├── requirements.txt ├── assets ├── 1.png ├── lstm_after.png ├── attention_1.png ├── lstm_before.png ├── graph_multi_attention.png └── graph_single_attention.png ├── .gitignore ├── attention_dense.py ├── attention_utils.py ├── attention_lstm.py ├── README.md └── LICENSE /requirements.txt: -------------------------------------------------------------------------------- 1 | Keras==2.0.2 2 | matplotlib==2.0.0 3 | numpy==1.13.0 4 | pandas==0.18.1 5 | -------------------------------------------------------------------------------- /assets/1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/1.png -------------------------------------------------------------------------------- /assets/lstm_after.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/lstm_after.png -------------------------------------------------------------------------------- /assets/attention_1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/attention_1.png -------------------------------------------------------------------------------- /assets/lstm_before.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/lstm_before.png -------------------------------------------------------------------------------- /assets/graph_multi_attention.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/graph_multi_attention.png -------------------------------------------------------------------------------- /assets/graph_single_attention.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/leriomaggio/keras-attention-mechanism/master/assets/graph_single_attention.png -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | .idea/ 9 | # Distribution / packaging 10 | .Python 11 | env/ 12 | build/ 13 | develop-eggs/ 14 | dist/ 15 | downloads/ 16 | eggs/ 17 | .eggs/ 18 | lib/ 19 | lib64/ 20 | parts/ 21 | sdist/ 22 | var/ 23 | wheels/ 24 | *.egg-info/ 25 | .installed.cfg 26 | *.egg 27 | 28 | # PyInstaller 29 | # Usually these files are written by a python script from a template 30 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 31 | *.manifest 32 | *.spec 33 | 34 | # Installer logs 35 | pip-log.txt 36 | pip-delete-this-directory.txt 37 | 38 | # Unit test / coverage reports 39 | htmlcov/ 40 | .tox/ 41 | .coverage 42 | .coverage.* 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | *.cover 47 | .hypothesis/ 48 | 49 | # Translations 50 | *.mo 51 | *.pot 52 | 53 | # Django stuff: 54 | *.log 55 | local_settings.py 56 | 57 | # Flask stuff: 58 | instance/ 59 | .webassets-cache 60 | 61 | # Scrapy stuff: 62 | .scrapy 63 | 64 | # Sphinx documentation 65 | docs/_build/ 66 | 67 | # PyBuilder 68 | target/ 69 | 70 | # Jupyter Notebook 71 | .ipynb_checkpoints 72 | 73 | # pyenv 74 | .python-version 75 | 76 | # celery beat schedule file 77 | celerybeat-schedule 78 | 79 | # SageMath parsed files 80 | *.sage.py 81 | 82 | # dotenv 83 | .env 84 | 85 | # virtualenv 86 | .venv 87 | venv/ 88 | ENV/ 89 | 90 | # Spyder project settings 91 | .spyderproject 92 | .spyproject 93 | 94 | # Rope project settings 95 | .ropeproject 96 | 97 | # mkdocs documentation 98 | /site 99 | 100 | # mypy 101 | .mypy_cache/ 102 | -------------------------------------------------------------------------------- /attention_dense.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | from attention_utils import get_activations, get_data 4 | 5 | np.random.seed(1337) # for reproducibility 6 | from keras.models import * 7 | from keras.layers import Input, Dense, merge 8 | 9 | input_dim = 32 10 | 11 | 12 | def build_model(): 13 | inputs = Input(shape=(input_dim,)) 14 | 15 | # ATTENTION PART STARTS HERE 16 | attention_probs = Dense(input_dim, activation='softmax', name='attention_vec')(inputs) 17 | attention_mul = merge([inputs, attention_probs], output_shape=32, name='attention_mul', mode='mul') 18 | # ATTENTION PART FINISHES HERE 19 | 20 | attention_mul = Dense(64)(attention_mul) 21 | output = Dense(1, activation='sigmoid')(attention_mul) 22 | model = Model(input=[inputs], output=output) 23 | return model 24 | 25 | 26 | if __name__ == '__main__': 27 | N = 10000 28 | inputs_1, outputs = get_data(N, input_dim) 29 | 30 | m = build_model() 31 | m.