Package: torch-explain
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 goingbeyond the current accuracy-interpretability trade-off;Concept Embedding Models (CEMs): a class of concept-based models goingbeyond the current accuracy-explainability trade-off;Logic Explained Networks (LENs): a class of concept-based models generating
accurate compound logic explanations for their predictionswithout the need for a post-hoc explainer.Table of ContentQuick startQuick tutorial on Concept Embedding ModelsQuick tutorial on Deep Concept ReasoningQuick tutorial on Logic Explained NetworksBenchmark datasetsTheoryAuthorsLicenceQuick startYou can installtorch_explainalong with all its dependencies fromPyPI:pipinstalltorch-explainQuick tutorial on Concept Embedding ModelsUsing concept embeddings we can solve concept-based problems very efficiently!
For this simple tutorial, let’s approach the XOR benchmark dataset:importtorchimporttorch_explainastefromtorch_explainimportdatasetsfromsklearn.metricsimportaccuracy_scorefromsklearn.model_selectionimporttrain_test_splitx,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:importtorchimporttorch_explainasteembedding_size=8concept_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:optimizer=torch.optim.AdamW(model.parameters(),lr=0.01)loss_form_c=torch.nn.BCELoss()loss_form_y=torch.nn.BCEWithLogitsLoss()model.train()forepochinrange(501):optimizer.zero_grad()# generate concept and task predictionsc_emb,c_pred=concept_encoder(x_train)y_pred=task_predictor(c_emb.reshape(len(c_emb),-1))# compute lossconcept_loss=loss_form_c(c_pred,c_train)task_loss=loss_form_y(y_pred,y_train)loss=concept_loss+0.5*task_lossloss.backward()optimizer.step()Once trained we can check the performance of the model on the test set: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 ReasoningUsing 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:fromtorch_explain.nn.conceptsimportConceptReasoningLayerimporttorch.nn.functionalasFy_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:optimizer=torch.optim.AdamW(model.parameters(),lr=0.01)loss_form=torch.nn.BCELoss()model.train()forepochinrange(501):optimizer.zero_grad()# generate concept and task predictionsc_emb,c_pred=concept_encoder(x_train)y_pred=task_predictor(c_emb,c_pred)# compute lossconcept_loss=loss_form(c_pred,c_train)task_loss=loss_form(y_pred,y_train)loss=concept_loss+0.5*task_lossloss.backward()optimizer.step()Once trained the Deep CoRe layer can explain its predictions by
providing both local and global logic rules: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 NetworksFor this simple experiment, let’s solve the XOR problem
(augmented with 100 dummy features):importtorchimporttorch_explainastefromtorch.nn.functionalimportone_hotx0=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 theEntropyLayeras the first one: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 theentropy_logic_lossloss function incorporating the human prior towards
simple explanations:optimizer=torch.optim.AdamW(model.parameters(),lr=0.001)loss_form=torch.nn.BCEWithLogitsLoss()model.train()forepochinrange(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:fromtorch_explain.logic.nnimportentropyfromtorch.nn.functionalimportone_hoty1h=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 bey=1if and only if(f1 AND ~f2) OR (f2  AND ~f1)corresponding tof1 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 datasetsWe provide a suite of 3 benchmark datasets to evaluate the performance of our models
in the foldertorch_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.TheoryTheoretical 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}
}AuthorsPietro 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.LicenceCopyright 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.