Section 2 provides the implementation details of Rubik's cube convolution within the image restoration Section 3 provides the evaluation of our proposed Rubik's cube convolution on the classification task. Section 4 provides more quantitative and qualitative results. Specifically, the input feature is separated into five groups, where the last four are shifted into four direction and the first is unchanged. When a up-shifting group interacts the next downshifting group, the (i, j) pixel will interweave with its neighboring pixel, (i + p, j), where p denotes the number of shifted pixels. Therefore, with the combined action of the shifting and interaction operation, the receptive field will be expanded along the downward direction.

One significant limitation of the approach presented in this paper, particularly in the context of Variational Quantum Eigensolvers (VQEs), relates to the scalability of Gaussian Processes (GPs). When a large number of points is added to the GP training set through additional observations, the computational scalability becomes a challenge, especially in scenarios involving a large number of observations. However, we consider a potential solution to address this issue by imposing a fixed limit on the training sample size. This approach involves removing previously observed points and replacing them with newer ones. We hypothesize that by leveraging the information from the CoRe, the newly added points would contain significantly more valuable information, making previous observations less informative. Consequently, removing those points from the training set would mitigate the inherent scalability problem associated with GPs. Exploring this idea further is an avenue for future research.

"Distributed nonconvex optimization over time-varying networks". "Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling". In: WIT Transactions on The Built Environment 37 (1998). "Federated Optimization:Distributed Optimization Beyond the Datacenter". "Fast linear iterations for distributed averaging". "Divergence measures based on the Shannon entropy". "Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs". "Distributed Subgradient Methods for Multi-Agent Optimization".

This criterion leads to pick for all our topologies, but "AWS

Large-scale, pre-trained neural networks have demonstrated strong capabilities in various tasks, including zero-shot image segmentation. To identify concrete objects in complex scenes, humans instinctively rely on deictic descriptions in natural language, i.e., referring to something depending on the context, such as "The object that is on the desk and behind the cup". However, deep learning approaches cannot reliably interpret such deictic representations as they have limited reasoning capabilities, particularly in complex scenarios. Therefore, we propose DeiSAM--a combination of large pre-trained neural networks with differentiable logic reasoners--for deictic promptable segmentation. Given a complex, textual segmentation description, DeiSAM leverages Large Language Models (LLMs) to generate first-order logic rules and performs differentiable forward reasoning on generated scene graphs. Subsequently, DeiSAM segments objects by matching them to the logically inferred image regions. As part of our evaluation, we propose the Deictic Visual Genome (DeiVG) dataset, containing paired visual input and complex, deictic textual prompts. Our empirical results demonstrate that DeiSAM is a substantial improvement over purely data-driven baselines for deictic promptable segmentation.

Lemma 3. Let X be a random variable taking values in X and let F be a family of measurable functions with f 2F: X Let G be a family of measurable functions with g 2G: X! [ M,M], Let ˆR Corollary 4. The inequalities in Lemma 3 can be strengthened to the following: X Using these sharper bounds in the expressions (obtained from McDiarmid's inequality) in Lemma 3 (and using 2 in place of) yields the first pair of equations. Lemma 5. Let h 2 H: A W X! [ M,M] such that if h 2 H, h 2 H, Y [ M,M], k: (A Z X) We analyze each of these four terms separately. A, X, Z! 0, so i Strictly Positive Definite, implies that E [h We tuned the architectures of the Naive Net and NMMR models on both the Demand and dSprite experiments. Within each experiment, the Naive Net and NMMR models used similar architectures. In the Demand experiment, both models consisted of 2-5 ("Network depth" in Table S1) fully connected layers with a variable number ("Network width") of hidden units.