EDUCE: E XPLAINING MODEL D ECISIONS THROUGH U NSUPERVISED C ONCEPTS E XTRACTION
Anonymous authors
Paper under double-blind review
A BSTRACT
Providing explanations along with predictions is crucial in some text processing tasks.
Therefore, we propose a new self-interpretable model that performs output prediction and simultaneously provides an explanation in terms of the presence of particular concepts in the input.
To do so, our model’s prediction relies solely on a low-dimensional binary representation of the input, where each feature denotes the presence or absence of concepts.
The presence of a concept is decided from an excerpt i.e. a small sequence of consecutive words in the text.
Relevant concepts for the prediction task at hand are automatically deﬁned by our model, avoiding the need for concept-level annotations.
To ease interpretability, we enforce that for each concept, the corresponding excerpts share similar semantics and are differentiable from each others.
We experimentally demonstrate the relevance of our approach on text classiﬁcation and multi-sentiment analysis tasks.
I NTRODUCTION
While deep learning models are powerful tools to perform a large variety of tasks, their predictive process often remains obscure.
Understanding their behavior becomes crucial.
This is particularly true with text data, where predicting without justiﬁcations has limited applicability.
There has been a recent focus on trying to make deep models more interpretable, see for example (Ribeiro et al., 2016; Bach et al., 2015; Shrikumar et al., 2017; Simonyan et al., 2014; Sundararajan et al., 2017).
Speciﬁcally, methods have been recently proposed to provide such explanations simultaneously with the prediction.
For example, (Lei et al., 2016; Yu et al., 2019; Bastings et al., 2019) select subsets of words in the input text that can account for the model’s prediction (called rationales).
In this work, we propose a model that provides an explanation based on the absence or presence “concepts” that are automatically discovered in the texts.
Suppose we ask a user to tell what is the category (or class) of the top text of Figure 1 (text x ).
She detects that the words the government said relate to a speciﬁc concept that is present in x , a concept she also detect in the words made ofﬁcial what in text x (cid:48) .
Let us call this concept “politics” in the remainder.
She also notes that the words retails sales bounced back refer to a concept different from the previous one.
Let us call this other concept “economy”.
As the text is concerned with politics and economy she infers that its category is Business.
Said otherwise, she detects excerpts that relate to particular concepts and decides on the text category based on the detected concepts.
Similarly, our paradigm assumes that an explanation of a model’s prediction is understandable if it relies on a few concepts, where each concept relates to parts of text (referred to as excerpts ) that are semantically consistent across multiple texts.
Our methodology is as follows.
First, our model encodes the input text into a binary low-dimensional vector, where each value (0 or 1) is computed from an excerpt and denotes the presence or absence of a speciﬁc concept in the input.
Then, the prediction is made from this binary vector alone, allowing an easy interpretation of the decision in term of presence/absence of concepts.
While we set a maximal value of the number of concepts (which is the dimensionality of the binary representation), the concepts are unsupervised and not deﬁned a priori .
The model automatically determines them in a way that eases interpretation: each concept is encouraged to be semantically consistent and not to overlap with other concepts.
Therefore, extracted excerpts for a concept must be discriminative of that concept only and share similar semantics.
This is enforced through a concept consistency and separability constraint added as an auxiliary loss in the learning optimization problem.
[Figure]
As a result
[Figure]
each discovered concept can be understood from the corresponding excerpts extracted that activate its appearance: in our previous example, the meaning of the ﬁrst concept the user identiﬁes is inferred from the excerpts she detected for that concept in x and x (cid:48) ,
i
[Figure]
e. the government said, made ofﬁcial what .
Looking at these excerpts, we identify that concept as politics.
Our idea relates to Latent Dirichlet Allocation (LDA) (Blei et al., 2003), where text documents are described by a set of topics that are semantically consistent.
However, LDA builds a probabilistic model of text generation, whereas our goal is to discover and deﬁne latent concepts that are relevant for a prediction task at hand.
In comparison to rationale-based text processing models (Lei et al., 2016; Yu et al., 2019; Bastings et al., 2019), we rely on a different paradigm: our model’s prediction is based on the absence or presence of discovered concepts, and makes no direct use of the words captured as excerpts.
We do so to ease interpretation of the prediction.
This makes the interpretation of a different nature than these methods, and simpler to understand for the user.
Our contribution with this work is a new self-interpretable model that predicts solely from the presence/absence of concepts in the input.
Concepts are learned unsupervisingly, and described by a semantically consistent set of excerpts.
We experiment on three text categorization tasks and a multiaspect sentiment analysis task, compare our model’s performance with state-of-the-art prediction models, and demonstrate its interpretability.
Note that an instance of our model for image processing is described in the supplementary Section D with illustrative experiments.
T HE EDUCE MODEL
We present our model, called EDUCE for Explaining model Decisions through Unsupervised Concepts Extraction, using a multi-class classiﬁcation task, but our method can be used to perform regression or multi-label classiﬁcation.
