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https://github.com/pietrobarbiero/pytorch_explain

PyTorch Explain: Interpretable Deep Learning in Python.
https://github.com/pietrobarbiero/pytorch_explain

deep-learning entropy explainability explainable-ai interpretability interpretable-ai interpretable-deep-learning interpretable-machine-learning lens logic machine-learning neural-network python pytorch sympy

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PyTorch Explain: Interpretable Deep Learning in Python.

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README 

        
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`PyTorch, Explain!` is an extension library for PyTorch to develop

explainable deep learning models going beyond the current accuracy-interpretability trade-off.



The library includes a set of tools to develop:



* Deep Concept Reasoner (Deep CoRe): an interpretable concept-based model going

  **beyond the current accuracy-interpretability trade-off**;

* Concept Embedding Models (CEMs): a class of concept-based models going

  **beyond the current accuracy-explainability trade-off**;

* Logic Explained Networks (LENs): a class of concept-based models generating

  accurate compound logic explanations for their predictions

  **without the need for a post-hoc explainer**.



Table of Content

-----------------

* `Quick start `_

* `Quick tutorial on Concept Embedding Models `_

* `Quick tutorial on Deep Concept Reasoning `_

* `Quick tutorial on Logic Explained Networks `_

* `Benchmark datasets `_

* `Theory `_

* `Authors `_

* `Licence `_



Quick start

---------------



You can install ``torch_explain`` along with all its dependencies from

`PyPI `__:



.. code:: bash



    pip install torch-explain



Quick tutorial on Concept Embedding Models

-----------------------------------------------



Using concept embeddings we can solve concept-based problems very efficiently!

For this simple tutorial, let's approach the XOR benchmark dataset:



.. code:: python



    import torch

    import torch_explain as te

    from torch_explain import datasets

    from sklearn.metrics import accuracy_score

    from sklearn.model_selection import train_test_split



    x, c, y = datasets.xor(500)

    x_train, x_test, c_train, c_test, y_train, y_test = train_test_split(x, c, y, test_size=0.33, random_state=42)



We just need to define a task predictor and a concept encoder using a

concept embedding layer:



.. code:: python



    import torch

    import torch_explain as te



    embedding_size = 8

    concept_encoder = torch.nn.Sequential(

        torch.nn.Linear(x.shape[1], 10),

        torch.nn.LeakyReLU(),

        te.nn.ConceptEmbedding(10, c.shape[1], embedding_size),

    )

    task_predictor = torch.nn.Sequential(

        torch.nn.Linear(c.shape[1]*embedding_size, 1),

    )

    model = torch.nn.Sequential(concept_encoder, task_predictor)



We can now train the network by optimizing the cross entropy loss

on concepts and tasks:



.. code:: python



    optimizer = torch.optim.AdamW(model.parameters(), lr=0.01)

    loss_form_c = torch.nn.BCELoss()

    loss_form_y = torch.nn.BCEWithLogitsLoss()

    model.train()

    for epoch in range(501):

        optimizer.zero_grad()



        # generate concept and task predictions

        c_emb, c_pred = concept_encoder(x_train)

        y_pred = task_predictor(c_emb.reshape(len(c_emb), -1))



        # compute loss

        concept_loss = loss_form_c(c_pred, c_train)

        task_loss = loss_form_y(y_pred, y_train)

        loss = concept_loss + 0.5*task_loss



        loss.backward()

        optimizer.step()



Once trained we can check the performance of the model on the test set:



.. code:: python



    c_emb, c_pred = concept_encoder.forward(x_test)

    y_pred = task_predictor(c_emb.reshape(len(c_emb), -1))



    task_accuracy = accuracy_score(y_test, y_pred > 0)

    concept_accuracy = accuracy_score(c_test, c_pred > 0.5)



As you can see the performance of the model is now great as the task

task accuracy is around ~100%.



Quick tutorial on Deep Concept Reasoning

-----------------------------------------------



Using deep concept reasoning we can solve the same problem as above,

but with an intrinsically interpretable model! In fact, Deep Concept Reasoners (Deep CoRes)

make task predictions by means of interpretable logic rules using concept embeddings.



