To efficiently calculate the dot products between a center word vector and multiple context or noise vectors in the skip-gram model, deep learning frameworks employ batch matrix multiplication. By permuting the axes of the context and noise word vectors and performing a batch dot product with the center word vectors, the model computes all pairwise dot products simultaneously for the minibatch. This linear algebra implementation step outputs a tensor of shape $(\text{batch size}, 1, \text{max\_len})$, representing the prediction scores.

def skip_gram(center, contexts_and_negatives, embed_v, embed_u):
    v = embed_v(center)
    u = embed_u(contexts_and_negatives)
    pred = torch.bmm(v, u.permute(0, 2, 1))
    return pred