Gated recurrent unit

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 gating mechanism to input or forget certain features,^[2] but lacks a context vector or output gate, resulting in fewer parameters than LSTM.^[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 showed that gating is indeed helpful in general, and Bengio's team came to 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 ${\displaystyle h_{0}=0}$.

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

Variables (${\displaystyle d}$ denotes the number of input features and ${\displaystyle e}$ the number of output features):

• ${\displaystyle x_{t}\in \mathbb {R} ^{d}}$: input vector
• ${\displaystyle h_{t}\in \mathbb {R} ^{e}}$: output vector
• ${\displaystyle {\hat {h}}_{t}\in \mathbb {R} ^{e}}$: candidate activation vector
• ${\displaystyle z_{t}\in (0,1)^{e}}$: update gate vector
• ${\displaystyle r_{t}\in (0,1)^{e}}$: reset gate vector
• ${\displaystyle W\in \mathbb {R} ^{e\times d}}$, ${\displaystyle U\in \mathbb {R} ^{e\times e}}$ and ${\displaystyle b\in \mathbb {R} ^{e}}$: parameter matrices and vector which need to be learned during training

Activation functions

• ${\displaystyle \sigma }$: The original is a logistic function.
• ${\displaystyle \phi }$: The original is a hyperbolic tangent.

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

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.

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

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

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

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

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

Minimal gated unit

The minimal gated unit (MGU) 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]

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

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

Light gated recurrent unit

The light gated recurrent unit (LiGRU)^[4] removes the reset gate altogether, replaces tanh with the ReLU activation, and applies batch normalization (BN):

${\displaystyle {\begin{aligned}z_{t}&=\sigma (\operatorname {BN} (W_{z}x_{t})+U_{z}h_{t-1})\\{\tilde {h}}_{t}&=\operatorname {ReLU} (\operatorname {BN} (W_{h}x_{t})+U_{h}h_{t-1})\\h_{t}&=z_{t}\odot h_{t-1}+(1-z_{t})\odot {\tilde {h}}_{t}\end{aligned}}}$

LiGRU has been studied from a Bayesian perspective.^[11] This analysis yielded a variant called light Bayesian recurrent unit (LiBRU), which showed slight improvements over the LiGRU on speech recognition tasks.

References

1. Cho, Kyunghyun; van Merrienboer, Bart; Bahdanau, DZmitry; Bougares, Fethi; Schwenk, Holger; Bengio, Yoshua (2014). "Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation". arXiv:1406.1078 [cs.CL].
2. Felix Gers; Jürgen Schmidhuber; Fred Cummins (1999). "Learning to forget: Continual prediction with LSTM". 9th International Conference on Artificial Neural Networks: ICANN '99. Vol. 1999. pp. 850–855. doi:10.1049/cp:19991218. ISBN 0-85296-721-7.
3. "Recurrent Neural Network Tutorial, Part 4 – Implementing a GRU/LSTM RNN with Python and Theano – WildML". Wildml.com. 2015-10-27. Archived from the original on 2021-11-10. Retrieved May 18, 2016.
4. Ravanelli, Mirco; Brakel, Philemon; Omologo, Maurizio; Bengio, Yoshua (2018). "Light Gated Recurrent Units for Speech Recognition". IEEE Transactions on Emerging Topics in Computational Intelligence. 2 (2): 92–102. arXiv:1803.10225. doi:10.1109/TETCI.2017.2762739. S2CID 4402991.
5. Su, Yuahang; Kuo, Jay (2019). "On extended long short-term memory and dependent bidirectional recurrent neural network". Neurocomputing. 356: 151–161. arXiv:1803.01686. doi:10.1016/j.neucom.2019.04.044. S2CID 3675055.
6. Chung, Junyoung; Gulcehre, Caglar; Cho, KyungHyun; Bengio, Yoshua (2014). "Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling". arXiv:1412.3555 [cs.NE].
7. Gruber, N.; Jockisch, A. (2020), "Are GRU cells more specific and LSTM cells more sensitive in motive classification of text?", Frontiers in Artificial Intelligence, 3: 40, doi:10.3389/frai.2020.00040, PMC 7861254, PMID 33733157, S2CID 220252321
8. Chung, Junyoung; Gulcehre, Caglar; Cho, KyungHyun; Bengio, Yoshua (2014). "Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling". arXiv:1412.3555 [cs.NE].
9. Dey, Rahul; Salem, Fathi M. (2017-01-20). "Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks". arXiv:1701.05923 [cs.NE].
10. Heck, Joel; Salem, Fathi M. (2017-01-12). "Simplified Minimal Gated Unit Variations for Recurrent Neural Networks". arXiv:1701.03452 [cs.NE].
11. Bittar, Alexandre; Garner, Philip N. (May 2021). "A Bayesian Interpretation of the Light Gated Recurrent Unit". ICASSP 2021. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Toronto, ON, Canada: IEEE. pp. 2965–2969. 10.1109/ICASSP39728.2021.9414259.