In [1]: import torch
   ...: x = torch.randn(1024, 256)
   ...: y = torch.randn(1024, 256)
   ...:
   ...: %timeit torch.norm(x-y, 1, 1)
   ...: %timeit (x-y).sum(1)
   ...:
   ...: %timeit torch.norm(x-y, 2, 1)
   ...: %timeit torch.sqrt((x-y).pow(2).sum(1))
   ...:
   ...: %timeit torch.norm(x-y, 3, 1)
   ...: %timeit torch.pow((x - y).abs().pow(3).sum(1), 1/3)
   ...:
362 µs ± 56.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
332 µs ± 33.2 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

340 µs ± 8.42 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
358 µs ± 5.87 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

352 µs ± 4.55 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
691 µs ± 49.2 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)