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy']) 32 | print(m.summary()) 33 | 34 | m.fit([inputs_1], outputs, epochs=20, batch_size=64, validation_split=0.5) 35 | 36 | testing_inputs_1, testing_outputs = get_data(1, input_dim) 37 | 38 | # Attention vector corresponds to the second matrix. 39 | # The first one is the Inputs output. 40 | attention_vector = get_activations(m, testing_inputs_1, 41 | print_shape_only=True, 42 | layer_name='attention_vec')[0].flatten() 43 | print('attention =', attention_vector) 44 | 45 | # plot part. 46 | import matplotlib.pyplot as plt 47 | import pandas as pd 48 | 49 | pd.DataFrame(attention_vector, columns=['attention (%)']).plot(kind='bar', 50 | title='Attention Mechanism as ' 51 | 'a function of input' 52 | ' dimensions.') 53 | plt.show() 54 | -------------------------------------------------------------------------------- /attention_utils.py: -------------------------------------------------------------------------------- 1 | import keras.backend as K 2 | import numpy as np 3 | 4 | 5 | def get_activations(model, inputs, print_shape_only=False, layer_name=None): 6 | # Documentation is available online on Github at the address below. 7 | # From: https://github.com/philipperemy/keras-visualize-activations 8 | print('----- activations -----') 9 | activations = [] 10 | inp = model.input 11 | if layer_name is None: 12 | outputs = [layer.output for layer in model.layers] 13 | else: 14 | outputs = [layer.output for layer in model.layers if layer.name == layer_name] # all layer outputs 15 | funcs = [K.function([inp] + [K.learning_phase()], [out]) for out in outputs] # evaluation functions 16 | layer_outputs = [func([inputs, 1.])[0] for func in funcs] 17 | for layer_activations in layer_outputs: 18 | activations.append(layer_activations) 19 | if print_shape_only: 20 | print(layer_activations.shape) 21 | else: 22 | print(layer_activations) 23 | return activations 24 | 25 | 26 | def get_data(n, input_dim, attention_column=1): 27 | """ 28 | Data generation. x is purely random except that it's first value equals the target y. 29 | In practice, the network should learn that the target = x[attention_column]. 30 | Therefore, most of its attention should be focused on the value addressed by attention_column. 31 | :param n: the number of samples to retrieve. 32 | :param input_dim: the number of dimensions of each element in the series. 33 | :param attention_column: the column linked to the target. Everything else is purely random. 34 | :return: x: model inputs, y: model targets 35 | """ 36 | x = np.random.standard_normal(size=(n, input_dim)) 37 | y = np.random.randint(low=0, high=2, size=(n, 1)) 38 | x[:, attention_column] = y[:, 0] 39 | return x, y 40 | 41 | 42 | def get_data_recurrent(n, time_steps, input_dim, attention_column=10): 43 | """ 44 | Data generation. x is purely random except that it's first value equals the target y. 45 | In practice, the network should learn that the target = x[attention_column]. 46 | Therefore, most of its attention should be focused on the value addressed by attention_column. 47 | :param n: the number of samples to retrieve. 48 | :param time_steps: the number of time steps of your series. 49 | :param input_dim: the number of dimensions of each element in the series. 50 | :param attention_column: the column linked to the target. Everything else is purely random. 