Figure 2.

Process of gradient refinement. Here, ${\theta }_{i,j}$ represents the angle between two local gradients $g^i$ and $g^j$ and ${\tilde{g}}^i$ represents the refined local gradients in client $i$. (a) When gradients $g^i$ and $g^j$ are conflicting (i.e., $\cos {\theta }_{i,j}$ < 0), the gradient $g^i$ is replaced with its projection ${\tilde{g}}^i$ onto the normal plane of $g^j$. (b) When gradients $g^i$ and $g^j$ are non-conflicting (i.e., $\cos {\theta }_{i,j}$ > 0), gradient $g^i$ is unchanged (i.e., ${\tilde{g}}^i=g^i$).