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Recurrent Highway Networks

Note: For Tensorflow 1.0, please use this branch.


This repository contains code accompanying the paper Recurrent Highway Networks (RHNs). RHNs are an extension of Long Short Term Memory Networks with forget gates to enable the learning of deep recurrent state transitions. We provide implementations in Tensorflow, Torch7 and Brainstorm libraries, and welcome additional implementations from the community.


The recurrent state transition in typical recurrent networks is modeled with a single step non-linear function. This can be very inefficient in principle for modeling complicated transitions, requiring very large networks. Increased recurrence depth allows RHNs to model complex transitions more efficiently achieving substantially improved results.

Moreover, using depth d in the recurrent state transition is much more powerful than stacking d recurrent layers. The figures below illustrate that if we consider the functions mapping one hidden state to another T time steps apart, its maximum depth scales as the product of d and T instead of the sum. Of course, in general RHNs can also be stacked to get the best of both worlds.

Stacked RNN Deep Transition RNN
Stacked RNN Deep Transition RNN

RHN Benchmarks reproducible with the provided code

Influence of recurrence depth on performance

The score (perplexity) of word-level language models on the Penn Treebank dataset dramatically improves as recurrence depth increases while keeping the model size fixed. WT refers to tying the input and output weights for regularization. This idea was independently developed by Inan and Khosravi and Press and Wolf. Recently, Inan et al. also posted a more detailed follow-up paper.

Rec. depth #Units/Layer Best Validation Test Best Validation (WT) Test (WT)
1 1275 92.4 89.2 93.2 90.6
2 1180 79.0 76.3 76.9 75.1
3 1110 75.0 72.6 72.7 70.6
4 1050 73.3 70.9 70.8 68.6
5 1000 72.0 69.8 69.7 67.7
6 960 71.9 69.3 69.1 66.6
7 920 71.7 68.7 68.7 66.4
8 890 71.2 68.5 68.2 66.1
9 860 71.3 68.5 68.1 66.0
10 830 71.3 68.3 68.3 66.0

Comparison to SOTA language models on Penn Treebank

Network Size Best Validation Test
LSTM+dropout 66 M 82.2 78.4
Variational LSTM 66 M 77.3 75.0
Variational LSTM with MC dropout 66 M - 73.4
Variational LSTM + WT 51 M 75.8 73.2
Pointer Sentinel LSTM 21 M 72.4 70.9
Ensemble of 38 large LSTMs+dropout 66 M per LSTM 71.9 68.7
Ensemble of 10 large Variational LSTMs 66 M per LSTM - 68.7
Variational RHN (depth=8) 32 M 71.2 68.5
Variational RHN + WT (depth=10) 23 M 67.9 65.4
Variational RHN + WT with MC dropout (depth=5)* 22 M - 64.4

*We used 1000 samples for MC dropout as done by Gal for LSTMs, but we've only evaluated the depth 5 model so far.

Wikipedia (enwik8) next character prediction modeling

Network Network size Test BPC
Grid-LSTM 16.8 M 1.47
MI-LSTM 17 M 1.44
mLSTM 21 M 1.42
Layernorm HyperNetworks 27 M 1.34
Layernorm HM-LSTM 35 M 1.32
RHN - Rec. depth 5 23 M 1.31
RHN - Rec. depth 10 21 M 1.30
Large RHN - Rec. depth 10 46 M 1.27

Wikipedia (text8) next character prediction modeling

Network Network size Test BPC
MI-LSTM 17 M 1.44
mLSTM 10 M 1.40
BN LSTM 16 M 1.36
HM-LSTM 35 M 1.32
Layernorm HM-LSTM 35 M 1.29
RHN - Rec. depth 10 20 M 1.29
Large RHN - Rec. depth 10 45 M 1.27



Tensorflow code for RHNs is built by heavily extending the LSTM language modeling example provided in Tensorflow. It supports Variational RHNs as used in the paper, which use the same dropout mask at each time step and at all layers inside the recurrence. Note that this implementation uses the same dropout mask for both the H and T non-linear transforms in RHNs while the Torch7 implementation uses different dropout masks for different transformations. The Theano implementation can be configured either way.


We recommend installing Tensorflow in a virtual environment. In addition to the usual Tensorflow dependencies, the code uses Sacred so you need to do:

$ pip install sacred


To reproduce SOTA results on Penn Treebank:

$ python with ptb_sota

To reproduce SOTA results on enwik8/text8 (Wikipedia), first download the dataset from or for text8 and unzip it into the data directory, then run:

$ python with enwik8_sota


$ python with text8_sota

Change some hyperparameters and run:

$ python with ptb_sota depth=20

This is a Sacred experiment, so you check the hyperparameter options using the print_config command, e.g.

$ python print_config with ptb_sota


Torch7 code is based on Yarin Gal's adaptation of Wojciech Zaremba's code implementing variational dropout. The main additions to Gal's code are the Recurrent Highway Network layer, the initial biasing of T-gate activations to facilitate learning and a few adjustments to other network parameters such as rnn_size and dropout probabilities.


We recommend installing Torch from the official website. To ensure the code runs some packages need to be installed:

$ luarocks install nngraph 
$ luarocks install cutorch
$ luarocks install nn
$ luarocks install hdf5


$ th torch_rhn_ptb.lua

To run on the enwik8 dataset, first download and prepare the data (see data/README for details):

$ cd data
$ python

Then you can train by running:

$ th toch_rhn_enwik8.lua


The Theano code's configuration and usage is similar to that of the Tensorflow code. In this implementation two configuration options were added:

  • Whether the same dropout masks are used for both the H and T non-linear transforms.
  • How all biases other than T's bias are initialized: randomly (as in the Tensorflow implementation) or with zeros (or any other fixed value).

The following isn't implemented:

  • MC dropout


Theano and Sacred.


As with the Tensorflow code, the SOTA results on Penn Treebank and on enwik8 (Wikipedia) can be reproduced:

$ python with ptb_sota
$ python with enwik8_sota


An RHN layer implementation is also provided in Brainstorm. This implementation does not use variational dropout. It can be used in a Brainstorm experiment by simply importing HighwayRNNCoupledGates from


If you use RHNs in your work, please cite us:

  title="{Recurrent Highway Networks}",
  author={Zilly, Julian Georg and Srivastava, Rupesh Kumar and Koutn{\'\i}k, Jan and Schmidhuber, J{\"u}rgen},
  journal={arXiv preprint arXiv:1607.03474},


MIT License.


Recurrent Highway Networks - Implementations for Tensorflow, Torch7, Theano and Brainstorm








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