51 | :return: x: model inputs, y: model targets 52 | """ 53 | x = np.random.standard_normal(size=(n, time_steps, input_dim)) 54 | y = np.random.randint(low=0, high=2, size=(n, 1)) 55 | x[:, attention_column, :] = np.tile(y[:], (1, input_dim)) 56 | return x, y 57 | -------------------------------------------------------------------------------- /attention_lstm.py: -------------------------------------------------------------------------------- 1 | from keras.layers import merge 2 | from keras.layers.core import * 3 | from keras.layers.recurrent import LSTM 4 | from keras.models import * 5 | 6 | from attention_utils import get_activations, get_data_recurrent 7 | 8 | INPUT_DIM = 2 9 | TIME_STEPS = 20 10 | # if True, the attention vector is shared across the input_dimensions where the attention is applied. 11 | SINGLE_ATTENTION_VECTOR = False 12 | APPLY_ATTENTION_BEFORE_LSTM = False 13 | 14 | 15 | def attention_3d_block(inputs): 16 | # inputs.shape = (batch_size, time_steps, input_dim) 17 | input_dim = int(inputs.shape[2]) 18 | a = Permute((2, 1))(inputs) 19 | a = Reshape((input_dim, TIME_STEPS))(a) # this line is not useful. It's just to know which dimension is what. 20 | a = Dense(TIME_STEPS, activation='softmax')(a) 21 | if SINGLE_ATTENTION_VECTOR: 22 | a = Lambda(lambda x: K.mean(x, axis=1), name='dim_reduction')(a) 23 | a = RepeatVector(input_dim)(a) 24 | a_probs = Permute((2, 1), name='attention_vec')(a) 25 | output_attention_mul = merge([inputs, a_probs], name='attention_mul', mode='mul') 26 | return output_attention_mul 27 | 28 | 29 | def model_attention_applied_after_lstm(): 30 | inputs = Input(shape=(TIME_STEPS, INPUT_DIM,)) 31 | lstm_units = 32 32 | lstm_out = LSTM(lstm_units, return_sequences=True)(inputs) 33 | attention_mul = attention_3d_block(lstm_out) 34 | attention_mul = Flatten()(attention_mul) 35 | output = Dense(1, activation='sigmoid')(attention_mul) 36 | model = Model(input=[inputs], output=output) 37 | return model 38 | 39 | 40 | def model_attention_applied_before_lstm(): 41 | inputs = Input(shape=(TIME_STEPS, INPUT_DIM,)) 42 | attention_mul = attention_3d_block(inputs) 43 | lstm_units = 32 44 | attention_mul = LSTM(lstm_units, return_sequences=False)(attention_mul) 45 | output = Dense(1, activation='sigmoid')(attention_mul) 46 | model = Model(input=[inputs], output=output) 47 | return model 48 | 49 | 50 | if __name__ == '__main__': 51 | 52 | N = 300000 53 | # N = 300 -> too few = no training 54 | inputs_1, outputs = get_data_recurrent(N, TIME_STEPS, INPUT_DIM) 55 | 56 | if APPLY_ATTENTION_BEFORE_LSTM: 57 | m = model_attention_applied_before_lstm() 58 | else: 59 | m = model_attention_applied_after_lstm() 60 | 61 | m.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy']) 62 | print(m.summary()) 63 | 64 | m.fit([inputs_1], outputs, epochs=1, batch_size=64, validation_split=0.1) 65 | 66 | attention_vectors = [] 67 | for i in range(300): 68 | testing_inputs_1, testing_outputs = get_data_recurrent(1, TIME_STEPS, INPUT_DIM) 69 | attention_vector = np.mean(get_activations(m, 70 | testing_inputs_1, 71 | print_shape_only=True, 72 | layer_name='attention_vec')[0], axis=2).squeeze() 73 | print('attention =', attention_vector) 74 | assert (np.sum(attention_vector) - 1.0) < 1e-5 75 | attention_vectors.append(attention_vector) 76 | 77 | attention_vector_final = np.mean(np.array(attention_vectors), axis=0) 78 | # plot part. 79 | import matplotlib.pyplot as plt 80 | import pandas as pd 81 | 82 | pd.DataFrame(attention_vector_final, columns=['attention (%)']).plot(kind='bar', 83 | title='Attention Mechanism as ' 84 | 'a function of input' 85 | ' dimensions.') 86 | plt.show() 87 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Keras Attention Mechanism 2 | [![license](https://img.shields.io/badge/License-Apache_2.0-brightgreen.svg)](https://github.com/philipperemy/keras-attention-mechanism/blob/master/LICENSE) [![dep1](https://img.shields.io/badge/Tensorflow-1.2+-blue.svg)](https://www.tensorflow.org/) [![dep2](https://img.shields.io/badge/Keras-2.0+-blue.svg)](https://keras.io/) 3 | 4 | Simple attention mechanism implemented in Keras for the following layers: 5 | 6 | - [x] **Dense (attention 2D block)** 7 | - [x] **LSTM, GRU (attention 3D block)** 8 | 9 |

