How to compute the cosine similarity between two cryptensors?

Feature

I wonder how to compute the cosine similarity between two cryptensors. Could anyone give me some suggestions?

For example,

import crypten

x = torch.tensor([1, 2, 3], dtype = torch.float)
x_enc = crypten.cryptensor(x)

y_enc = crypten.cryptensor([2.0, 3.0, 4.0])

Alternatives

Additional context

[lvdmaaten]

@knottb Note that PyTorch implementation does something to prevent division by zero. We may need something similar if we were to add cosine similarity in CrypTen.

[hobbitlzy]

Actually, this epsilon for numerical precision only matters when the reciprocal of the norms is very small (product is less than 1e-8), which means the norms are large (product is at least 1e8). If our norms are this large, then the inverse square root will fail. Currently our precision allows for inputs up to around [0.05, 200] (it may be useful to work on improving this).

Hi, what if the data is beyond the valid range [0.05,200]? Is there any way to compute them correctly now?