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| author | Philippe Remy |
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| license | MIT |
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# Keras TCN
*Keras Temporal Convolutional Network*. [[paper](https://arxiv.org/abs/1803.01271)]
Tested with Tensorflow 2.6, 2.7, 2.8 and 2.9.0rc2 (May 4, 2022).
[](https://pepy.tech/project/keras-tcn)
[](https://pepy.tech/project/keras-tcn)
```bash
pip install keras-tcn
pip install keras-tcn --no-dependencies # without the dependencies if you already have TF/Numpy.
```
For MacOS M1 users: `pip install --no-binary keras-tcn keras-tcn`. The `--no-binary` option will force pip to download the sources (tar.gz) and re-compile it locally. Also make sure `grpcio` and `h5py` are installed correctly. There are some tutorials on how to do that online.
## Why Temporal Convolutional Network instead of LSTM/GRU?
- TCNs exhibit longer memory than recurrent architectures with the same capacity.
- Performs better than LSTM/GRU on a vast range of tasks (Seq. MNIST, Adding Problem, Copy Memory, Word-level PTB...).
- Parallelism (convolutional layers), flexible receptive field size (possible to specify how far the model can see), stable gradients (backpropagation through time, vanishing gradients)...
<p align="center">
<img src="misc/Dilated_Conv.png">
<b>Visualization of a stack of dilated causal convolutional layers (Wavenet, 2016)</b><br><br>
</p>
## Index
* [Keras TCN](#keras-tcn)
* [API](#api)
* [Arguments](#arguments)
* [Input shape](#input-shape)
* [Output shape](#output-shape)
* [Receptive field](#receptive-field)
* [Non-causal TCN](#non-causal-tcn)
* [Installation from the sources](#installation-from-the-sources)
* [Run](#run)
* [Reproducible results](#reproducible-results)
* [Tasks](#tasks)
* [Adding Task](#adding-task)
* [Explanation](#explanation)
* [Implementation results](#implementation-results)
* [Copy Memory Task](#copy-memory-task)
* [Explanation](#explanation-1)
* [Implementation results (first epochs)](#implementation-results-first-epochs)
* [Sequential MNIST](#sequential-mnist)
* [Explanation](#explanation-2)
* [Implementation results](#implementation-results-1)
* [Testing](#testing)
* [References](#references)
* [Related](#related)
## API
The usual way is to import the TCN layer and use it inside a Keras model. An example is provided below for a regression task (cf. [tasks](tasks) for other examples):
```python
from tcn import TCN, tcn_full_summary
from tensorflow.keras.layers import Dense
from tensorflow.keras.models import Sequential
# if time_steps > tcn_layer.receptive_field, then we should not
# be able to solve this task.
batch_size, time_steps, input_dim = None, 20, 1
def get_x_y(size=1000):
import numpy as np
pos_indices = np.random.choice(size, size=int(size // 2), replace=False)
x_train = np.zeros(shape=(size, time_steps, 1))
y_train = np.zeros(shape=(size, 1))
x_train[pos_indices, 0] = 1.0 # we introduce the target in the first timestep of the sequence.
y_train[pos_indices, 0] = 1.0 # the task is to see if the TCN can go back in time to find it.
return x_train, y_train
tcn_layer = TCN(input_shape=(time_steps, input_dim))
# The receptive field tells you how far the model can see in terms of timesteps.
print('Receptive field size =', tcn_layer.receptive_field)
m = Sequential([
tcn_layer,
Dense(1)
])
m.compile(optimizer='adam', loss='mse')
tcn_full_summary(m, expand_residual_blocks=False)
x, y = get_x_y()
m.fit(x, y, epochs=10, validation_split=0.2)
```
A ready-to-use TCN model can be used that way (cf. [tasks](tasks) for some examples):
```python
from tcn import compiled_tcn
model = compiled_tcn(...)
model.fit(x, y) # Keras model.