Using the same example as before, we can just change the task predictor

using a Deep CoRe layer:



.. code:: python



    from torch_explain.nn.concepts import ConceptReasoningLayer

    import torch.nn.functional as F



    y_train = F.one_hot(y_train.long().ravel()).float()

    y_test = F.one_hot(y_test.long().ravel()).float()



    task_predictor = ConceptReasoningLayer(embedding_size, y_train.shape[1])

    model = torch.nn.Sequential(concept_encoder, task_predictor)



We can now train the network by optimizing the cross entropy loss

on concepts and tasks:



.. code:: python



    optimizer = torch.optim.AdamW(model.parameters(), lr=0.01)

    loss_form = torch.nn.BCELoss()

    model.train()

    for epoch in range(501):

        optimizer.zero_grad()



        # generate concept and task predictions

        c_emb, c_pred = concept_encoder(x_train)

        y_pred = task_predictor(c_emb, c_pred)



        # compute loss

        concept_loss = loss_form(c_pred, c_train)

        task_loss = loss_form(y_pred, y_train)

        loss = concept_loss + 0.5*task_loss



        loss.backward()

        optimizer.step()



Once trained the Deep CoRe layer can explain its predictions by

providing both local and global logic rules:



.. code:: python



    local_explanations = task_predictor.explain(c_emb, c_pred, 'local')

    global_explanations = task_predictor.explain(c_emb, c_pred, 'global')



For global explanations, the reasoner will return a dictionary with entries such as

``{'class': 'y_0', 'explanation': '~c_0 & ~c_1', 'count': 94}``, specifying

for each logic rule, the task it is associated with and the number of samples

associated with the explanation.



Quick tutorial on Logic Explained Networks

---------------------------------------------



For this simple experiment, let's solve the XOR problem

(augmented with 100 dummy features):



.. code:: python



    import torch

    import torch_explain as te

    from torch.nn.functional import one_hot



    x0 = torch.zeros((4, 100))

    x_train = torch.tensor([

        [0, 0],

        [0, 1],

        [1, 0],

        [1, 1],

    ], dtype=torch.float)

    x_train = torch.cat([x_train, x0], dim=1)

    y_train = torch.tensor([0, 1, 1, 0], dtype=torch.long)

    y_train_1h = one_hot(y_train).to(torch.float)



We can instantiate a simple feed-forward neural network

with 3 layers using the ``EntropyLayer`` as the first one:



.. code:: python



    layers = [

        te.nn.EntropyLinear(x_train.shape[1], 10, n_classes=y_train_1h.shape[1]),

        torch.nn.LeakyReLU(),

        torch.nn.Linear(10, 4),

        torch.nn.LeakyReLU(),

        torch.nn.Linear(4, 1),

    ]

    model = torch.nn.Sequential(*layers)



We can now train the network by optimizing the cross entropy loss and the

``entropy_logic_loss`` loss function incorporating the human prior towards

simple explanations:



.. code:: python



    optimizer = torch.optim.AdamW(model.parameters(), lr=0.001)

    loss_form = torch.nn.BCEWithLogitsLoss()

    model.train()

    for epoch in range(2001):

        optimizer.zero_grad()

        y_pred = model(x_train).squeeze(-1)

        loss = loss_form(y_pred, y_train_1h) + 0.0001 * te.nn.functional.entropy_logic_loss(model)

        loss.backward()

        optimizer.step()



Once trained we can extract first-order logic formulas describing

how the network composed the input features to obtain the predictions:



.. code:: python



    from torch_explain.logic.nn import entropy

    from torch.nn.functional import one_hot



    y1h = one_hot(y_train)

    global_explanations, local_explanations = entropy.explain_classes(model, x_train, y_train, c_threshold=0.5, y_threshold=0.)



Explanations will be logic formulas in disjunctive normal form.

In this case, the explanation will be ``y=1`` if and only if ``(f1 AND ~f2) OR (f2  AND ~f1)``

corresponding to ``f1 XOR f2``.



The function automatically assesses the quality of logic explanations in terms

of classification accuracy and rule complexity.

In this case the accuracy is 100% and the complexity is 4.



Benchmark datasets

-------------------------



We provide a suite of 3 benchmark datasets to evaluate the performance of our models

in the folder `torch_explain/datasets`. These 3 datasets were proposed as benchmarks

for concept-based models in the paper "Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off".



