Algorithm 1 pseudocode for the proposed algorithm

1. initialize network 2. reset : inputs = 0, Activations = 0      forward propagation: 3. initialize the inputs do 4. roll over: Activations; cell states 5. loop over a cell, end for 6. do   for t=0 to n do     Calculates the gate values :         inputs gates: $\mathrm{i}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{xi}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hi}}{\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-1\right){\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-2\right)+{\mathrm{w}}_{\mathrm{ci}}\mathrm{c}\left(\mathrm{t}-1\right)+{\mathrm{b}}_{\mathrm{i}}\right)$         forget gates: $\mathrm{f}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{xf}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hf}}{\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-1\right){\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-2\right)+{\mathrm{w}}_{\mathrm{cf}}\mathrm{c}\left(\mathrm{t}-1\right)+{\mathrm{b}}_{\mathrm{f}}\right)$         loop over the cells is block now         output gates: $\mathrm{o}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{xo}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{ho}}{\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-1\right){\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-2\right)+{\mathrm{w}}_{\mathrm{co}}\mathrm{c}\left(\mathrm{t}-1\right)+{\mathrm{b}}_{\mathrm{o}}\right)$         update the cell:$\mathrm{c}\left(\mathrm{t}\right)\leftarrow {\mathrm{f}}_{\mathrm{t}}\mathrm{c}\left(\mathrm{t}-1\right)+\mathrm{i}\left(\mathrm{t}\right){\tan \mathrm{h}}_{\mathrm{f}}\left({\mathrm{w}}_{\mathrm{xc}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hc}}{\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-1\right){\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}-2\right)+{\mathrm{b}}_{\mathrm{c}}\right)$           final hidden state/ final output : ${\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}\right)\leftarrow \mathrm{o}\left(\mathrm{t}\right)\odot {\tanh }_{\mathrm{f}}\mathrm{c}\left(\mathrm{t}\right)$    end for 7. Single activity detect 8.  do   Update the weight   end for 9. backward propagation do      for t=0 to n      inputs gates: ${\mathsf{\delta }}_{\mathrm{i}}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{yi}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hi}}{\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+1\right){\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+2\right)+{\mathrm{w}}_{\mathrm{ci}}\mathrm{c}\left(\mathrm{t}+1\right)+{\mathrm{b}}_{\mathrm{i}}\right)$     forget gates: ${\mathsf{\delta }}_{\mathrm{f}}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{yf}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hf}}{\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+1\right){\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+2\right)+{\mathrm{w}}_{\mathrm{cf}}\mathrm{c}\left(\mathrm{t}+1\right)+{\mathrm{b}}_{\mathrm{f}}\right)$     output gates: ${\mathsf{\delta }}_{\mathrm{o}}\left(\mathrm{t}\right)\leftarrow \mathsf{\sigma }\left({\mathrm{w}}_{\mathrm{yo}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{ho}}{\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+1\right){\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+2\right)+{\mathrm{w}}_{\mathrm{co}}\mathrm{c}\left(\mathrm{t}+1\right)+{\mathrm{b}}_{\mathrm{o}}\right)$     cell output: ${\mathsf{\delta }}_{\mathrm{c}}\left(\mathrm{t}\right)\leftarrow {\mathrm{f}}_{\mathrm{t}}{\mathsf{\delta }}_{\mathrm{c}}\left(\mathrm{t}+1\right)+{\mathsf{\delta }}_{\mathrm{i}}\left(\mathrm{t}\right){\tan \mathrm{h}}_{\mathrm{b}}\left({\mathrm{w}}_{\mathrm{yc}}\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{w}}_{\mathrm{hc}}{\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+1\right){\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}+2\right)+{\mathrm{b}}_{\mathrm{c}}\right)$ 10. Hidden state / final output : ${\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}\right)\leftarrow {\mathsf{\delta }}_{\mathrm{o}}\left(\mathrm{t}\right)\odot {\tan \mathrm{h}}_{\mathrm{b}}{\mathsf{\delta }}_{\mathrm{c}}\left(\mathrm{t}\right)$   end for 11. do     z = ${\mathrm{h}}_{\mathrm{f}}\left(\mathrm{t}\right) \mathrm{tends} \mathrm{to} 1$ and ${\mathrm{h}}_{\mathrm{b}}\left(\mathrm{t}\right) \mathrm{tends} \mathrm{to} 1$     Concurrent activity detect   end For 12. do for t=0 to n, k = 0 to n-1 do $\mathsf{\Phi }({\mathrm{z}}_{\mathrm{t}},{\mathrm{z}}_{\mathrm{t}-1},\mathrm{y},\mathrm{t})=\exp {\displaystyle {\displaystyle \sum }_{\mathrm{k}}}{\mathsf{\lambda }}_{\mathrm{k}}{\mathrm{f}}_{\mathrm{k}}({\mathrm{z}}_{\mathrm{t}},{\mathrm{z}}_{\mathrm{t}-1},\mathrm{y},\mathrm{t}),\mathsf{\Psi }({\mathrm{z}}_{\mathcal{u}},{\mathrm{z}}_{\mathcal{v}},\mathrm{y},\mathcal{u},\mathcal{v})=\exp {\displaystyle {\displaystyle \sum }_{\mathrm{k}}}{\mathsf{\lambda }}_{\mathrm{k}}^{\prime }{\mathrm{f}}_{\mathrm{k}}^{\prime }({\mathrm{z}}_{\mathcal{u}},{\mathrm{z}}_{\mathcal{v}},\mathrm{y},\mathcal{u},\mathcal{v})$                   $\frac{\partial \mathrm{P}\left(\mathrm{z}|\mathrm{y}\right)}{\partial {\mathsf{\lambda }}_{\mathrm{k}}}=\frac{\partial \mathcal{L}}{\partial {\mathsf{\lambda }}_{\mathrm{k}}}=\frac{{\mathsf{\lambda }}_{\mathrm{k}}}{{\mathsf{\sigma }}^2}$         end for 13. Interleaved activity detect 14. end for 15. end for 16. end