```
### Arguments
```python
TCN(
nb_filters=64,
kernel_size=3,
nb_stacks=1,
dilations=(1, 2, 4, 8, 16, 32),
padding='causal',
use_skip_connections=True,
dropout_rate=0.0,
return_sequences=False,
activation='relu',
kernel_initializer='he_normal',
use_batch_norm=False,
use_layer_norm=False,
use_weight_norm=False,
**kwargs
)
```
- `nb_filters`: Integer. The number of filters to use in the convolutional layers. Would be similar to `units` for LSTM. Can be a list.
- `kernel_size`: Integer. The size of the kernel to use in each convolutional layer.
- `dilations`: List/Tuple. A dilation list. Example is: [1, 2, 4, 8, 16, 32, 64].
- `nb_stacks`: Integer. The number of stacks of residual blocks to use.
- `padding`: String. The padding to use in the convolutions. 'causal' for a causal network (as in the original implementation) and 'same' for a non-causal network.
- `use_skip_connections`: Boolean. If we want to add skip connections from input to each residual block.
- `return_sequences`: Boolean. Whether to return the last output in the output sequence, or the full sequence.
- `dropout_rate`: Float between 0 and 1. Fraction of the input units to drop.
- `activation`: The activation used in the residual blocks o = activation(x + F(x)).
- `kernel_initializer`: Initializer for the kernel weights matrix (Conv1D).
- `use_batch_norm`: Whether to use batch normalization in the residual layers or not.
- `use_layer_norm`: Whether to use layer normalization in the residual layers or not.
- `use_weight_norm`: Whether to use weight normalization in the residual layers or not.
- `kwargs`: Any other set of arguments for configuring the parent class Layer. For example "name=str", Name of the model. Use unique names when using multiple TCN.
### Input shape
3D tensor with shape `(batch_size, timesteps, input_dim)`.
`timesteps` can be None. This can be useful if each sequence is of a different length: [Multiple Length Sequence Example](tasks/multi_length_sequences.py).
### Output shape
- if `return_sequences=True`: 3D tensor with shape `(batch_size, timesteps, nb_filters)`.
- if `return_sequences=False`: 2D tensor with shape `(batch_size, nb_filters)`.
### How do I choose the correct set of parameters to configure my TCN layer?
Here are some of my notes regarding my experience using TCN:
- `nb_filters`: Present in any ConvNet architecture. It is linked to the predictive power of the model and affects the size of your network. The more, the better unless you start to overfit. It's similar to the number of units in an LSTM/GRU architecture too.
- `kernel_size`: Controls the spatial area/volume considered in the convolutional ops. Good values are usually between 2 and 8. If you think your sequence heavily depends on t-1 and t-2, but less on the rest, then choose a kernel size of 2/3. For NLP tasks, we prefer bigger kernel sizes. A large kernel size will make your network much bigger.
- `dilations`: It controls how deep your TCN layer is. Usually, consider a list with multiple of two. You can guess how many dilations you need by matching the receptive field (of the TCN) with the length of features in your sequence. For example, if your input sequence is periodic, you might want to have multiples of that period as dilations.
- `nb_stacks`: Not very useful unless your sequences are very long (like waveforms with hundreds of thousands of time steps).
- `padding`: I have only used `causal` since a TCN stands for Temporal Convolutional Networks. Causal prevents information leakage.
- `use_skip_connections`: Skip connections connects layers, similarly to DenseNet. It helps the gradients flow. Unless you experience a drop in performance, you should always activate it.
- `return_sequences`: Same as the one present in the LSTM layer. Refer to the Keras doc for this parameter.
- `dropout_rate`: Similar to `recurrent_dropout` for the LSTM layer. I usually don't use it much. Or set it to a low value like `0.05`.
- `activation`: Leave it to default. I have never changed it.
- `kernel_initializer`: If the training of the TCN gets stuck, it might be worth changing this parameter. For example: `glorot_uniform`.
- `use_batch_norm`, `use_weight_norm`, `use_weight_norm`: Use normalization if your network is big enough and the task contains enough data. I usually prefer using `use_layer_norm`, but you can try them all and see which one works the best.