Real-world datasets can be downloaded from the links provided in the supplementary material of the paper.



Theory

--------

Theoretical foundations can be found in the following papers.



Deep Concept Reasoning (recently accepted at ICML-23)::



    @article{barbiero2023interpretable,

      title={Interpretable Neural-Symbolic Concept Reasoning},

      author={Barbiero, Pietro and Ciravegna, Gabriele and Giannini, Francesco and Zarlenga, Mateo Espinosa and Magister, Lucie Charlotte and Tonda, Alberto and Lio, Pietro and Precioso, Frederic and Jamnik, Mateja and Marra, Giuseppe},

      journal={arXiv preprint arXiv:2304.14068},

      year={2023}

    }



Concept Embedding Models::



    @article{espinosa2022concept,

      title={Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off},

      author={Espinosa Zarlenga, Mateo and Barbiero, Pietro and Ciravegna, Gabriele and Marra, Giuseppe and Giannini, Francesco and Diligenti, Michelangelo and Shams, Zohreh and Precioso, Frederic and Melacci, Stefano and Weller, Adrian and others},

      journal={Advances in Neural Information Processing Systems},

      volume={35},

      pages={21400--21413},

      year={2022}

    }



Logic Explained Networks::



    @article{ciravegna2023logic,

      title={Logic explained networks},

      author={Ciravegna, Gabriele and Barbiero, Pietro and Giannini, Francesco and Gori, Marco and Li{\'o}, Pietro and Maggini, Marco and Melacci, Stefano},

      journal={Artificial Intelligence},

      volume={314},

      pages={103822},

      year={2023},

      publisher={Elsevier}

    }



Entropy-based LENs::



    @inproceedings{barbiero2022entropy,

      title={Entropy-based logic explanations of neural networks},

      author={Barbiero, Pietro and Ciravegna, Gabriele and Giannini, Francesco and Li{\'o}, Pietro and Gori, Marco and Melacci, Stefano},

      booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},

      volume={36},

      number={6},

      pages={6046--6054},

      year={2022}

    }



Psi network ("learning of constraints")::



    @inproceedings{ciravegna2020constraint,

      title={A constraint-based approach to learning and explanation},

      author={Ciravegna, Gabriele and Giannini, Francesco and Melacci, Stefano and Maggini, Marco and Gori, Marco},

      booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},

      volume={34},

      number={04},

      pages={3658--3665},

      year={2020}

    }



Learning with constraints::



    @inproceedings{marra2019lyrics,

      title={LYRICS: A General Interface Layer to Integrate Logic Inference and Deep Learning},

      author={Marra, Giuseppe and Giannini, Francesco and Diligenti, Michelangelo and Gori, Marco},

      booktitle={Joint European Conference on Machine Learning and Knowledge Discovery in Databases},

      pages={283--298},

      year={2019},

      organization={Springer}

    }



Constraints theory in machine learning::



    @book{gori2017machine,

      title={Machine Learning: A constraint-based approach},

      author={Gori, Marco},

      year={2017},

      publisher={Morgan Kaufmann}

    }



Authors

-------



* `Pietro Barbiero `__, University of Cambridge, UK.

* Mateo Espinosa Zarlenga, University of Cambridge, UK.

* Giuseppe Marra, Katholieke Universiteit Leuven, BE.

* Steve Azzolin, University of Trento, IT.

* Francesco Giannini, University of Florence, IT.

* Gabriele Ciravegna, University of Florence, IT.

* Dobrik Georgiev, University of Cambridge, UK.



Licence

-------



Copyright 2020 Pietro Barbiero, Mateo Espinosa Zarlenga, Giuseppe Marra,

Steve Azzolin, Francesco Giannini, Gabriele Ciravegna, and Dobrik Georgiev.



Licensed under the Apache License, Version 2.0 (the "License"); you may

not use this file except in compliance with the License. You may obtain

a copy of the License at: http://www.apache.org/licenses/LICENSE-2.0.



Unless required by applicable law or agreed to in writing, software

distributed under the License is distributed on an "AS IS" BASIS,

WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.



See the License for the specific language governing permissions and

limitations under the License.