AppendixofSynergy-of-experts 1 TheoreticalProofs

From Figure 1(a), learning multiple linear sub-models and averaging the predictions (ensemble) is still a linear model, so it cannot tackleXOR problem. We compare the training cost of all methods from the two aspects;1). Thesub-model training enables themost adversarial attacks ofsub-models could be successfully defended. In particular, we train two kinds of models to defend against the attacks: 1). FromFigure2(a)and2(b),when0.01 ϵ 0.04, SoE without the collaboration training achieves a similar robustness compared with SoE.