### Receptive field
The receptive field is defined as: the maximum number of steps back in time from current sample at time T, that a filter from (block, layer, stack, TCN) can hit (effective history) + 1. The receptive field of the TCN can be calculated using the formula:
<p align="center">
<img width="400" src="https://user-images.githubusercontent.com/4516927/112719508-a55bd200-8f3c-11eb-83c0-88c6171a07d7.png">
</p>
where N<sub>stack</sub> is the number of stacks, N<sub>b</sub> is the number of residual blocks per stack, d is a vector containing the dilations of each residual block in each stack, and K is the kernel size. The 2 is there because there are two `Conv1d` layers in a single `ResidualBlock`.
Ideally you want your receptive field to be bigger than the largest length of input sequence, if you pass a sequence longer than your receptive field into the model, any extra values (further back in the sequence) will be replaced with zeros.
#### Examples
*NOTE*: Unlike the TCN, example figures only include a single `Conv1d` per layer, so the formula becomes R<sub>field</sub> = 1 + (K-1)⋅N<sub>stack</sub>⋅Σi di (without the factor 2).
- If a dilated conv net has only one stack of residual blocks with a kernel size of `2` and dilations `[1, 2, 4, 8]`, its receptive field is `16`. The image below illustrates it:
<p align="center">
<img src="https://user-images.githubusercontent.com/40159126/41830054-10e56fda-7871-11e8-8591-4fa46680c17f.png">
<b>ks = 2, dilations = [1, 2, 4, 8], 1 block</b><br><br>
</p>
- If a dilated conv net has 2 stacks of residual blocks, you would have the situation below, that is, an increase in the receptive field up to 31:
<p align="center">
<img src="https://user-images.githubusercontent.com/40159126/41830618-a8f82a8a-7874-11e8-9d4f-2ebb70a31465.jpg">
<b>ks = 2, dilations = [1, 2, 4, 8], 2 blocks</b><br><br>
</p>
- If we increased the number of stacks to 3, the size of the receptive field would increase again, such as below:
<p align="center">
<img src="https://user-images.githubusercontent.com/40159126/41830628-ae6e73d4-7874-11e8-8ecd-cea37efa33f1.jpg">
<b>ks = 2, dilations = [1, 2, 4, 8], 3 blocks</b><br><br>
</p>
### Non-causal TCN
Making the TCN architecture non-causal allows it to take the future into consideration to do its prediction as shown in the figure below.
However, it is not anymore suitable for real-time applications.
<p align="center">
<img src="misc/Non_Causal.png">
<b>Non-Causal TCN - ks = 3, dilations = [1, 2, 4, 8], 1 block</b><br><br>
</p>
To use a non-causal TCN, specify `padding='valid'` or `padding='same'` when initializing the TCN layers.
## Installation from the sources
```bash
git clone git@github.com:philipperemy/keras-tcn.git && cd keras-tcn
virtualenv -p python3 venv
source venv/bin/activate
pip install -r requirements.txt
pip install .
```
## Run
Once `keras-tcn` is installed as a package, you can take a glimpse of what is possible to do with TCNs. Some tasks examples are available in the repository for this purpose:
```bash
cd adding_problem/
python main.py # run adding problem task
cd copy_memory/
python main.py # run copy memory task
cd mnist_pixel/
python main.py # run sequential mnist pixel task
```
## Reproducible results
Reproducible results are possible on (NVIDIA) GPUs using the [tensorflow-determinism](https://github.com/NVIDIA/tensorflow-determinism) library. It was tested with keras-tcn by @lingdoc and he got reproducible results.
## Tasks
### Word PTB
Language modeling remains one of the primary applications of recurrent networks. In this example, we show that TCN can beat LSTM without too much tuning. More here: [WordPTB](tasks/word_ptb/README.md).
<p align="center">
<img src="tasks/word_ptb/result.png" width="800"><br>
<i>TCN vs LSTM (comparable number of weights)</i><br><br>
</p>
### Adding Task
The task consists of feeding a large array of decimal numbers to the network, along with a boolean array of the same length. The objective is to sum the two decimals where the boolean array contain the two 1s.
#### Explanation
<p align="center">
<img src="misc/Adding_Task.png">
<b>Adding Problem Task</b><br><br>
</p>
#### Implementation results
```
782/782 [==============================] - 154s 197ms/step - loss: 0.8437 - val_loss: 0.1883
782/782 [==============================] - 154s 196ms/step - loss: 0.0702 - val_loss: 0.0111
[...]
