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Gated recurrent units (GRUs) are a gating mechanism in recurrent neural networks, introduced in 2014 by Kyunghyun Cho et al.^[1] The GRU is like a long short-term memory (LSTM) with a forget gate,^[2] but has fewer parameters than LSTM, as it lacks an output gate.^[3] GRU's performance on certain tasks of polyphonic music modeling, speech signal modeling and natural language processing was found to be similar to that of LSTM.^[4][5] GRUs shown that gating is indeed helpful in general and Bengio's team concluding that no concrete conclusion on which of the two gating units was better.^[6][7]

Architecture

There are several variations on the full gated unit, with gating done using the previous hidden state and the bias in various combinations, and a simplified form called minimal gated unit.^[8]

The operator ${\displaystyle \odot }$ denotes the Hadamard product in the following.

Fully gated unit

Gated Recurrent Unit, fully gated version

Initially, for ${\displaystyle t=0}$, the output vector is ${\displaystyle h_{0}=0}$.

${\displaystyle {\begin{aligned}z_{t}&=\sigma _{g}(W_{z}x_{t}+U_{z}h_{t-1}+b_{z})\\r_{t}&=\sigma _{g}(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\\{\hat {h))_{t}&=\phi _{h}(W_{h}x_{t}+U_{h}(r_{t}\odot h_{t-1})+b_{h})\\h_{t}&=z_{t}\odot h_{t-1}+(1-z_{t})\odot {\hat {h))_{t}\end{aligned))}$

Variables

• ${\displaystyle x_{t))$: input vector
• ${\displaystyle h_{t))$: output vector
• ${\displaystyle {\hat {h))_{t))$: candidate activation vector
• ${\displaystyle z_{t))$: update gate vector
• ${\displaystyle r_{t))$: reset gate vector
• ${\displaystyle W}$, ${\displaystyle U}$ and ${\displaystyle b}$: parameter matrices and vector

Activation functions

• ${\displaystyle \sigma _{g))$: The original is a sigmoid function.
• ${\displaystyle \phi _{h))$: The original is a hyperbolic tangent.

Alternative activation functions are possible, provided that ${\displaystyle \sigma _{g}(x)\in [0,1]}$.

Type 1

Type 2

Type 3

Alternate forms can be created by changing ${\displaystyle z_{t))$ and ${\displaystyle r_{t))$^[9]

• Type 1, each gate depends only on the previous hidden state and the bias.

  ${\displaystyle {\begin{aligned}z_{t}&=\sigma _{g}(U_{z}h_{t-1}+b_{z})\\r_{t}&=\sigma _{g}(U_{r}h_{t-1}+b_{r})\\\end{aligned))}$

• Type 2, each gate depends only on the previous hidden state.

  ${\displaystyle {\begin{aligned}z_{t}&=\sigma _{g}(U_{z}h_{t-1})\\r_{t}&=\sigma _{g}(U_{r}h_{t-1})\\\end{aligned))}$

• Type 3, each gate is computed using only the bias.

  ${\displaystyle {\begin{aligned}z_{t}&=\sigma _{g}(b_{z})\\r_{t}&=\sigma _{g}(b_{r})\\\end{aligned))}$

Minimal gated unit

The minimal gated unit is similar to the fully gated unit, except the update and reset gate vector is merged into a forget gate. This also implies that the equation for the output vector must be changed:^[10]

${\displaystyle {\begin{aligned}f_{t}&=\sigma _{g}(W_{f}x_{t}+U_{f}h_{t-1}+b_{f})\\{\hat {h))_{t}&=\phi _{h}(W_{h}x_{t}+U_{h}(f_{t}\odot h_{t-1})+b_{h})\\h_{t}&=(1-f_{t})\odot h_{t-1}+f_{t}\odot {\hat {h))_{t}\end{aligned))}$

Variables

• ${\displaystyle x_{t))$: input vector
• ${\displaystyle h_{t))$: output vector
• ${\displaystyle {\hat {h))_{t))$: candidate activation vector
• ${\displaystyle f_{t))$: forget vector
• ${\displaystyle W}$, ${\displaystyle U}$ and ${\displaystyle b}$: parameter matrices and vector

Learning Algorithm Recommendation Framework

A Learning Algorithm Recommendation Framework may help guiding the selection of learning algorithm and scientific discipline (e.g. RNN, GAN, RL, CNN,...). The framework has the advantage of having been generated from an extensive analysis of the literature and dedicated to recurrent neural networks and their variations. ^[11]