In this paper https://arxiv.org/pdf/1511.05493.pdf (GATED GRAPH SEQUENCE NEURAL NETWORKS,2016), it is stated that in a Graph Neural network initialising hidden states is not required, as

'In GNNs, there is no point in initializing node representations because the contraction map constraint ensures that the fixed point is independent of the initializations'

'This is no longer the case with GG-NNs, which lets us incorporate node labels as additional inputs'

How exactly does the contraction map theory, which I am understanding to state that given a metric space, and a mapping, that mapping is contractive if there exists a constant such that the distance between points A and B after applying the mapping is always less than the original distance between A and B times that constant.

Is this some kind of guarantee towards convergence? Is it valid to say that the constant c refers to the 'fixed point', and because c doesn't depend on the hidden state, the start point doesn't really matter.

Why does it no longer apply after we incorporate node labels?


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