Proposition 3. If F is a discrete O(d) bundle over a connected graph and r:= max Proposition 4. If F is a discrete O(d) bundle over a connected graph and x H Proposition 5. Let F be a discrete O(d) bundle over a connected graph G with n nodes and let ||(P If ϵ = 0 there is nothing to prove. Assume that ϵ > 0. By Proposition 4 we derive that the harmonic space is trivial and hence λ In particular, we can assume this cycle to be non-degenerate, otherwise if there existed a non-trivial degenerate loop contained in γ that does not fix x we could consider this loop instead of γ for our argument. Let F be a discrete O(d) bundle over a connected graph G. Then dim(H We first note that the argument below extends to weighted O(d)-bundles as well. We prove only one direction. Let W be a choice of valid weight matrix for the graph G. We state the following Lemma without proof based on Theorem 3.1 in Hansen and Ghrist [35].

If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions.

In this supplementary material, we present more few-shot generation results evaluated extensively with different artistic domains where there are only a few examples available in practical. The goal is to illustrate the effectiveness of the proposed method in generating diverse high-quality results without being over-fitted to the few given examples. Figure 1 shows the generations of source and target domain by feeding the same latent code into the source and adapted model. It clearly tells that while the adaptation renders new appearance of target domain, other attributes such as the pose, glass and hairstyle, are well inherited and preserved from the source domain. For each target domain, we only use 10 examples for the adaptation and present 100 new results.

See all the highlights from Google's annual 2025 Developers Conference in Mountain View, California. Check out the latest updates from Android XR to Gemini Live, and more. Topics Android Artificial Intelligence Google Google Gemini Latest Videos Everything Announced at AMD's 2025 Computex Keynote in 19 Minutes Watch highlights from AMD's Computex press conference. 1 hour ago By Mashable Video'Caught Stealing' trailer sees Zoë Kravitz and Austin Butler's cat-sitting gone awry Darren Aronofsky's swaggering new film looks like a rollicking time. Loading... Subscribe These newsletters may contain advertising, deals, or affiliate links. By clicking Subscribe, you confirm you are 16 and agree to ourTerms of Use and Privacy Policy.

Topics Android Artificial Intelligence Google Google Gemini Latest Videos Everything Announced at AMD's 2025 Computex Keynote in 19 Minutes Watch highlights from AMD's Computex press conference. 1 hour ago By Mashable Video'Caught Stealing' trailer sees Zoë Kravitz and Austin Butler's cat-sitting gone awry Darren Aronofsky's swaggering new film looks like a rollicking time. Loading... Subscribe These newsletters may contain advertising, deals, or affiliate links. By clicking Subscribe, you confirm you are 16 and agree to ourTerms of Use and Privacy Policy. See you at your inbox! Mashable is a registered trademark of Ziff Davis and may not be used by third parties without express written permission.

You've probably heard that statistic that every search on ChatGPT uses the equivalent of a bottle of water. And while that's technically true, it misses some of the nuance. The MIT Technology Review dropped a massive report that reveals how the artificial intelligence industry uses energy -- and exactly how much energy it costs to use a service like ChatGPT. The report determined that the energy cost of large-language models like ChatGPT cost anywhere from 114 joules per response to 6,706 joules per response -- that's the difference between running a microwave for one-tenth of a second to running a microwave for eight seconds. The lower-energy models, according to the report, use less energy because they uses fewer parameters, which also means the answers tend to be less accurate.

This supplementary material is organized as follows: In Section A, we discuss additional priors that were not presented in the main paper, but which are in principle compatible with our framework, and we provide more details about potential games. In Section B, we provide implementation details that are useful to reproduce the results of our paper (note that the code is also provided). In Section C, we present additional quantitative results and additional results regarding inference speed of our models that were not included in the main paper for space limitation reasons. Finally, in Section D, we present additional qualitative results (which require zooming on a computer screen). A.1 Additional Priors Our framework makes it possible to handle models of the form: In the main paper, several regularization functions have been considered, including the total variation, variance reduction, or non-local group regularization penalties.

However, there are only a few datasets that include concept-level meta-labels and most of these meta-labels are relevant for natural images that do not require domain expertise. Previous densely annotated datasets in medicine focused on meta-labels that are relevant to a single disease such as osteoarthritis or melanoma. In dermatology, skin disease is described using an established clinical lexicon that allows clinicians to describe physical exam findings to one another. To provide a medical dataset densely annotated by domain experts with annotations useful across multiple disease processes, we developed SkinCon: a skin disease dataset densely annotated by dermatologists. SkinCon includes 3230 images from the Fitzpatrick 17k skin disease dataset densely annotated with 48 clinical concepts, 22 of which have at least 50 images representing the concept. The concepts used were chosen by two dermatologists considering the clinical descriptor terms used to describe skin lesions.

We thank the reviewers for their feedback. Our paper will be updated to reflect the responses below. E.g., for ResNet18 on ImageNet at 50% sparsity DSG suffers an accuracy loss of 4.6%. Reviewer 2: (1) "Drastic drop due to sparse activations in forward pass": In Figure 1 we isolate the Notably, this means we use the full activation for the backward pass. Thus, STR, CS, GMP only update the active parameters. L1 response of channels is computed.