I want to reduce the running time of this computation. Is there any way?

Cosine Similarity

• $$ text{cosine_similarity}(u, w) = frac{u cdot w}{|u| |w|} $$

  $$ p_t(w|u) = frac{ text{cos}(u’, w)}{sum_{u_0 in V} text{cos}(u, w)} $$

Here is the Python code I am using:

def cosine_similarity(vec1, vec2):
    dot_product = np.dot(vec1, vec2)
    norm_vec1 = np.linalg.norm(vec1)
    norm_vec2 = np.linalg.norm(vec2)
    return dot_product / (norm_vec1 * norm_vec2)

# Compute translation probability using cosine similarity
def compute_translation_probability(target_word, candidate_word, word_embeddings):
    if target_word in word_embeddings and candidate_word in word_embeddings:
        target_vec = word_embeddings[target_word]
        candidate_vec = word_embeddings[candidate_word]

        # Calculate cosine similarity between target word and candidate word
        cosine_sim = cosine_similarity(target_vec, candidate_vec)
        
        # Calculate sum of cosine similarities between target word and all words in the embedding
        sum_cosine_similarities = sum(cosine_similarity(target_vec, word_embeddings[word]) for word in word_embeddings.index_to_key)

        # Return normalized cosine_sim
        if sum_cosine_similarities != 0:
            normalized_cosine_sim = cosine_sim / sum_cosine_similarities
            return normalized_cosine_sim
    
    return 0.0