Popular models for predicting the output (or label, response, outcome)yfrom theinput (orcovariate)xhavebeenfound erroneous when confronted with a distribution change, even from an essentially irrelevant perturbation like a position shift or background change forimages [91,6,102,41,2,27].

Since both the singing and the annotation demand great professional efforts, it leads to much more challenges than that of speech.

The WBP problem is related to the optimal transport (OT) problem, in that both are based on the Wassersteindistance, buttheWBP issignificantly harder.

As a summary, this paper makes the following contributions.

In physical systems a particle instead interacts only with a finite number of other particles, hence the density field remains highly fluctuating. The effect of theθ(w x) term is to select one particular half-space over which the integralisdone. To estimate the fluctuations due to a finite number of nodes, we will have to estimate the width of the output distribution for a given set of parameters. Toestimate the error inFigure 1d ofthe main text, we ask what are the values ofxk = xcosθ such that the average output plus or minus a standard deviation, divided by M, would be equal to the threshold. Since the standard deviation involves|x|2, we estimate its average value for points 3 with a givenxk, i.e.

In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to performaclassificationtask.