作文自动评分-位置编码position-encoding(PE)解释

import numpy as np
def position_encoding(sentence_size, embedding_size):
    """
    Position Encoding 
    """
    # sentence_size = J
    # embedding_size = d
    # i = k
    # j = j
    J = sentence_size
    d = embedding_size
    encoding = np.ones((embedding_size, sentence_size), dtype=np.float32)
    ls = sentence_size+1
    le = embedding_size+1
    for k in range(1, le):
        for j in range(1, ls):
            encoding[k-1, j-1] = (2*k/d-1)*(2*j/J - 1)
    encoding += 1
    return np.transpose(encoding)/2

def position_encoding(sentence_size, embedding_size):
    """
    Position Encoding described in section 4.1 [1]
    """
    encoding = np.ones((embedding_size, sentence_size), dtype=np.float32)
    ls = sentence_size+1
    le = embedding_size+1
    for i in range(1, le):
        for j in range(1, ls):
            encoding[i-1, j-1] = (i - (le-1)/2) * (j - (ls-1)/2)
    encoding = 1 + 4 * encoding / embedding_size / sentence_size
    return np.transpose(encoding)