In this section, we briefly introduce the four kinds of emebddings consists the fusion embedding. The goal of position embedding module is to calibrate the position of each time point in the sequence so that the self-attention mechanism can recognize the relative positions between different time points in the input sequence. We design the token embedding module in order to enrich the features of each time point by fusion of other features from the adjacent time points within a certain interval. The role of spatial embedding is to locate and encode the spatial locations of different nodes, by which each node at different location possesses a unique spatial embedding. Thus, it enabling the model to identify nodes in different spatial and temporal planes after the dimensionality is compressed in the later computation.

We provide more details of training the teacher network in Section A, more experimental results on synthetic functions in Section B, and the hyperparameter settings for benchmark datasets in Section C. Here, we omit the iteration subscript t for simplicity. To solve Eq. (10), we obtain the hypergradient regarding to and backpropagate it to = {W 2 R As shown in Algorithm 1, we train the teacher network one step when each time it is called by an underperforming student model, where the step refers to one iteration on synthetic functions and one epoch of the validation set on benchmark datasets in the experiment. In Section 4.1, we have shown the experimental results of HPM on two population synthetic functions, i.e., the Branin and Hartmann6D functions. In the following, we will provide more details about synthetic functions and the implementation, as well as more results on the other two functions. We used the Branin and Hartmann6D functions in Section 4.1.

We thank all reviewers for their time and constructive comments. We first address concerns that were brought up by multiple reviewers. NMODE is more sample efficient than other methods (Appendix C.2, first paragraph), so for density estimation The quantifier for Prop 5.1 should be "for some"; this will be fixed. Note that for small dimensions (e.g. Riemannian metric, and are thus Riemannian.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples as well as the generated samples are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the Isolated Points Model is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width, so each generated point is influenced by at most one true point. Our model enables precise characterization of the conditions for convergence, both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

During training, we also apply a random translation augmentation to all the particle positions to artificially generate more training data. Next, we describe the KL variant of this model. Note that for the cosmology example in section 4.3, we use the L

Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is known to converge to a stationary point for specific classes of games, but current convergence analyses require a bounded variance assumption. SCO is used successfully for solving large-scale adversarial problems, but its convergence guarantees are limited to its deterministic variant. In this work, we introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO under this condition for solving a class of stochastic variational inequality problems that are potentially non-monotone. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size, and we propose insightful stepsize-switching rules to guarantee convergence to the exact solution. In addition, our convergence guarantees hold under the arbitrary sampling paradigm, and as such, we give insights into the complexity of minibatching.

For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? Our method proposes to learn efficient data structure for accurate prediction in large-output space. It helps existing large-scale retrieval systems used in various online applications to efficiently produce more accurate results. To the best of our knowledge, this poses no negative impacts on society.

Author Response for: "Inverting Gradients - How easy is it to break privacy in federated learning" General Comments: We thank all reviewers for their valuable feedback and interest in this attack. Some questions arose about the theoretical analysis for fully connected layers. Finally knowledge of the feature representation already enables attacks like Melis et al. This non-uniformity is a significant result for the privacy of gradient batches. Fig.4 of [35] looks better because the attack scenario there is easier.

We show the combined results in Figure 1.

Recently, AutoRegressive (AR) models for the whole image generation empowered by transformers have achieved comparable or even better performance compared to Generative Adversarial Networks (GANs). Unfortunately, directly applying such AR models to edit/change local image regions, may suffer from the problems of missing global information, slow inference speed, and information leakage of local guidance. To address these limitations, we propose a novel model - image Local Autoregressive Transformer (iLAT), to better facilitate the locally guided image synthesis. Our iLAT learns the novel local discrete representations, by the newly proposed local autoregressive (LA) transformer of the attention mask and convolution mechanism. Thus iLAT can efficiently synthesize the local image regions by key guidance information. Our iLAT is evaluated on various locally guided image syntheses, such as pose-guided person image synthesis and face editing. Both quantitative and qualitative results show the efficacy of our model.