I have tensors X of shape BxNxD and Y of shape BxNxD.
I want to compute the pairwise distances for each element in the batch, i.e. I a BxMxN tensor.
How do I do this?
There is some discussion on this topic here: https://github.com/pytorch/pytorch/issues/9406, but I don’t understand it as there are many implementation details while no actual solution is highlighted.
import torch
import numpy as np
B = 32
N = 128
M = 256
D = 3
X = torch.from_numpy(np.random.normal(size=(B, N, D)))
Y = torch.from_numpy(np.random.normal(size=(B, M, D)))
def pairwise_distances(x, y=None):
x_norm = (x**2).sum(1).view(-1, 1)
if y is not None:
y_t = torch.transpose(y, 0, 1)
y_norm = (y**2).sum(1).view(1, -1)
else:
y_t = torch.transpose(x, 0, 1)
y_norm = x_norm.view(1, -1)
dist = x_norm + y_norm - 2.0 * torch.mm(x, y_t)
return torch.clamp(dist, 0.0, np.inf)
out = []
for b in range(B):
out.append(pairwise_distances(X[b], Y[b]))
print(torch.stack(out).shape)
def pairwise_distances(x, y):
'''
Modified from https://discuss.pytorch.org/t/efficient-distance-matrix-computation/9065/3
Input: x is a bxNxd matrix
y is an optional bxMxd matirx
Output: dist is a bxNxM matrix where dist[b,i,j] is the square norm between x[b,i,:] and y[b,j,:]
i.e. dist[i,j] = ||x[b,i,:]-y[b,j,:]||^2
'''
x_norm = x.norm(dim=2)[:,:,None]
y_t = y.permute(0,2,1).contiguous()
y_norm = y.norm(dim=2)[:,None]
dist = x_norm + y_norm - 2.0 * torch.bmm(x, y_t)
return torch.clamp(dist, 0.0, np.inf)
but after a comparison with the “direct expansion” approach the approximation was so high that I didn’t use it (maybe there is a bug that I cannot see).
The issue was in the slicing on the norms. I’ve reconciled the reshapes and confirmed equivalence to the original non-batch pairwise_distances function:
def batch_pairwise_squared_distances(x, y):
'''
Modified from https://discuss.pytorch.org/t/efficient-distance-matrix-computation/9065/3
Input: x is a bxNxd matrix y is an optional bxMxd matirx
Output: dist is a bxNxM matrix where dist[b,i,j] is the square norm between x[b,i,:] and y[b,j,:]
i.e. dist[i,j] = ||x[b,i,:]-y[b,j,:]||^2
'''
x_norm = (x**2).sum(2).view(x.shape[0],x.shape[1],1)
y_t = y.permute(0,2,1).contiguous()
y_norm = (y**2).sum(2).view(y.shape[0],1,y.shape[1])
dist = x_norm + y_norm - 2.0 * torch.bmm(x, y_t)
dist[dist != dist] = 0 # replace nan values with 0
return torch.clamp(dist, 0.0, np.inf)
I put this in my loss function and when I try to train my model with this, the weights become NaN after a few iterations. However, when I remove torch.bmm(x, y_t) , the model is able to train. Does anyone know what in torch.bmm() can cause this issue to occur?
At first I thought maybe I had to normalize my inputs x,y but that did not make a difference. I also tried using a much lower learning rate but it does not make a difference.