Alignment in deep networks is governed by flag varieties, with subspace intersection dimension as the unique reparameterization-invariant observable, explaining regularization and activation effects from first principles.
We do not have training checkpoints and cannot verify whether R(ℓ) increases monotonically during training
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Flag Varieties: A Geometric Framework for Deep Network Alignment
Alignment in deep networks is governed by flag varieties, with subspace intersection dimension as the unique reparameterization-invariant observable, explaining regularization and activation effects from first principles.