782/782 [==============================] - 152s 194ms/step - loss: 6.9630e-04 - val_loss: 3.7180e-04
```
### Copy Memory Task
The copy memory consists of a very large array:
- At the beginning, there's the vector x of length N. This is the vector to copy.
- At the end, N+1 9s are present. The first 9 is seen as a delimiter.
- In the middle, only 0s are there.
The idea is to copy the content of the vector x to the end of the large array. The task is made sufficiently complex by increasing the number of 0s in the middle.
#### Explanation
<p align="center">
<img src="misc/Copy_Memory_Task.png">
<b>Copy Memory Task</b><br><br>
</p>
#### Implementation results (first epochs)
```
118/118 [==============================] - 17s 143ms/step - loss: 1.1732 - accuracy: 0.6725 - val_loss: 0.1119 - val_accuracy: 0.9796
[...]
118/118 [==============================] - 15s 125ms/step - loss: 0.0268 - accuracy: 0.9885 - val_loss: 0.0206 - val_accuracy: 0.9908
118/118 [==============================] - 15s 125ms/step - loss: 0.0228 - accuracy: 0.9900 - val_loss: 0.0169 - val_accuracy: 0.9933
```
### Sequential MNIST
#### Explanation
The idea here is to consider MNIST images as 1-D sequences and feed them to the network. This task is particularly hard because sequences are 28*28 = 784 elements. In order to classify correctly, the network has to remember all the sequence. Usual LSTM are unable to perform well on this task.
<p align="center">
<img src="misc/Sequential_MNIST_Task.png">
<b>Sequential MNIST</b><br><br>
</p>
#### Implementation results
```
1875/1875 [==============================] - 46s 25ms/step - loss: 0.0949 - accuracy: 0.9706 - val_loss: 0.0763 - val_accuracy: 0.9756
1875/1875 [==============================] - 46s 25ms/step - loss: 0.0831 - accuracy: 0.9743 - val_loss: 0.0656 - val_accuracy: 0.9807
[...]
1875/1875 [==============================] - 46s 25ms/step - loss: 0.0486 - accuracy: 0.9840 - val_loss: 0.0572 - val_accuracy: 0.9832
1875/1875 [==============================] - 46s 25ms/step - loss: 0.0453 - accuracy: 0.9858 - val_loss: 0.0424 - val_accuracy: 0.9862
```
## Testing
Testing is based on Tox.
```
pip install tox
tox
```
## References
- https://github.com/locuslab/TCN/ (TCN for Pytorch)
- https://arxiv.org/pdf/1803.01271 (An Empirical Evaluation of Generic Convolutional and Recurrent Networks
for Sequence Modeling)
- https://arxiv.org/pdf/1609.03499 (Original Wavenet paper)
## Related
- https://github.com/Baichenjia/Tensorflow-TCN (Tensorflow Eager implementation of TCNs)
## Citation
```
@misc{KerasTCN,
author = {Philippe Remy},
title = {Temporal Convolutional Networks for Keras},
year = {2020},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/philipperemy/keras-tcn}},
}
```
## Contributors
<a href="https://github.com/philipperemy/keras-tcn/graphs/contributors">
<img src="https://contrib.rocks/image?repo=philipperemy/keras-tcn" />
</a>
Raw data
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"description": "# Keras TCN\n\n*Keras Temporal Convolutional Network*. [[paper](https://arxiv.org/abs/1803.01271)]\n\nTested with Tensorflow 2.6, 2.7, 2.8 and 2.9.0rc2 (May 4, 2022).\n\n[](https://pepy.tech/project/keras-tcn)\n[](https://pepy.tech/project/keras-tcn)\n\n```bash\npip install keras-tcn\npip install keras-tcn --no-dependencies # without the dependencies if you already have TF/Numpy.\n```\n\nFor MacOS M1 users: `pip install --no-binary keras-tcn keras-tcn`. The `--no-binary` option will force pip to download the sources (tar.gz) and re-compile it locally. Also make sure `grpcio` and `h5py` are installed correctly. There are some tutorials on how to do that online.\n\n## Why Temporal Convolutional Network instead of LSTM/GRU?\n\n- TCNs exhibit longer memory than recurrent architectures with the same capacity.