Optimization Flaws in Matrix Components

8

Components Tracked

5

Dimensions (32-512)

34.9x

Cond. # Error @ d=512

67%

Multiplier Improvement

4

Strategies Tested

Component Learning Errors vs. Dimension

SGD vs Adam: Component Errors (d=128)

Corrective Strategies (d=64)

Key Findings (Revised)

Component	Error @ d=128	Scaling	Multiplier Helps?	Category
Row Norms	0.134	Stable	Yes (67%)	Scale (known)
Column Norms	0.134	Stable	Yes (71%)	Scale (known)
Singular Values	0.134	Stable	Yes (69%)	Scale (known)
Condition Number	2.77	Grows 130x (d=32 to 512)	No (10%)	Spectral (NEW)
Spectral Gap	0.029	Stable	Partially	Well-learned
Effective Rank	0.001	Stable	N/A	Well-learned
Frobenius Norm	0.134	Stable	Yes (73%)	Scale (known)