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extending bubbles to general tensors #787

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extending bubbles to general tensors #787

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9 changes: 7 additions & 2 deletions init2winit/optimizer_lib/linalg/pth_inv_root_rmn.py
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Expand Up @@ -142,8 +142,13 @@ def pth_inv_root_rmn(
x = x.astype(jnp.float32)
n = x.shape[-1]

alpha = jax.lax.sqrt(jnp.linalg.norm(x, ord=1))
alpha *= jax.lax.sqrt(jnp.linalg.norm(x, ord=jnp.inf))
# Based on Gelfand's inequality, the lines below provide a
# tighter upper bound on the norm of the matrix.
# \sigma_max \leq (\parallel X X^T \parallel_F^k)^{1/2k}
xx = x @ x.T
alpha = jnp.power(jnp.linalg.norm(xx @ xx), 0.25)
# alpha = jax.lax.sqrt(jnp.linalg.norm(x, ord=1))
# alpha *= jax.lax.sqrt(jnp.linalg.norm(x, ord=jnp.inf))
alpha = lax.select(alpha == 0, jnp.ones_like(alpha), alpha)
beta = _scalar_inverse_root(alpha, p)

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