\n- Performs better than LSTM/GRU on a vast range of tasks (Seq. MNIST, Adding Problem, Copy Memory, Word-level PTB...).\n- Parallelism (convolutional layers), flexible receptive field size (possible to specify how far the model can see), stable gradients (backpropagation through time, vanishing gradients)...\n\n<p align=\"center\">\n <img src=\"misc/Dilated_Conv.png\">\n <b>Visualization of a stack of dilated causal convolutional layers (Wavenet, 2016)</b><br><br>\n</p>\n\n\n## Index\n\n * [Keras TCN](#keras-tcn)\n * [API](#api)\n * [Arguments](#arguments)\n * [Input shape](#input-shape)\n * [Output shape](#output-shape)\n * [Receptive field](#receptive-field)\n * [Non-causal TCN](#non-causal-tcn)\n * [Installation from the sources](#installation-from-the-sources)\n * [Run](#run)\n * [Reproducible results](#reproducible-results)\n * [Tasks](#tasks)\n * [Adding Task](#adding-task)\n * [Explanation](#explanation)\n * [Implementation results](#implementation-results)\n * [Copy Memory Task](#copy-memory-task)\n * [Explanation](#explanation-1)\n * [Implementation results (first epochs)](#implementation-results-first-epochs)\n * [Sequential MNIST](#sequential-mnist)\n * [Explanation](#explanation-2)\n * [Implementation results](#implementation-results-1)\n * [Testing](#testing)\n * [References](#references)\n * [Related](#related)\n\n\n## API\n\nThe usual way is to import the TCN layer and use it inside a Keras model. An example is provided below for a regression task (cf. [tasks](tasks) for other examples):\n\n```python\nfrom tcn import TCN, tcn_full_summary\nfrom tensorflow.keras.layers import Dense\nfrom tensorflow.keras.models import Sequential\n\n# if time_steps > tcn_layer.receptive_field, then we should not\n# be able to solve this task.\nbatch_size, time_steps, input_dim = None, 20, 1\n\n\ndef get_x_y(size=1000):\n import numpy as np\n pos_indices = np.random.choice(size, size=int(size // 2), replace=False)\n x_train = np.zeros(shape=(size, time_steps, 1))\n y_train = np.zeros(shape=(size, 1))\n x_train[pos_indices, 0] = 1.0 # we introduce the target in the first timestep of the sequence.\n y_train[pos_indices, 0] = 1.0 # the task is to see if the TCN can go back in time to find it.\n return x_train, y_train\n\n\ntcn_layer = TCN(input_shape=(time_steps, input_dim))\n# The receptive field tells you how far the model can see in terms of timesteps.\nprint('Receptive field size =', tcn_layer.receptive_field)\n\nm = Sequential([\n tcn_layer,\n Dense(1)\n])\n\nm.compile(optimizer='adam', loss='mse')\n\ntcn_full_summary(m, expand_residual_blocks=False)\n\nx, y = get_x_y()\nm.fit(x, y, epochs=10, validation_split=0.2)\n```\n\nA ready-to-use TCN model can be used that way (cf. [tasks](tasks) for some examples):\n\n```python\nfrom tcn import compiled_tcn\n\nmodel = compiled_tcn(...)\nmodel.fit(x, y) # Keras model.\n```\n\n### Arguments\n\n\n\n```python\nTCN(\n nb_filters=64,\n kernel_size=3,\n nb_stacks=1,\n dilations=(1, 2, 4, 8, 16, 32),\n padding='causal',\n use_skip_connections=True,\n dropout_rate=0.0,\n return_sequences=False,\n activation='relu',\n kernel_initializer='he_normal',\n use_batch_norm=False,\n use_layer_norm=False,\n use_weight_norm=False,\n **kwargs\n)\n```\n\n- `nb_filters`: Integer. The number of filters to use in the convolutional layers. Would be similar to `units` for LSTM. Can be a list.\n- `kernel_size`: Integer. The size of the kernel to use in each convolutional layer.\n- `dilations`: List/Tuple. A dilation list. Example is: [1, 2, 4, 8, 16, 32, 64].\n- `nb_stacks`: Integer. The number of stacks of residual blocks to use.\n- `padding`: String. The padding to use in the convolutions. 'causal' for a causal network (as in the original implementation) and 'same' for a non-causal network.