行内公式c = a 2 + b 2 c=\sqrt{a^2 + b^2} c = a 2 + b 2
行间公式
c = a 2 + b 2 c=\sqrt{a^2 + b^2} c = a 2 + b 2 BP算法
训练集 { ( x ( 1 ) , y ( 1 ) ) , … , ( x ( m ) , y ( m ) ) } \left\{\left(x^{(1)}, y^{(1)}\right), \ldots,\left(x^{(m)}, y^{(m)}\right)\right\} { ( x ( 1 ) , y ( 1 ) ) , … , ( x ( m ) , y ( m ) ) }
设 Δ i j ( l ) = 0 ( for all l , i , j ) \Delta_{i j}^{(l)}=0(\text { for all } l, i, j) Δ ij ( l ) = 0 ( for all l , i , j )
For i = 1 to m \begin{array}{l}{\text {For } i=1 \text { to } m}\end{array} For i = 1 to m
Set a ( 1 ) = x ( i ) Perform forward propagation to compute a ( l ) for l = 2 , 3 , … , L Using y ( i ) , compute δ ( L ) = a ( L ) − y ( i ) Compute δ ( L − 1 ) , δ ( l + 1 ) , … , δ ( 2 ) Δ i j ( l ) : = Δ i j ( l ) + a j ( l ) δ i ( l + 1 ) \begin{array}{l}{\text { Set } a^{(1)}=x^{(i)}} \\ {\text { Perform forward propagation to compute } a^{(l)} \text { for } l=2,3, \ldots, L} \\ {\text { Using } y^{(i)}, \text { compute } \delta^{(L)}=a^{(L)}-y^{(i)}} \\ {\text { Compute } \delta^{(L-1)}, \delta^{(l+1)}, \ldots, \delta^{(2)}} \\ {\Delta_{i j}^{(l)} :=\Delta_{i j}^{(l)}+a_{j}^{(l)} \delta_{i}^{(l+1)}}\end{array} Set a ( 1 ) = x ( i ) Perform forward propagation to compute a ( l ) for l = 2 , 3 , … , L Using y ( i ) , compute δ ( L ) = a ( L ) − y ( i ) Compute δ ( L − 1 ) , δ ( l + 1 ) , … , δ ( 2 ) Δ ij ( l ) := Δ ij ( l ) + a j ( l ) δ i ( l + 1 ) D i j ( l ) : = 1 m Δ i j ( l ) + λ Θ i j ( l ) if j ≠ 0 D i j ( l ) : = 1 m Δ i j ( l ) if j = 0 \begin{array}{l}{D_{i j}^{(l)} :=\frac{1}{m} \Delta_{i j}^{(l)}+\lambda \Theta_{i j}^{(l)}} & {\text { if } j \neq 0} \\ {D_{i j}^{(l)} :=\frac{1}{m} \Delta_{i j}^{(l)}} & {\text { if } j=0}\end{array} D ij ( l ) := m 1 Δ ij ( l ) + λ Θ ij ( l ) D ij ( l ) := m 1 Δ ij ( l ) if j = 0 if j = 0
其中 ∂ ∂ Θ i j ( l ) J ( Θ ) = D i j ( l ) \frac{\partial}{\partial \Theta_{i j}^{(l)}} J(\Theta)=D_{i j}^{(l)} ∂ Θ ij ( l ) ∂ J ( Θ ) = D ij ( l )
调了很久很久，原来是必须要先删除kramed后再安装markdown-it-down-plus，否则删不完全。
此外，hexo-math也是必须要安装的。