Supplemental Material for AC-GC: Lossy Activation Compression with Guaranteed Convergence

The appendices of this supplemental material are focused on providing detailed proofs (Appendix A), per-layer derivations for activation errors (Appendix B), algorithm and implementationdetails(AppendixC),datasetsandhyperparameters(AppendixD),extended experimental data (Appendix E) and additional experiments (Appendix F) to accompany the main paper. A code example and trained models are available for CIFAR10/ResNet50 by accessing https://github.com/rdevans0/acgc. L and η depend on the model being trained and dataset, and are thus problem-dependent constants. Preliminary on Separation of Norms Given two, independent random vectorsA= (an) RN and B =(bn) RN, whereE[bn]=0 n. Given f which obeys (4), and a convex functionD( X) which bounds the gradient error from above for all X, θ, and X; provided that D( X) e2V2 the variance of the compressed gradients satisfies E[kˆ θf(θ,Xnt)k2] (1+e2)V2 (16) Proof.