\n- `use_skip_connections`: Boolean. If we want to add skip connections from input to each residual block.\n- `return_sequences`: Boolean. Whether to return the last output in the output sequence, or the full sequence.\n- `dropout_rate`: Float between 0 and 1. Fraction of the input units to drop.\n- `activation`: The activation used in the residual blocks o = activation(x + F(x)).\n- `kernel_initializer`: Initializer for the kernel weights matrix (Conv1D).\n- `use_batch_norm`: Whether to use batch normalization in the residual layers or not.\n- `use_layer_norm`: Whether to use layer normalization in the residual layers or not.\n- `use_weight_norm`: Whether to use weight normalization in the residual layers or not.\n- `kwargs`: Any other set of arguments for configuring the parent class Layer. For example \"name=str\", Name of the model. Use unique names when using multiple TCN.\n\n### Input shape\n\n3D tensor with shape `(batch_size, timesteps, input_dim)`.\n\n`timesteps` can be None. This can be useful if each sequence is of a different length: [Multiple Length Sequence Example](tasks/multi_length_sequences.py).\n\n### Output shape\n\n- if `return_sequences=True`: 3D tensor with shape `(batch_size, timesteps, nb_filters)`.\n- if `return_sequences=False`: 2D tensor with shape `(batch_size, nb_filters)`.\n\n\n### How do I choose the correct set of parameters to configure my TCN layer?\n\nHere are some of my notes regarding my experience using TCN:\n\n- `nb_filters`: Present in any ConvNet architecture. It is linked to the predictive power of the model and affects the size of your network. The more, the better unless you start to overfit. It's similar to the number of units in an LSTM/GRU architecture too.\n- `kernel_size`: Controls the spatial area/volume considered in the convolutional ops. Good values are usually between 2 and 8. If you think your sequence heavily depends on t-1 and t-2, but less on the rest, then choose a kernel size of 2/3. For NLP tasks, we prefer bigger kernel sizes. A large kernel size will make your network much bigger.\n- `dilations`: It controls how deep your TCN layer is. Usually, consider a list with multiple of two. You can guess how many dilations you need by matching the receptive field (of the TCN) with the length of features in your sequence. For example, if your input sequence is periodic, you might want to have multiples of that period as dilations.\n- `nb_stacks`: Not very useful unless your sequences are very long (like waveforms with hundreds of thousands of time steps).\n- `padding`: I have only used `causal` since a TCN stands for Temporal Convolutional Networks. Causal prevents information leakage.\n- `use_skip_connections`: Skip connections connects layers, similarly to DenseNet. It helps the gradients flow. Unless you experience a drop in performance, you should always activate it.\n- `return_sequences`: Same as the one present in the LSTM layer. Refer to the Keras doc for this parameter.\n- `dropout_rate`: Similar to `recurrent_dropout` for the LSTM layer. I usually don't use it much. Or set it to a low value like `0.05`.\n- `activation`: Leave it to default. I have never changed it.\n- `kernel_initializer`: If the training of the TCN gets stuck, it might be worth changing this parameter. For example: `glorot_uniform`.\n\n- `use_batch_norm`, `use_weight_norm`, `use_weight_norm`: Use normalization if your network is big enough and the task contains enough data. I usually prefer using `use_layer_norm`, but you can try them all and see which one works the best.