will it be 2d as (1000)* (3*32*32)?
or
will it be 4d as (1000)* (3) (32)(32)?
The structure of the training set should be as follow:
...
In few words, the label of the class, and the value of (32 x 32 x 3) pixel, in order R values, G values and B Values.
As well as CIFAR10 Classification Problem, the training set consists of 2D Data (in this case the first solution you wrote in the question title).
A good reference for a baseline approach to CIFAR10:
https://www.cs.toronto.edu/~kriz/cifar.html
Hope this could be useful for your research.
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