10 | 11 |
Example: Attention block 12 |

13 | 14 | ## Dense Layer 15 | 16 | ``` 17 | inputs = Input(shape=(input_dims,)) 18 | attention_probs = Dense(input_dims, activation='softmax', name='attention_probs')(inputs) 19 | attention_mul = merge([inputs, attention_probs], output_shape=input_dims, name='attention_mul', mode='mul') 20 | ``` 21 | 22 | Let's consider this Hello World example: 23 | 24 | - A vector *v* of 32 values as input to the model (simple feedforward neural network). 25 | - *v[1]* = target. 26 | - Target is binary (either 0 or 1). 27 | - All the other values of the vector *v* (*v[0]* and *v[2:32]*) are purely random and do not contribute to the target. 28 | 29 | We expect the attention to be focused on *v[1]* only, or at least strongly. We recap the setup with this drawing: 30 | 31 |

32 | Attention Mechanism explained

33 | 34 |

35 | 36 | 37 | The first two are samples taken randomly from the training set. The last plot is the attention vector that we expect. A high peak indexed by 1, and close to zero on the rest. 38 | 39 | Let's train this model and visualize the attention vector applied to the inputs: 40 | 41 |

42 | Attention Mechanism explained

43 | 44 |

45 | 46 | We can clearly see that the network figures this out for the inference. 47 | 48 | ### Behind the scenes 49 | 50 | The attention mechanism can be implemented in three lines with Keras: 51 | ``` 52 | inputs = Input(shape=(input_dims,)) 53 | attention_probs = Dense(input_dims, activation='softmax', name='attention_probs')(inputs) 54 | attention_mul = merge([inputs, attention_probs], output_shape=32, name='attention_mul', mode='mul') 55 | ``` 56 | 57 | We apply a `Dense - Softmax` layer with the same number of output parameters than the `Input` layer. The attention matrix has a shape of `input_dims x input_dims` here. 58 | 59 | Then we merge the `Inputs` layer with the attention layer by multiplying element-wise. 60 | 61 | Finally, the activation vector (probability distribution) can be derived with: 62 | 63 | ``` 64 | attention_vector = get_activations(m, testing_inputs_1, print_shape_only=True)[1].flatten() 65 | ``` 66 | 67 | Where `1` is the index of definition of the attention layer in the model definition (`Inputs` is indexed by `0`). 68 | 69 | ## Recurrent Layers (LSTM, GRU...) 70 | 71 | ### Application of attention at input level 72 | 73 | We consider the same example as the one used for the Dense layers. The attention index is now on the 10th value. We therefore expect an attention spike around this value. There are two main ways to apply attention to recurrent layers: 74 | 75 | - Directly on the inputs (same as the Dense example above): `APPLY_ATTENTION_BEFORE_LSTM = True` 76 | 77 |

78 | Attention vector applied on the inputs (before)

79 | 80 |

81 | 82 | ### Application of attention on the LSTM's output 83 | 84 | - After the LSTM layer: `APPLY_ATTENTION_BEFORE_LSTM = False` 85 | 86 |

87 | Attention vector applied on the output of the LSTM layer (after)

88 | 89 |

90 | 91 | Both have their own advantages and disadvantages. One obvious advantage of applying the attention directly at the inputs is that we clearly understand this space. The high dimensional space spanned by the LSTM might be a bit trickier to interpret, although they share the time steps in common with the inputs (`return_sequences=True` is used here). 92 | 93 | ### Attention of multi dimensional time series 94 | 95 | Also, sometimes, the time series can be N-dimensional. It could be interesting to have one attention vector per dimension. Let's say we have a 2-D time series on 20 steps. Setting `SINGLE_ATTENTION_VECTOR = False` gives an attention vector of shape `(20, 2)`. If `SINGLE_ATTENTION_VECTOR` is set to `True`, it means that the attention vector will be of shape `(20,)` and shared across the input dimensions. 96 | 97 | - `SINGLE_ATTENTION_VECTOR = False` 98 | 99 |

100 | Attention defined per time series (each TS has its own attention)

