Sharp Spectral Bounds for Symmetric Positive Definite Tensors via Multiple Algebraic Invariants

What the math gives to ML

The paper turns spectral information into a sharp finite-dimensional extremization problem rather than relaxing it with AM–GM. Its most transferable asset is the structural result that an extremizer subject to K algebraic spectral invariants has at most K distinct spectral values, reducing a high-dimensional eigenvalue problem to enumeration of low-dimensional multiplicity patterns. This can provide tighter, computable upper bounds on neural-layer spectral norms from cheap estimates of power sums, enabling conditioning control or adaptive normalization without explicitly computing the largest singular value.