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The non-linear effects that have been observed in adaptive filtering scenarios are explained from the point of view of the structure that underlies the desired data. While the model structure used by the conventional adaptive filter is a linear combination of tapped-delay line signals, that adaptive filter model does not generally correspond to the interference contaminated adaptive equalization, and adaptive line prediction are explained here as being the result of forcing a filter model onto an essentially different data structure. The tapped delay line model can then only be compatible with the data if the filter weights become time-varying. If the adaptation captures the time-varying weight behavior, the adaptive filter performance can approach that associated with the data structure and thereby exceed the best performance associated with the corresponding conventional Wiener filter.