We consider a training dataset D of inputs ( x 1 , ...., x N ) , x n ∈ X and corresponding labels ( y 1 , ..., y N ) , y n ∈ Y .
Contrarily to back-box models that use complex computations over low-level input features to predict the output class y , our objective is to enforce the model to map an x input to an easy-to-interpret representation z ( x ) ∈ { 0 , 1 } C , on which the output prediction relies.
EDUCE’s inference process consists in the following steps.
Step 1 :
For each concept c (i.e. each dimension of z ( x ) ), compute p γ ( s | x, c ) : the probability of each excerpt s in x to be selected.
Sample a unique excerpt s c ( x ) ∼ p γ ( s | x, c ) per concept (per dimension of z ( x ) ).
Note that the same excerpt can be selected for multiple concepts.
Step 2 : Decide on each value z c ( x ) of the representation z ( x ) by sampling from p α
( z c | s c ( x ) , c ) .
Given s c ( x ) , z c ( s c ( x )) =
1 means concept c is detected as present and z c ( s c ( x ))
=
means it is absent.
Step 3 : Predict the output class y from z ( x ) =
( z 1 ( s 1 ( x )) , ..., z C ( s C ( x )) ).
We do not have concept-level annotations.
To ensure semantic consistency and prevent overlap of the concepts, we jointly train a concept classiﬁer to recognize, for every excerpt s c ( x ) such that z c ( s c ( x ))
= 1 , the concept (i.e. the dimension) it was extracted for: the label for each s c ( x ) is simply c ∈ [1 , C ] .
Figure 1 illustrates these steps, which we detail below.
2. G ENERATING PREDICTIONS AND EXPLANATIONS
Step 1: Extract a unique excerpt s c ( x ) per concept c .
Given an input sentence x : w 1 , ..., w M , where each w i is a word, a excerpt s consists of a span of consecutive words of ﬂexible size between 3 and 10 words: s = w k , ..., w k + l , 3 ≤ l ≤ 10 .
For each concept, we extract a unique excerpt, deﬁned by its ﬁrst and last word.
Our extraction process is very similar to the one proposed in
Question-Answering models (e.g Devlin et al.
An excerpt is sampled by ﬁrst sampling its start word and then its end word conditioned on the start word.
We denote the probability over each excerpt s to represent concept c in x as p γ
( s | x, c ) and we write as the product of (i) p start ( w k | x, c ) , the probability for s ’s ﬁrst word to be the start word of the excerpt to extract and (ii) p stop ( w k + l | x, c, w k ) the probability of w k + l to be the stop word given the start word w k : p γ ( s | x, c ) =
p γ ( w k , ..., w k + l | x, c ) =
p stop ( w k + l | x, c, w k ) p start ( w k | x, c ) .
We parametrize p start ( w k | x, c ) and p stop ( w k + l | x, c, w k ) using recurrent neural networks.
First we feed the entire input sentence x : w 1 , ..., w M through a bidirectional LSTM, and we represent each word w i in the sentence as the concatenation of the forward pass and backward pass hidden states for that word: h k =
[ −→ h k , ←− h k ] , ∀ k ∈ [1 , M ] .
Second, each h k is fed to a linear layer with parameters γ start which outputs a score for w k , followed by the softmax activation function over all possible words to have the probability distribution over each word to be the start word :
[Equation] [Equation]
Using this distribution, we can sample a speciﬁc start word w start ∼ p start ( w k | x, c ) .
Third, we feed again the vectors h k to another linear layer with parameters γ stop that gives a score for each word to be the stop word .
We mask out these scores before taking the softmax, such that the probabilities for w start + l with l < 3 and l > 10 to be the stop word are 0 .
[Equation]
We then sample a speciﬁc stop word w stop ∼ p stop ( w start + l | x, c, w start ) 1 .
We now have the start word w start and stop word w stop .
The corresponding excerpt is w start , ..., w stop and is represented as a ﬁxed size vector s c ( x ) by computing the average of (pre-trained, ﬁxed) words embeddings vectors of w start , ..., w stop .
Hence sampled excerpts s c ( x ) belong to R d , where d is the dimension of embedding vectors.
This process is illustrated in Figure 1: For text x , the excerpt Retails sales bounced back is selected for concept c 1 , the government said for concept c 2 and a midsummer slump for concept c 3 .
Step 2:
For each c , from the excerpt s c ( x ) , decide on the value z c ( x ) denoting the presence/absence of concept c .
Each extracted excerpt (one per concept) is processed to decide on the absence or presence of each concept in x .
Speciﬁcally, for each concept c we take the dot product of a weight vector α c ∈ R d with s c ( x ) , followed by a sigmoid activation function, in order to obtain the Bernoulli probability
[Equation]
This is the probability that s c ( x ) extracted from x for concept c triggers the presence of concept c .
