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equivariant_layers.py
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equivariant_layers.py
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import pdb
import torch
import torch.nn as nn
def check_shape(x, shape):
assert len(x.shape) == len(shape)
for xs, s in zip(x.shape, shape):
assert xs == s
def ops_1_to_1(inputs, normalize=False):
dim = inputs.shape[-1]
N, d, m = inputs.shape
dim = inputs.shape[-1]
sums = inputs.sum(dim=2, keepdim=True)
op1 = inputs
op2 = torch.tile(sums, (1, 1, dim))
return torch.stack([op1, op2], dim=2)
def ops_1_to_2(inputs, normalize=False):
'''
inputs: N x D x m tensor
'''
N, D, m = inputs.shape
dim = inputs.shape[-1]
sum_all = inputs.sum(dim=2, keepdim=True) # N x D x 1
op1 = torch.diag_embed(inputs)
op2 = torch.diag_embed(torch.tile(sum_all, (1, 1, dim)))
op3 = torch.tile(inputs.unsqueeze(2), (1, 1, dim, 1))
op4 = torch.tile(inputs.unsqueeze(3), (1, 1, 1, dim))
op5 = torch.tile(sum_all.unsqueeze(3), (1, 1, dim, dim))
return torch.stack([op1, op2, op3, op4, op5], dim=2)
def ops_2_to_1(inputs, normalize=False):
N, D, m, m = inputs.shape
dim = inputs.shape[-1]
diag_part = torch.diagonal(inputs, dim1=-2, dim2=-1)
sum_diag_part = diag_part.sum(dim=2, keepdims=True)
sum_rows = inputs.sum(dim=3)
sum_cols = inputs.sum(dim=2)
sum_all = inputs.sum(dim=(2,3))
op1 = diag_part
op2 = torch.tile(sum_diag_part, (1, 1, dim))
op3 = sum_rows
op4 = sum_cols
op5 = torch.tile(sum_all.unsqueeze(2), (1, 1, dim))
ops = [op1, op2, op3, op4, op5]
return torch.stack([op1, op2, op3, op4, op5], dim=2)
def ops_2_to_2(inputs, normalize=True):
N, D, m, m = inputs.shape
dim = inputs.shape[-1]
diag_part = torch.diagonal(inputs, dim1=-2, dim2=-1) # N x D x m
sum_diag_part = diag_part.sum(dim=2, keepdims=True) # N x D x 1
sum_rows = inputs.sum(dim=3) # N x D x m
sum_cols = inputs.sum(dim=2) # N x D x m
sum_all = inputs.sum(dim=(2,3)) # N x D
ops = [None] * (15 + 1)
ops[1] = torch.diag_embed(diag_part) # N x D x m x m
ops[2] = torch.diag_embed(torch.tile(sum_diag_part, (1, 1, dim)))
ops[3] = torch.diag_embed(sum_rows)
ops[4] = torch.diag_embed(sum_rows)
ops[5] = torch.diag_embed(torch.tile(sum_all.unsqueeze(-1), (1, 1, dim)))
ops[6] = torch.tile(sum_cols.unsqueeze(3), (1, 1, 1, dim))
ops[7] = torch.tile(sum_rows.unsqueeze(3), (1, 1, 1, dim))
ops[8] = torch.tile(sum_cols.unsqueeze(2), (1, 1, dim, 1))
ops[9] = torch.tile(sum_rows.unsqueeze(2), (1, 1, dim, 1))
ops[10] = inputs
ops[11] = torch.transpose(inputs, 2, 3)
ops[12] = torch.tile(diag_part.unsqueeze(3), (1, 1, 1, dim))
ops[13] = torch.tile(diag_part.unsqueeze(2), (1, 1, dim, 1))
ops[14] = torch.tile(sum_diag_part.unsqueeze(3), (1, 1, dim, dim))
ops[15] = torch.tile(sum_all.unsqueeze(-1).unsqueeze(-1), (1, 1, dim, dim))
for i in range(1, 16):
op = ops[i]
if i == 5 or i == 15:
ops[i] = torch.divide(op, dim * dim)
else:
ops[i] = torch.divide(op, dim)
return torch.stack(ops[1:], dim=2)
def set_ops_3_to_3(inputs, normalize=True):
N, D, m, m, m = inputs.shape
dim = inputs.shape[-1]
# only care about marginalizing over each of the individual indices
sum_all = inputs.sum(dim=(-1, -2, -3))
sum_c1 = inputs.sum(dim=-1)
sum_c2 = inputs.sum(dim=-2)
sum_c3 = inputs.sum(dim=-3)
sum_c12 = inputs.sum(dim=(-1, -2))
sum_c13 = inputs.sum(dim=(-1, -3))
sum_c23 = inputs.sum(dim=(-2, -3))
# dont really care about diagonal
ops = [None] * 20
ops[1] = torch.tile(sum_all.view(N, D, 1, 1, 1), (1, 1, dim, dim, dim))
ops[2] = torch.tile(sum_c1.unsqueeze(-1), (1, 1, 1, 1, m))
ops[3] = torch.tile(sum_c1.unsqueeze(-2), (1, 1, 1, m, 1))
ops[4] = torch.tile(sum_c1.unsqueeze(-3), (1, 1, m, 1, 1))
