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" Rubik's Cube: High-Order Channel Interactions with a Hierarchical Receptive Field " Supplementary Material

Neural Information Processing Systems

Section 2 provides the implementation details of Rubik's cube convolution within the image restora-4 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. Rubik's cube convolution operation into the baseline will achieve the performance improvement, "Acc-1" and "Acc-5" indicate the top-1 and As illustrated in Figure 3 and 4, integrating our Rubik's cube In contrast, the baseline combined with our Rubik's cube convolution operator achieves details









Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making

arXiv.org Artificial Intelligence

Three strands of prior work motivate this study: minimax-quantile bounds restricted to non-interactive estimation; unified interactive analyses that focus on expected risk rather than risk level specific quantile bounds; and high-probability bandit bounds that still lack a quantile-specific toolkit for general interactive protocols. To close this gap, within the interactive statistical decision making framework, we develop high-probability Fano and Le Cam tools and derive risk level explicit minimax-quantile bounds, including a quantile-to-expectation conversion and a tight link between strict and lower minimax quan-tiles. Instantiating these results for the two-armed Gaussian bandit immediately recovers optimal-rate bounds. Index T erms-- information theory, learning theory 1. INTRODUCTION The concept of minimax risk has become a staple in learning theory and statistics [1-3]. In interactive or online learning settings, the minimax risk is often replaced by its counterpart, the minimax regret.