Unverified50% confidenceBenchmarkExact time
In experiments, the product-of-scales family reaches R of approximately 1.5 under long-distance high-dimensional movement, meaning NGD requires approximately 50% more steps than an optimizer advancing along the Fisher–Rao geodesic.
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Long-term
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10/7/2026
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UnverifiedThe paper defines the inefficiency ratio R as the Fisher length of the mixture geodesic divided by the Fisher–Rao distance, where R is always greater than or equal to 1.65% similarUnverified在ASR场景中，即使单一维度的分布偏移就可能导致WER增加50%以上，多维度偏移会使模型性能断崖式下降65% similarUnverifiedIn the experiment, ResNet-56 has only 2,752 more parameters than plain-56 (approximately one-third of a percent of the total), and these extra parameters come solely from 1×1 projection layers at locations where the number of channels changes.60% similarUnverifiedFor products of scale families (including Gaussian covariance parameters, Gamma rate parameters, etc.), R grows unboundedly as Θ(√log d) with dimension d.60% similarUnverifiedDDIM已将采样步数从1000步降至约50步60% similar
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