\n\n\n### Receptive field\n\nThe receptive field is defined as: the maximum number of steps back in time from current sample at time T, that a filter from (block, layer, stack, TCN) can hit (effective history) + 1. The receptive field of the TCN can be calculated using the formula:\n<p align=\"center\">\n <img width=\"400\" src=\"https://user-images.githubusercontent.com/4516927/112719508-a55bd200-8f3c-11eb-83c0-88c6171a07d7.png\">\n</p>\n\nwhere N<sub>stack</sub> is the number of stacks, N<sub>b</sub> is the number of residual blocks per stack, d is a vector containing the dilations of each residual block in each stack, and K is the kernel size. The 2 is there because there are two `Conv1d` layers in a single `ResidualBlock`.\n\nIdeally you want your receptive field to be bigger than the largest length of input sequence, if you pass a sequence longer than your receptive field into the model, any extra values (further back in the sequence) will be replaced with zeros.\n\n#### Examples\n\n*NOTE*: Unlike the TCN, example figures only include a single `Conv1d` per layer, so the formula becomes R<sub>field</sub> = 1 + (K-1)\u22c5N<sub>stack</sub>\u22c5\u03a3i di (without the factor 2).\n\n- If a dilated conv net has only one stack of residual blocks with a kernel size of `2` and dilations `[1, 2, 4, 8]`, its receptive field is `16`. The image below illustrates it:\n\n<p align=\"center\">\n <img src=\"https://user-images.githubusercontent.com/40159126/41830054-10e56fda-7871-11e8-8591-4fa46680c17f.png\">\n <b>ks = 2, dilations = [1, 2, 4, 8], 1 block</b><br><br>\n</p>\n\n- If a dilated conv net has 2 stacks of residual blocks, you would have the situation below, that is, an increase in the receptive field up to 31:\n\n<p align=\"center\">\n <img src=\"https://user-images.githubusercontent.com/40159126/41830618-a8f82a8a-7874-11e8-9d4f-2ebb70a31465.jpg\">\n <b>ks = 2, dilations = [1, 2, 4, 8], 2 blocks</b><br><br>\n</p>\n\n\n- If we increased the number of stacks to 3, the size of the receptive field would increase again, such as below:\n\n<p align=\"center\">\n <img src=\"https://user-images.githubusercontent.com/40159126/41830628-ae6e73d4-7874-11e8-8ecd-cea37efa33f1.jpg\">\n <b>ks = 2, dilations = [1, 2, 4, 8], 3 blocks</b><br><br>\n</p>\n\n\n### Non-causal TCN\n\nMaking the TCN architecture non-causal allows it to take the future into consideration to do its prediction as shown in the figure below.\n\nHowever, it is not anymore suitable for real-time applications.\n\n<p align=\"center\">\n <img src=\"misc/Non_Causal.png\">\n <b>Non-Causal TCN - ks = 3, dilations = [1, 2, 4, 8], 1 block</b><br><br>\n</p>\n\nTo use a non-causal TCN, specify `padding='valid'` or `padding='same'` when initializing the TCN layers.\n\n## Installation from the sources\n\n```bash\ngit clone git@github.com:philipperemy/keras-tcn.git && cd keras-tcn\nvirtualenv -p python3 venv\nsource venv/bin/activate\npip install -r requirements.txt\npip install .\n```\n\n## Run\n\nOnce `keras-tcn` is installed as a package, you can take a glimpse of what is possible to do with TCNs. Some tasks examples are available in the repository for this purpose:\n\n```bash\ncd adding_problem/\npython main.py # run adding problem task\n\ncd copy_memory/\npython main.py # run copy memory task\n\ncd mnist_pixel/\npython main.py # run sequential mnist pixel task\n```\n\n## Reproducible results\n\nReproducible results are possible on (NVIDIA) GPUs using the [tensorflow-determinism](https://github.com/NVIDIA/tensorflow-determinism) library. It was tested with keras-tcn by @lingdoc and he got reproducible results.\n\n## Tasks\n\n### Word PTB\n\nLanguage modeling remains one of the primary applications of recurrent networks. In this example, we show that TCN can beat LSTM without too much tuning. More here: [WordPTB](tasks/word_ptb/README.md).