The implementation of taylor polynomials

[zeal-up]

It is weird that you implement the taylor polynomials mentioned in your paper in this way:

 w_x = tf.tile(_variable_on_cpu('weight_x', shape, initializer), [batch_size, num_point, K_knn, 1])
 w_y = tf.tile(_variable_on_cpu('weight_y', shape, initializer), [batch_size, num_point, K_knn, 1])
 w_z = tf.tile(_variable_on_cpu('weight_z', shape, initializer), [batch_size, num_point, K_knn, 1])
...
      g1 = w_x * X + w_y * Y + w_z * Z + w_xyz * X * Y * Z
      g2 = w_xy * X * Y + w_yz * Y * Z + w_xz * X * Z + biases
      g3 = w_xx * X * X + w_yy * Y * Y + w_zz * Z * Z
      g4 = w_xxy * X * X * Y + w_xyy * X * Y * Y + w_xxz * X * X * Z
      g5 = w_xzz * X * Z * Z + w_yyz * Y * Y * Z + w_yzz * Y * Z * Z
      g6 = w_xxx * X * X * X + w_yyy * Y * Y * Y + w_zzz * Z * Z * Z
      g_d = g1 + g2 + g3 + g4 + g5 + g6

I think it equal if you concatenate of [X, Y, Z, XX, YY, ...., XYZ] and multiply a [20xtaylor_channel] matrix (equal to a fully connected layer).
Do I miss something or understanding wrong?

[usherbob]

Equation 7 in the paper I believe is the same as the implementation in the code.