ops[5] = torch.tile(sum_c2.unsqueeze(-1), (1, 1, 1, 1, m))
ops[6] = torch.tile(sum_c2.unsqueeze(-2), (1, 1, 1, m, 1))
ops[7] = torch.tile(sum_c2.unsqueeze(-3), (1, 1, m, 1, 1))
ops[8] = torch.tile(sum_c3.unsqueeze(-1), (1, 1, 1, 1, m))
ops[9] = torch.tile(sum_c3.unsqueeze(-2), (1, 1, 1, m, 1))
ops[10] = torch.tile(sum_c3.unsqueeze(-3), (1, 1, m, 1, 1))
ops[11] = torch.tile(sum_c12.view(N, D, m, 1, 1), (1, 1, 1, m, m))
ops[12] = torch.tile(sum_c12.view(N, D, 1, m, 1), (1, 1, m, 1, m))
ops[13] = torch.tile(sum_c12.view(N, D, 1, 1, m), (1, 1, m, m, 1))
ops[14] = torch.tile(sum_c13.view(N, D, m, 1, 1), (1, 1, 1, m, m))
ops[15] = torch.tile(sum_c13.view(N, D, 1, m, 1), (1, 1, m, 1, m))
ops[16] = torch.tile(sum_c13.view(N, D, 1, 1, m), (1, 1, m, m, 1))
ops[17] = torch.tile(sum_c23.view(N, D, m, 1, 1), (1, 1, 1, m, m))
ops[18] = torch.tile(sum_c23.view(N, D, 1, m, 1), (1, 1, m, 1, m))
ops[19] = torch.tile(sum_c23.view(N, D, 1, 1, m), (1, 1, m, m, 1))
if normalize:
ops[1] = torch.divide(ops[1], dim * dim * dim)
for d in range(2, 11):
ops[d] = torch.divide(ops[d], dim)
for d in range(11, 20):
ops[d] = torch.divide(ops[d], dim * dim)
return torch.stack(ops[1:], dim=2)
def set_ops_4_to_4(inputs, normalize=False):
N, D, m, _, _, _ = inputs.shape
sum_all = inputs.sum(dim=(-1, -2, -3, -4))
c1, c2, c3 = [], [], []
# collapse 1 dim
sum_c1 = inputs.sum(dim=-1)
sum_c2 = inputs.sum(dim=-2)
sum_c3 = inputs.sum(dim=-3)
sum_c4 = inputs.sum(dim=-4)
c1s = [sum_c1, sum_c2, sum_c3, sum_c4]
# collapse 2
sum_c12 = inputs.sum(dim=(-1, -2))
sum_c13 = inputs.sum(dim=(-1, -3))
sum_c14 = inputs.sum(dim=(-1, -4))
sum_c23 = inputs.sum(dim=(-2, -3))
sum_c24 = inputs.sum(dim=(-2, -4))
sum_c34 = inputs.sum(dim=(-3, -4))
c2s = [sum_c12, sum_c13, sum_c14, sum_c23, sum_c24, sum_c34]
# collapse 3
sum_c123 = inputs.sum(dim=(-1, -2, -3))
sum_c124 = inputs.sum(dim=(-1, -2, -4))
sum_c134 = inputs.sum(dim=(-1, -3, -4))
sum_c234 = inputs.sum(dim=(-2, -3, -4))
c3s = [sum_c123, sum_c124, sum_c134, sum_c234]
# broadcast
ops = []
ops.append(torch.tile(sum_all.view(N, D, 1, 1, 1, 1), (1, 1, m, m, m, m)))
# broadcast collapsed 1 dims
for c1 in c1s:
ops.append(torch.tile(c1.view(N, D, m, m, m, 1), (1, 1, 1, 1, 1, m)))
ops.append(torch.tile(c1.view(N, D, m, m, 1, m), (1, 1, 1, 1, m, 1)))
ops.append(torch.tile(c1.view(N, D, m, 1, m, m), (1, 1, 1, m, 1, 1)))
ops.append(torch.tile(c1.view(N, D, 1, m, m, m), (1, 1, m, 1, 1, 1)))
for c2 in c2s:
ops.append(torch.tile(c2.view(N, D, m, m, 1, 1), (1, 1, 1, 1, m, m)))
ops.append(torch.tile(c2.view(N, D, m, 1, m, 1), (1, 1, 1, m, 1, m)))
ops.append(torch.tile(c2.view(N, D, 1, m, m, 1), (1, 1, m, 1, 1, m)))
ops.append(torch.tile(c2.view(N, D, m, 1, 1, m), (1, 1, 1, m, m, 1)))
ops.append(torch.tile(c2.view(N, D, 1, m, 1, m), (1, 1, m, 1, m, 1)))
ops.append(torch.tile(c2.view(N, D, 1, 1, m, m), (1, 1, m, m, 1, 1)))
for c3 in c3s:
ops.append(torch.tile(c3.view(N, D, m, 1, 1, 1), (1, 1, 1, m, m, m)))
ops.append(torch.tile(c3.view(N, D, 1, m, 1, 1), (1, 1, m, 1, m, m)))
ops.append(torch.tile(c3.view(N, D, 1, 1, m, 1), (1, 1, m, m, 1, m)))
ops.append(torch.tile(c3.view(N, D, 1, 1, 1, m), (1, 1, m, m, m, 1)))
return torch.stack(ops, dim=2)
if __name__ == '__main__':
N = 32
D = 16
m = 2
x = torch.rand(N, D, m)
x = torch.rand(N, D, m)
x2 = torch.rand(N, D, m, m)
x3 = torch.rand(N, D, m, m, m)
x4 = torch.rand(N, D, m, m, m, m)
o = ops_1_to_1(x)
print('1->1 okay')
o2 = ops_1_to_2(x)
print('1->2 okay')
o1 = ops_2_to_1(x2)
print('2->1 okay')
o22 = ops_2_to_2(x2)
print('2->2 okay')
t33 = set_ops_3_to_3(x3)
print(t33.shape)
t44 = set_ops_4_to_4(x4)
print(t44.shape)