101 | 102 |

103 | 104 | - `SINGLE_ATTENTION_VECTOR = True` 105 | 106 |

107 | Attention shared across all the time series

108 | 109 |

110 | 111 | ## Resources 112 | - https://github.com/fchollet/keras/issues/1472 113 | - http://distill.pub/2016/augmented-rnns/ 114 | 115 | 116 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. Definitions. 8 | 9 | "License" shall mean the terms and conditions for use, reproduction, 10 | and distribution as defined by Sections 1 through 9 of this document. 11 | 12 | "Licensor" shall mean the copyright owner or entity authorized by 13 | the copyright owner that is granting the License. 14 | 15 | "Legal Entity" shall mean the union of the acting entity and all 16 | other entities that control, are controlled by, or are under common 17 | control with that entity. For the purposes of this definition, 18 | "control" means (i) the power, direct or indirect, to cause the 19 | direction or management of such entity, whether by contract or 20 | otherwise, or (ii) ownership of fifty percent (50%) or more of the 21 | outstanding shares, or (iii) beneficial ownership of such entity. 22 | 23 | "You" (or "Your") shall mean an individual or Legal Entity 24 | exercising permissions granted by this License. 25 | 26 | "Source" form shall mean the preferred form for making modifications, 27 | including but not limited to software source code, documentation 28 | source, and configuration files. 29 | 30 | "Object" form shall mean any form resulting from mechanical 31 | transformation or translation of a Source form, including but 32 | not limited to compiled object code, generated documentation, 33 | and conversions to other media types. 34 | 35 | "Work" shall mean the work of authorship, whether in Source or 36 | Object form, made available under the License, as indicated by a 37 | copyright notice that is included in or attached to the work 38 | (an example is provided in the Appendix below). 39 | 40 | "Derivative Works" shall mean any work, whether in Source or Object 41 | form, that is based on (or derived from) the Work and for which the 42 | editorial revisions, annotations, elaborations, or other modifications 43 | represent, as a whole, an original work of authorship. For the purposes 44 | of this License, Derivative Works shall not include works that remain 45 | separable from, or merely link (or bind by name) to the interfaces of, 46 | the Work and Derivative Works thereof. 47 | 48 | "Contribution" shall mean any work of authorship, including 49 | the original version of the Work and any modifications or additions 50 | to that Work or Derivative Works thereof, that is intentionally 51 | submitted to Licensor for inclusion in the Work by the copyright owner 52 | or by an individual or Legal Entity authorized to submit on behalf of 53 | the copyright owner. For the purposes of this definition, "submitted" 54 | means any form of electronic, verbal, or written communication sent 55 | to the Licensor or its representatives, including but not limited to 56 | communication on electronic mailing lists, source code control systems, 57 | and issue tracking systems that are managed by, or on behalf of, the 58 | Licensor for the purpose of discussing and improving the Work, but 59 | excluding communication that is conspicuously marked or otherwise 60 | designated in writing by the copyright owner as "Not a Contribution." 61 | 62 | "Contributor" shall mean Licensor and any individual or Legal Entity 63 | on behalf of whom a Contribution has been received by Licensor and 64 | subsequently incorporated within the Work. 65 | 66 | 2. Grant of Copyright License. Subject to the terms and conditions of 67 | this License, each Contributor hereby grants to You a perpetual, 68 | worldwide, non-exclusive, no-charge, royalty-free, irrevocable 69 | copyright license to reproduce, prepare Derivative Works of, 70 | publicly display, publicly perform, sublicense, and distribute the 71 | Work and such Derivative Works in Source or Object form. 72 | 73 | 3. Grant of Patent License. Subject to the terms and conditions of 74 | this License, each Contributor hereby grants to You a perpetual, 75 | worldwide, non-exclusive, no-charge, royalty-free, irrevocable 76 | (except as stated in this section) patent license to make, have made, 77 | use, offer to sell, sell, import, and otherwise transfer the Work, 78 | where such license applies only to those patent claims licensable 79 | by such Contributor that are necessarily infringed by their 80 | Contribution(s) alone or by combination of their Contribution(s) 81 | with the Work to which such Contribution(s) was submitted. If You 82 | institute patent litigation against any entity (including a 83 | cross-claim or counterclaim in a lawsuit) alleging that the Work 84 | or a Contribution incorporated within the Work constitutes direct 85 | or contributory patent infringement, then any patent licenses 86 | granted to You under this License for that Work shall terminate 87 | as of the date such litigation is filed. 