Yes, it is a well known problem called Curse of Dimensionality. It happens when a finite number of data samples is used to train a network with a high-dimensional feature space (very deep network).
With regard to your question: yes, smaller networks (representational spaces with lower dimensions) describe better smaller datasets.
Because of data sparsity. As the features to represent a single sample increases the space between samples in the network representation also increases. When the samples are represented in too sparse space (all samples are very far away from each other in this high-dimensional space) then you can not draw any conclusions or relationships about them.
There is a balance between network dimensionality and dataset size, both of them must be in accordance to each other. You can think of this in this way: if data is represented in a very low dimensional space you can not tell them appart (1D space), if the data is represented in a very high dimensional space, then you can not find relationships within it. The dimensionality must be just the right one.
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