\n\n<p align=\"center\">\n <img src=\"tasks/word_ptb/result.png\" width=\"800\"><br>\n <i>TCN vs LSTM (comparable number of weights)</i><br><br>\n</p>\n\n### Adding Task\n\nThe task consists of feeding a large array of decimal numbers to the network, along with a boolean array of the same length. The objective is to sum the two decimals where the boolean array contain the two 1s.\n\n#### Explanation\n\n<p align=\"center\">\n <img src=\"misc/Adding_Task.png\">\n <b>Adding Problem Task</b><br><br>\n</p>\n\n#### Implementation results\n\n```\n782/782 [==============================] - 154s 197ms/step - loss: 0.8437 - val_loss: 0.1883\n782/782 [==============================] - 154s 196ms/step - loss: 0.0702 - val_loss: 0.0111\n[...]\n782/782 [==============================] - 152s 194ms/step - loss: 6.9630e-04 - val_loss: 3.7180e-04\n```\n\n### Copy Memory Task\n\nThe copy memory consists of a very large array:\n- At the beginning, there's the vector x of length N. This is the vector to copy.\n- At the end, N+1 9s are present. The first 9 is seen as a delimiter.\n- In the middle, only 0s are there.\n\nThe idea is to copy the content of the vector x to the end of the large array. The task is made sufficiently complex by increasing the number of 0s in the middle.\n\n#### Explanation\n\n<p align=\"center\">\n <img src=\"misc/Copy_Memory_Task.png\">\n <b>Copy Memory Task</b><br><br>\n</p>\n\n#### Implementation results (first epochs)\n\n```\n118/118 [==============================] - 17s 143ms/step - loss: 1.1732 - accuracy: 0.6725 - val_loss: 0.1119 - val_accuracy: 0.9796\n[...]\n118/118 [==============================] - 15s 125ms/step - loss: 0.0268 - accuracy: 0.9885 - val_loss: 0.0206 - val_accuracy: 0.9908\n118/118 [==============================] - 15s 125ms/step - loss: 0.0228 - accuracy: 0.9900 - val_loss: 0.0169 - val_accuracy: 0.9933\n```\n\n### Sequential MNIST\n\n#### Explanation\n\nThe idea here is to consider MNIST images as 1-D sequences and feed them to the network. This task is particularly hard because sequences are 28*28 = 784 elements. In order to classify correctly, the network has to remember all the sequence. Usual LSTM are unable to perform well on this task.\n\n<p align=\"center\">\n <img src=\"misc/Sequential_MNIST_Task.png\">\n <b>Sequential MNIST</b><br><br>\n</p>\n\n#### Implementation results\n\n```\n1875/1875 [==============================] - 46s 25ms/step - loss: 0.0949 - accuracy: 0.9706 - val_loss: 0.0763 - val_accuracy: 0.9756\n1875/1875 [==============================] - 46s 25ms/step - loss: 0.0831 - accuracy: 0.9743 - val_loss: 0.0656 - val_accuracy: 0.9807\n[...]\n1875/1875 [==============================] - 46s 25ms/step - loss: 0.0486 - accuracy: 0.9840 - val_loss: 0.0572 - val_accuracy: 0.9832\n1875/1875 [==============================] - 46s 25ms/step - loss: 0.0453 - accuracy: 0.9858 - val_loss: 0.0424 - val_accuracy: 0.9862\n```\n\n## Testing\n\nTesting is based on Tox.\n\n```\npip install tox\ntox\n```\n\n## References\n- https://github.com/locuslab/TCN/ (TCN for Pytorch)\n- https://arxiv.org/pdf/1803.01271 (An Empirical Evaluation of Generic Convolutional and Recurrent Networks\nfor Sequence Modeling)\n- https://arxiv.org/pdf/1609.03499 (Original Wavenet paper)\n\n## Related\n- https://github.com/Baichenjia/Tensorflow-TCN (Tensorflow Eager implementation of TCNs)\n\n## Citation\n\n```\n@misc{KerasTCN,\n author = {Philippe Remy},\n title = {Temporal Convolutional Networks for Keras},\n year = {2020},\n publisher = {GitHub},\n journal = {GitHub repository},\n howpublished = {\\url{https://github.com/philipperemy/keras-tcn}},\n}\n```\n\n## Contributors\n\n<a href=\"https://github.com/philipperemy/keras-tcn/graphs/contributors\">\n <img src=\"https://contrib.rocks/image?repo=philipperemy/keras-tcn\" />\n</a>\n",
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