Stochastic gradient descent (SGD) is a prevalent optimization technique for largescale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck in the distributed setting. Gradient compression methods can be used to alleviate this problem, and a recent line of work shows that SGD augmented with gradient compression converges to an ε-first-order stationary point. In this paper we extend these results to convergence to an ε-second-order stationary point (ε-SOSP), which is to the best of our knowledge the first result of this type. In addition, we show that, when the stochastic gradient is not Lipschitz, compressed SGD with RANDOMK compressor converges to an ε-SOSP with the same number of iterations as uncompressed SGD [25], while improving the total communication by a factor of Θ( dε 3/4), where dis the dimension of the optimization problem. We present additional results for the cases when the compressor is arbitrary and when the stochastic gradient is Lipschitz.

This appendix is organized as follows: Section A: the detailed dataset statistics and a summary of model properties w.r.t. We present the details on each dataset in Table 4. Under the online continual setting, the tasks are observed following a fixed order and the data from each task is observed as a (one-pass) stream of samples. The batch size is 10 for all the datasets. We do not randomize the order of tasks or optimize the task orders.

Text-to-Image diffusion models have made tremendous progress over the past two years, enabling the generation of highly realistic images based on open-domain text descriptions. However, despite their success, text descriptions often struggle to adequately convey detailed controls, even when composed of long and complex texts. Moreover, recent studies have also shown that these models face challenges in understanding such complex texts and generating the corresponding images. Therefore, there is a growing need to enable more control modes beyond text description. In this paper, we introduce Uni-ControlNet, a unified framework that allows for the simultaneous utilization of different local controls (e.g., edge maps, depth map, segmentation masks) and global controls (e.g., CLIP image embeddings) in a flexible and composable manner within one single model. Unlike existing methods, Uni-ControlNet only requires the fine-tuning of two additional adapters upon frozen pre-trained text-to-image diffusion models, eliminating the huge cost of training from scratch. Moreover, thanks to some dedicated adapter designs, Uni-ControlNet only necessitates a constant number (i.e., 2) of adapters, regardless of the number of local or global controls used. This not only reduces the fine-tuning costs and model size, making it more suitable for real-world deployment, but also facilitate composability of different conditions. Through both quantitative and qualitative comparisons, Uni-ControlNet demonstrates its superiority over existing methods in terms of controllability, generation quality and composability.

When Pam Cronrath's husband Bill died last year, after nearly 60 years of marriage, she knew what she wanted to do, but not exactly how. I promised him a super wake, she told the BBC. What she didn't expect was that keeping the promise would lead her into the world of holograms, technology more commonly associated with celebrities than memorial services in rural America. A self-confessed tech enthusiast, she says her outlook was shaped by a career that stretched back to the early days of the internet. Several years ago, while speaking at a medical conference, she watched a doctor appear as a full-body hologram broadcast live across the United States.