push is very very tiny. So that's the push. Combining these two primitives now we have to we have a whole like better picture assert the value changed only if the push clear the floor the push is the addent step roughly the learning rate the floor is the nearest the BF16 rounding boundary roughly theta over 256 take theta equal one the BF6 boundary is about 039 a typical added step here is around 3 millions so the update is more than a thousand smaller than the boundary so the BF visible value will not change. This is not saying the master weights uh in is frozen forever. It is saying the value that rollout engine would serve does not change on this part. So the whole magnet is pushing is is pushed versus four. Let's visualize this to have better understanding. The x-axis is the weight magnitude and the y-axis is the update magnitude. First we look at the red line. The red diagonal is the bxis invisible boundary. It's like theta over 256. And now we look at the green bound. This is the atom push. Is this roughly around the learning rate and with a conservative upper bound? So now we ask like where the most point fits for most of the weights. The red floor is above the green push. Those updates exists in the master weights but they are not visible in the served BI6 view. This step small weights on the left can move. Large weight on the right. They will just stay the same. They will be absorbed it. This is the addon absorption. This is why the serve update become very sparse.