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How to perform operations on very big torch tensors without splitting them

My Task:

I’m trying to calculate the pair-wise distance between every two samples in two big tensors (for k-Nearest-Neighbours), That is – given tensor test with shape (b1,c,h,w) and tensor train with shape (b2,c,h,w), I need || test[i]-train[j] || for every i,j. (where both test[i] and train[j] have shape (c,h,w), as those are sampes in the batch).

The Problem

both train and test are very big, so I can’t fit them into RAM

My current solution

For a start, I did not construct these tensors in one go – As I build them, I split the data Tensor and save them separately to memory, so I end up with files {Testtest_1,...,Testtest_n} and {Traintrain_1,...,Traintrain_m}. Then, I load in a nested for loop every Testtest_i and Traintrain_j, calculate the current distance, and save it.

This semi-pseudo-code might explain

test_files = [f'Testtest_{i}' for i in range(n)]
train_files = [f'Traintrain_{j}' for j in range(m)]
dist = lambda t1,t2: torch.cdist(t1.flatten(1), t2.flatten(1)) 
all_distances = []
for test_i in test_files:
    test_i = torch.load(test_i) # shape (c,h,w)
    dist_of_i_from_all_j = torch.Tensor([])
    for train_j in train_files:
        train_j = torch.load(train_j) # shape (c,h,w)
        dist_of_i_from_all_j = torch.cat((dist_of_i_from_all_j, dist(test_i,train_j))
    all_distances.append(dist_of_i_from_all_j)
# and now I can take the k-smallest from all_distances

What I thought might work

I came across FAISS repository, in which they explain that this process can be sped up (maybe?) using their solutions, though I’m not quite sure how. Regardless, any approach would help!

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Answer

Did you check the FAISS documentation?

If what you need is the L2 norm (torch.cidst uses p=2 as default parameter) then it is quite straightforward. Code below is an adaptation of the FAISS docs to your example:

import faiss
import numpy as np
d = 64                           # dimension
nb = 100000                      # database size
nq = 10000                       # nb of queries
np.random.seed(1234)             # make reproducible
x_test = np.random.random((nb, d)).astype('float32')
x_test[:, 0] += np.arange(nb) / 1000.
x_train = np.random.random((nq, d)).astype('float32')
x_train[:, 0] += np.arange(nq) / 1000.

index = faiss.IndexFlatL2(d)   # build the index
print(index.is_trained)
index.add(x_test)                  # add vectors to the index
print(index.ntotal)

k= 100 # take the 100 closest neighbors
D, I = index.search(x_train, k)     # actual search
print(I[:5])                   # neighbors of the 100 first queries
print(I[-5:])                  # neighbors of the 100 last queries
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