# How to balance memory and speed

Hi, I’m trying to calculate the result of two tensors for the following function in every forward propagation. However, I tried different methods, they either are too slow or make my tensor too big to be able to reside in memory. Can someone help me?

Details:
Tensor1: Size([15, 24, 4, 120])
Tensor2: Size([5608, 4, 120])
I need a result =calculate_average_similarity_score(tensor1, tensor2, sim_dim=-1., avg_dim=-2). The result is of Size(24, 15, 5608)

Method1:
I unsqueeze and expand both tensor1 and tensor 2 so that they both have Size([15, 24, 5608, 4, 120]) as input to the function. However, this makes a giant tensor more than 3.8Gb

Method2:
I tried to loop through two tensors like this but found it to be super slow:

``````res = []
for tensor1_dim0 in tensor1:
tensor1_res=[]
for tensor1_dim1 in dim0:
tensor2_res = []
for tensor2_dim0 in tensor2:
sc=calculate_average_similarity_score(tensor1_dim1, tensor2_dim0, sim_dim=-1, sim_dim=-2)
tensor2_res.append(sc)
tensor1_res.append(tensor2_res)
res.append(tensor1_res)
output = torch.tensor(res)
``````

Method3:
I tried the map method described in https://discuss.pytorch.org/t/giant-tensor-consumes-gpu-memory/142691

The function to apply to both tensors

``````def calculate_average_similarity_score(tensor1, tensor2, sim_dim=None, avg_dim=None):
"""
Calculate the similarity between two tensors.

This similarity is both calculated using a CosineSimilarity and an
average.
E.g.
t1 = torch.tensor([[[1, 2, 3], [3, 2, 1]], [[1, 2, 3], [3, 2, 1]]],
dtype=torch.double) # 2*2*3 tensor
t2 = torch.tensor([[[1, 2, 3], [3, 2, 1]], [[1, 2, 1], [1, 2, 1]]],
dtype=torch.double) # 2*2*3 tensor
if sim_dim=-1, avg_dim = -2,
This will first calculate cos similarity along dim -1, and then
average over dim -2 (original dim -2, not the dim after cos
similarity).
The result is tensor([1.000, 0.8729]) because the average of the two
similarity scores are 1.000 and 0.9729 respectively

:param tensor1: input1
:param tensor2: input1
:param sim_dim: the dimension along which similarity is calculated
This dimension becomes 1 after calculation. The sim_dim has to be
expressed as a negative interger (for the ease of implementation).
:param avg_dim: the dimension along which an arithmetic average is
calculated. The sim_dim has to be expressed as a negative integer (for
the ease of implementation).
:return: a tensor of average scores
"""
if sim_dim >= 0 or (avg_dim is not None and avg_dim >= 0):
raise NotImplementedError("kernels.py::arctan_sc(). Currently "
"this function is implemented assuming "
"sim_dim and avg_dim both are negative. "
"Change the implementation if using "
"positive dimension")

cos = CosineSimilarity(dim=sim_dim)
sc = cos(tensor1, tensor2)
if avg_dim is not None:
if sim_dim > avg_dim:  # The sim_dim disappear after Cos,
# so avg_dim changes as well
avg_dim = avg_dim - sim_dim
sc = torch.mean(sc, dim=avg_dim)
return sc
``````