740 + 850 x 100=? And there!!
The purpose of the tensor-on-tensor regression, which we examine, is to relate tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without being aware of its intrinsic rank beforehand.
By examining the impact of rank over-parameterization, we suggest the Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) methods to address the problem of unknown rank. By demonstrating that RGD and RGN, respectively, converge linearly and quadratically to a statistically optimal estimate in both rank correctly-parameterized and over-parameterized scenarios, we offer the first convergence guarantee for the generic tensor-on-tensor regression. According to our theory, Riemannian optimization techniques automatically adjust to over-parameterization without requiring implementation changes.
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Answer:
It is similar to a mountain in that it is dramatically higher than what is immediately around it. But mountains usually have a distinct apex or peak that is very small relative to the base and not typically level. Plateaus and mesas have tops only a little smaller than the base, and relatively flat. If the aspect ratio is less than 1, plateau. If greater than 1, mesa.
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