cuda_rasterizer-->backward.cu中的361行-->368行中的final_A, final_D,final_D2需要随着循环变化吗？

[zhuyu2015]

#else
			dL_dweight += (final_D2 + m_d * m_d * final_A - 2 * m_d * final_D) * dL_dreg;
#endif
			dL_dalpha += dL_dweight - last_dL_dT;
			// propagate the current weight W_{i} to next weight W_{i-1}
			last_dL_dT = dL_dweight * alpha + (1 - alpha) * last_dL_dT;
			float dL_dmd = 2.0f * (T * alpha) * (m_d * final_A - final_D) * dL_dreg;
			dL_dz += dL_dmd * dmd_dd;

尤其367行的final_A和final_D要随循环的变化而变化吗？

[zhuyu2015]

第367行是这一行：

float dL_dmd = 2.0f * (T * alpha) * (m_d * final_A - final_D) * dL_dreg;

[hbb1]

Hi, here is the formulation for back-propagation of the depth-distortion loss:

$$L= \sum_{i=0}^{N-1}\sum_{j=0}^{N-1}w_iw_j(d_i-d_j)^2$$

Now we specifically analyze the $k$-th item and do some simplification,

$$ L_k = \sum_{j=0}^{k-1}w_kw_j(d_k-d_j)^2 + \sum_{i=k+1}^{N-1}w_iw_k(d_i-d_k)^2 $$

$$ L_k = \sum_{j=0}^{k-1}w_kw_j(d_k^2-2d_kd_j + d_j^2) + \sum_{i=k+1}^{N-1}w_iw_k(d_i^2-2d_id_k+d_k^2)$$

factorize the nested composition terms and we have got:
$$dL_k / dw_k = \sum_{j=0}^{k-1}w_j(d_k^2-2d_kd_j+d_j^2) + \sum_{i=k+1}^{N-1}w_i(d_i^2-2d_id_k+d_k^2)$$

$$dL_k / dw_k = D^2-w_kd_k^2 + d_k^2(A_k-w_k) - 2d_k(\sum_{j=0}^{k-1}w_jd_j + \sum_{i=k+1}^{N-1}w_id_i +w_kd_k -w_kd_k) = D^2 +d_k^2A-2d_kD $$

$$dL_k / dd_k = 2(\sum_{j=0}^{k-1}w_kw_j(d_k-d_j) + \sum_{i=k+1}^{N-1}w_iw_k(d_k-d_i)) = 2(w_k(d_k(A-w_k) - (D-d_kw_k))) = 2(w_k(d_kA - D))$$