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The paper explores whether any neural network can be redesigned to train effectively with gradient descent, proving a universality result that for any network, there exists an extension that reproduces given weights and outputs via gradient descent.
This paper proves that graph neural networks with random node features can universally approximate permutation-invariant or equivariant functions on directed graphs, and provides approximation rate bounds for differentiable functions.
This paper develops a systematic framework for establishing universality of machine learning models that handle inputs of varying dimensions (e.g., graphs with different node counts). It shows that many existing architectures fail to be universal and proposes simple modifications to restore universality.