We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors.

However, also in classical ML, kernel methods allow us to implicitly work with high-or infinite dimensional function spaces [25, 26].

However, also in classical ML, kernel methods allow us to implicitly work with high-or infinite dimensional function spaces [25, 26].

GTs directly connect nodes, using the graph structure asasoft bias through positionalencoding[37].

Ourfirsttaskisecharacterize termsofside (leftvsright), contact (contactvsno-contact), andsegmenteachhand object.

We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection.

When arenoisy, this =1 inEg (called over -fitting tothetruetar24, 31, 32, 33, 34, 35, 36, 37, 38, 39, 16].

We aim to deepen the theoretical understanding of Graph Neural Networks (GNNs) on large graphs, with a focus on their expressive power.