import torch
def make_weight_cp(t, wa, wb):
temp = torch.einsum('i j k l, j r -> i r k l', t, wb)
return torch.einsum('i j k l, i r -> r j k l', temp, wa)
def rebuild_conventional(up, down, shape, dyn_dim=None):
up = up.reshape(up.size(0), -1)
down = down.reshape(down.size(0), -1)
if dyn_dim is not None:
up = up[:, :dyn_dim]
down = down[:dyn_dim, :]
return (up @ down).reshape(shape).to(up.dtype)
def rebuild_cp_decomposition(up, down, mid):
up = up.reshape(up.size(0), -1)
down = down.reshape(down.size(0), -1)
return torch.einsum('n m k l, i n, m j -> i j k l', mid, up, down).to(up.dtype)
def factorization(dimension: int, factor:int=-1) -> tuple[int, int]:
"""
return a tuple of two value of input dimension decomposed by the number closest to factor
second value is higher or equal than first value.
In LoRA with Kroneckor Product, first value is a value for weight scale.
second value is a value for weight.
Because of non-commutative property, A⊗B ≠ B⊗A. Meaning of two matrices is slightly different.
examples
factor
-1 2 4 8 16 ...
127 -> 1, 127 127 -> 1, 127 127 -> 1, 127 127 -> 1, 127 127 -> 1, 127
128 -> 8, 16 128 -> 2, 64 128 -> 4, 32 128 -> 8, 16 128 -> 8, 16
250 -> 10, 25 250 -> 2, 125 250 -> 2, 125 250 -> 5, 50 250 -> 10, 25
360 -> 8, 45 360 -> 2, 180 360 -> 4, 90 360 -> 8, 45 360 -> 12, 30
512 -> 16, 32 512 -> 2, 256 512 -> 4, 128 512 -> 8, 64 512 -> 16, 32
1024 -> 32, 32 1024 -> 2, 512 1024 -> 4, 256 1024 -> 8, 128 1024 -> 16, 64
"""
if factor > 0 and (dimension % factor) == 0:
m = factor
n = dimension // factor
if m > n:
n, m = m, n
return m, n
if factor < 0:
factor = dimension
m, n = 1, dimension
length = m + n
while m<n:
new_m = m + 1
while dimension%new_m != 0:
new_m += 1
new_n = dimension // new_m
if new_m + new_n > length or new_m>factor:
break
m, n = new_m, new_n
if m > n:
n, m = m, n
return m, n