<p>I'm not aware of any research specifically dealing with quantization of input data, but you may want to check out some related work on quantization of CNN parameters: <a href="http://arxiv.org/pdf/1512.06473v2.pdf" rel="nofollow">http://arxiv.org/pdf/1512.06473v2.pdf</a>.  Depending on what your end goal is, the "Q-CNN" approach may be useful for you.</p>

<p>My own experience with using various quantizations of the input data for CNNs has been that there's a heavy dependency between the degree of quantization and the model itself.  For example, I've played around with using various interpolation methods to reduce image sizes and reducing the color palette size, and in the end, I discovered that each variant required a different tuning of hyper-parameters to achieve optimal results.  Generally, I found that minor quantization of data had a negligible impact, but there was a knee in the curve where throwing away additional information dramatically impacted the achievable accuracy.  Unfortunately, I'm not aware of any way to determine what degree of quantization will be optimal without experimentation, and even deciding what's optimal involves a trade-off between efficiency and accuracy which doesn't necessarily have a one-size-fits-all answer.</p>

<p>On a theoretical note, keep in mind that CNNs need to be able to find useful, spatially-local features, so it's probably reasonable to assume that any encoding that disrupts the basic "structure" of the input would have a significantly detrimental effect on the accuracy achievable.</p>
Encoding invariance for deep neural network
<p>I have a set of data, 2D matrix (like Grey pictures).
And use CNN for classifier.
Would like to know if there is any study/experience on the accuracy impact
if we change the encoding from traditionnal encoding.</p>

<p>I suppose yes, question is rather which transformation of the encoding make the accuracy invariant, which one deteriorates....</p>

<p>To clarify, this concerns mainly the quantization process of the raw data into input data.</p>

<p>EDIT:</p>

<p>Quantize the raw data into input data is already a pre-processing of the data, adding or removing some features (even minor). It seems not very clear the impact in term of accuracy on this quantization process on real dnn computation.
Maybe, some research available.</p>