I've come across the following claim in a [paper][1] of Mallat:

"High frequency instabilities [of a signal representation] to deformations can be avoided by grouping frequencies into dyadic packets in $\mathbb{R}^d$, with a wavelet transform."

I know what the wavelet packet decomposition is and I know what stability to deformations is (in the case of $C^2$ diffeomorphisms), but I don't understand why the quoted statement is true. 

Perhaps I missed the explanation in the paper, but could someone provide a reference, an explanation or both? I assume it has something to do with the fact that a wavelet is localized. 


<sup>1</sup> Stéphane Mallat: *Group Invariant Scattering*, 
Communications on Pure and Applied Mathematics, Vol. LXV, 1331–1398 (2012), [DOI: 10.1002/cpa.21413](https://doi.org/10.1002/cpa.21413)


  [1]: https://www.di.ens.fr/~mallat/papiers/ScatCPAM.pdf