A Schur Multiplier with Unequal Operator and Completely Bounded Norms on $S_4$

What the math gives to ML

The paper constructs an explicit Schur multiplier whose ordinary action on a Schatten class is strictly less stable than its completely bounded, tensor-amplified action near p=4. This distinguishes stability on scalar feature matrices from stability when every scalar entry is replaced by a learned channel block. The transferable mechanism is to regularize entrywise masks using finite amplification norms, especially for attention or graph layers whose behavior can worsen under channel replication.