maths.md

• In N-ary Tree-LSTM, each unit at node :math:j maintains a hidden
• representation :math:h_j and a memory cell :math:c_j. The unit
• :math:j takes the input vector :math:x_j and the hidden
• representations of the child units: :math:h_{jl}, 1\leq l\leq N as
• input, then update its new hidden representation :math:h_j and memory
• cell :math:c_j by:

Tree-LSTM math::

$$ i_j & = & \sigma\left(W^{(i)}x_j + \sum_{l=1}^{N}U^{(i)}l h{jl} + b^{(i)}\right), & (1)\ f_{jk} & = & \sigma\left(W^{(f)}x_j + \sum_{l=1}^{N}U_{kl}^{(f)} h_{jl} + b^{(f)} \right), & (2)\ o_j & = & \sigma\left(W^{(o)}x_j + \sum_{l=1}^{N}U_{l}^{(o)} h_{jl} + b^{(o)} \right), & (3) \ u_j & = & \textrm{tanh}\left(W^{(u)}x_j + \sum_{l=1}^{N} U_l^{(u)}h_{jl} + b^{(u)} \right), & (4)\ c_j & = & i_j \odot u_j + \sum_{l=1}^{N} f_{jl} \odot c_{jl}, &(5) \ h_j & = & o_j \cdot \textrm{tanh}(c_j), &(6) \ $$