In this work, we combine these observations to assess whether such trainable, transferrable subnetworks exist in pre-trained BERT models. For a range of downstream tasks, we indeed find matching subnetworks at 40% to 90% sparsity.

Therefore, a series of attempts Chung et al. [2020], Wu et al. [2020], Wang et al. [2020c], Gordon et al. [2020a], Tang et al. [2019], Aguilar et al. [2019] have been made to review the techniques for effective

Recently, researchers from convex optimization proposed the notions of "relative Lipschitz continuity" and "relative strong convexity". Both of the notions are generalizations oftheirclassicalcounterparts.

Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results for convergence rates with compressed communication, a lower bound is still missing. Analyses of algorithms with communication compression have identified two abstract properties that guarantee convergence: the unbiased property or the contrac-tive property.

Tomakesure functions represented by neural networks are homogeneous, we also prove that HomoGNN and HomoMLP can only represent homogeneous functions, in Section B.2.2.