions as shown in Appendix M. However, once we picked the x0-parametrization ( 4.2) the advantage of sqrt schedule is not salient. We train Diffusion-LMs using AdamW optimizer and a linearly decay learning rate starting at 1e-4, dropout of 0.1, batch size of 64, and the total number of training iteration is 200K for E2E dataset, and 800K for ROCStories dataset. Our Diffusion-LMs are trained on a single GPU: NVIDIARTXA5000, NVIDIAGeForce RTX 3090, or NVIDIAA100.

Recent years have witnessed an increasing use of coordinated accounts on social media, operated by misinformation campaigns to influence public opinion and manipulate social outcomes. Consequently, there is an urgent need to develop an effective methodology for coordinated group detection to combat the misinformation on social media. However, the sparsity of account activities on social media limits the performance of existing deep learning based coordination detectors as they can not exploit useful prior knowledge. Instead, the detectors incorporated with prior knowledge suffer from limited expressive power and poor performance. Therefore, in this paper we propose a coordination detection framework incorporating neural temporal point process with prior knowledge such as temporal logic or pre-defined filtering functions. Specifically, when modeling the observed data from social media with neural temporal point process, we jointly learn a Gibbs distribution of group assignment based on how consistent an assignment is to (1) the account embedding space and (2) the prior knowledge.