no code implementations • 17 Feb 2022 • Mohammad Fereydounian, Hamed Hassani, Amin Karbasi
We prove that: (i) a GNN, as a graph function, is necessarily permutation compatible; (ii) conversely, any permutation compatible function, when restricted on input graphs with distinct node features, can be generated by a GNN; (iii) for arbitrary node features (not necessarily distinct), a simple feature augmentation scheme suffices to generate a permutation compatible function by a GNN; (iv) permutation compatibility can be verified by checking only quadratically many functional constraints, rather than an exhaustive search over all the permutations; (v) GNNs can generate \textit{any} graph function once we augment the node features with node identities, thus going beyond graph isomorphism and permutation compatibility.
no code implementations • 23 Jun 2020 • Mohammad Fereydounian, Zebang Shen, Aryan Mokhtari, Amin Karbasi, Hamed Hassani
More precisely, by assuming that Reliable-FW has access to a (stochastic) gradient oracle of the objective function and a noisy feasibility oracle of the safety polytope, it finds an $\epsilon$-approximate first-order stationary point with the optimal ${\mathcal{O}}({1}/{\epsilon^2})$ gradient oracle complexity (resp.