88 | 89 | 4. Redistribution. You may reproduce and distribute copies of the 90 | Work or Derivative Works thereof in any medium, with or without 91 | modifications, and in Source or Object form, provided that You 92 | meet the following conditions: 93 | 94 | (a) You must give any other recipients of the Work or 95 | Derivative Works a copy of this License; and 96 | 97 | (b) You must cause any modified files to carry prominent notices 98 | stating that You changed the files; and 99 | 100 | (c) You must retain, in the Source form of any Derivative Works 101 | that You distribute, all copyright, patent, trademark, and 102 | attribution notices from the Source form of the Work, 103 | excluding those notices that do not pertain to any part of 104 | the Derivative Works; and 105 | 106 | (d) If the Work includes a "NOTICE" text file as part of its 107 | distribution, then any Derivative Works that You distribute must 108 | include a readable copy of the attribution notices contained 109 | within such NOTICE file, excluding those notices that do not 110 | pertain to any part of the Derivative Works, in at least one 111 | of the following places: within a NOTICE text file distributed 112 | as part of the Derivative Works; within the Source form or 113 | documentation, if provided along with the Derivative Works; or, 114 | within a display generated by the Derivative Works, if and 115 | wherever such third-party notices normally appear. The contents 116 | of the NOTICE file are for informational purposes only and 117 | do not modify the License. You may add Your own attribution 118 | notices within Derivative Works that You distribute, alongside 119 | or as an addendum to the NOTICE text from the Work, provided 120 | that such additional attribution notices cannot be construed 121 | as modifying the License. 122 | 123 | You may add Your own copyright statement to Your modifications and 124 | may provide additional or different license terms and conditions 125 | for use, reproduction, or distribution of Your modifications, or 126 | for any such Derivative Works as a whole, provided Your use, 127 | reproduction, and distribution of the Work otherwise complies with 128 | the conditions stated in this License. 129 | 130 | 5. Submission of Contributions. Unless You explicitly state otherwise, 131 | any Contribution intentionally submitted for inclusion in the Work 132 | by You to the Licensor shall be under the terms and conditions of 133 | this License, without any additional terms or conditions. 134 | Notwithstanding the above, nothing herein shall supersede or modify 135 | the terms of any separate license agreement you may have executed 136 | with Licensor regarding such Contributions. 137 | 138 | 6. Trademarks. This License does not grant permission to use the trade 139 | names, trademarks, service marks, or product names of the Licensor, 140 | except as required for reasonable and customary use in describing the 141 | origin of the Work and reproducing the content of the NOTICE file. 142 | 143 | 7. Disclaimer of Warranty. Unless required by applicable law or 144 | agreed to in writing, Licensor provides the Work (and each 145 | Contributor provides its Contributions) on an "AS IS" BASIS, 146 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or 147 | implied, including, without limitation, any warranties or conditions 148 | of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A 149 | PARTICULAR PURPOSE. You are solely responsible for determining the 150 | appropriateness of using or redistributing the Work and assume any 151 | risks associated with Your exercise of permissions under this License. 152 | 153 | 8. Limitation of Liability. In no event and under no legal theory, 154 | whether in tort (including negligence), contract, or otherwise, 155 | unless required by applicable law (such as deliberate and grossly 156 | negligent acts) or agreed to in writing, shall any Contributor be 157 | liable to You for damages, including any direct, indirect, special, 158 | incidental, or consequential damages of any character arising as a 159 | result of this License or out of the use or inability to use the 160 | Work (including but not limited to damages for loss of goodwill, 161 | work stoppage, computer failure or malfunction, or any and all 162 | other commercial damages or losses), even if such Contributor 163 | has been advised of the possibility of such damages. 164 | 165 | 9. Accepting Warranty or Additional Liability. While redistributing 166 | the Work or Derivative Works thereof, You may choose to offer, 167 | and charge a fee for, acceptance of support, warranty, indemnity, 168 | or other liability obligations and/or rights consistent with this 169 | License. However, in accepting such obligations, You may act only 170 | on Your own behalf and on Your sole responsibility, not on behalf 171 | of any other Contributor, and only if You agree to indemnify, 172 | defend, and hold each Contributor harmless for any liability 173 | incurred by, or claims asserted against, such Contributor by reason 174 | of your accepting any such warranty or additional liability. 175 | 176 | END OF TERMS AND CONDITIONS 177 | 178 | APPENDIX: How to apply the Apache License to your work. 179 | 180 | To apply the Apache License to your work, attach the following 181 | boilerplate notice, with the fields enclosed by brackets "{}" 182 | replaced with your own identifying information. (Don't include 183 | the brackets!) The text should be enclosed in the appropriate 184 | comment syntax for the file format. We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright {yyyy} {name of copyright owner} 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | --------------------------------------------------------------------------------