The binary vector z ( x ) is obtained by independently sampling each dimension: ∀ c z c ∼ p
α
( z c | s c ( x ) , c ) .
This step can be seen as C independent binary classiﬁers, each of them deciding on the presence of a particular concept.
We illustrate this in Step 2 in Figure 1: For text x , the excerpt Retails sales bounced back activates the presence of concept c 1 , the government said activates the presence of cbut a midsummer slump does not activate the presence of c 3 .
Step 3: Predict y from z ( x ) .
As shown in Step 3 of Figure 1, given an input x , the prediction of the output y is made solely from the intermediate binary representation z ( x ) .
We use a linear classiﬁer without bias, parametrized by a weight matrix δ ∈ R |Y|×C followed by a softmax activation function, returning p δ ( y | z ( x ))
∀ y ∈ Y .
Output classiﬁcation training objective.
The parameters { γ, α, δ } are learned in a end-to-end manner by minimizing cross-entropy, which writes for each x as:
[Equation]
We give details about the optimization in Section 2.3.
2. U NSUPERVISED D ISCOVERY OF L ATENT C ONCEPTS
To ease interpretation of the concepts’ meaning, we want each dimension z to correspond to semantically consistent concepts.
In other words, for a given concept c (i.e. a given dimension z c ), for all inputs where that concept is present (i.e. ∀ x s.t.
z c ( s c ( x )) = 1 ), the corresponding excerpts s c ( x ) should share common semantics.
While the C binary classiﬁers deciding on the presence of each concept c
(Step 2) enforce consistency within the set of extracted excerpts s c , there is no guarantee that the concepts are not overlapping (i.e. are separable).
We want concepts to be separable so that each concept captures a particular notion.
Excerpts extracted for concept c must be distinguishable from the excerpts extracted for another concept c (cid:48) .
If we take the example of Figure 1: In Step 2 the excerpt Retails sales bounced back is identiﬁable as relating to economy/ﬁnance, contrarily to the government said, made ofﬁcial what which trigger the concept politics.
We rephrase our desiderata for consistency and separability as classiﬁcation of the excerpts, with as many classes as the number of concepts.
An external classiﬁer should recognize that elements in the set { s c ( x ) |∀ x z c ( s c ( x ))
= 1 } belong to concept c , and { s c (cid:48)
( x ) |∀ x z c (cid:48) ( s c (cid:48)
( x ))
= 1 } belong to concept c (cid:48) and not c .
Recall that we do not have labels for the concepts .
The ground-truth label of each extracted excerpt s c ( x ) is the index c of the dimension of z ( x ) for which it was extracted.
We learn a linear concept classiﬁer without bias, parametrized by a weight matrix θ ∈ R |C|× d followed by a softmax activation function, returning p θ ( c (cid:48) | s c ( x )) , ∀ c (cid:48) ∈
[1 , C ] .
The concept classiﬁer is trained by minimizing cross-entropy, where the label of each excerpt s c ( x ) the index of the concept for which it was extracted (i.e. c ):
[Equation]
where s ( x ) refers to the set of excerpts extracted for each concept: s ( x )
= { s c ( x ) , c = 1 , ..., C } .
The loss considers concepts that are present in x (i.e. z c ( s c ( x )) = 1 ).
The role of the concept classiﬁer is to further enforce concepts consistency and to prevent overlap of concepts, and is jointly train with the rest of the model.
Note that adding a sparsity constraint on the number of concepts present in the inputs enforces semantic consistency, as sparse coding has been shown to induce useful, interpretable representations (Bengio et al., 2013a; Mairal et al., 2010).
We experimentally demonstrate that a sparsity constraint is not sufﬁcient, and can harm output prediction performance.
On the opposite, with our concept classiﬁer, sparsity is encouraged as L concept depends on the concepts that are present, but if concepts are consistent and separable L concept can be low without harming task performance.
2. EDUCE OBJECTIVE FUNCTION AND OPTIMIZATION
We jointly learn the concept classiﬁer and output classiﬁer and our objective function is the sum
Equations 3 and 4:
[Equation]
where λ controls the strength of the concept consistency constraint wrt the output prediction.
The loss
L ( x ) is differentiable, therefore the gradients with respect to the output classiﬁer’s weights ( δ ) and concept classiﬁer’s weights ( θ ) can be computed and back-propagated.
However, the gradients with respect to the parameters of the excerpts extraction ( γ ) and the Bernoulli distribution over presence of concepts ( α ) pose an issue due to the sampling of these discrete random variables in Steps 1 and 2.
As the explicit computation of the expectation involves expensive summations over all possible values of s ( x ) and z ( x ) , we resort to Monte-Carlo approximations of the gradient (Sutton & Barto, 1998), with the loss L ( x ) used as reinforcement signal.
The gradient derivation is provided in Supplementary
Material.
Our code will be released upon acceptance.
Note that the concept classiﬁer encourages concept consistency and concept separability.
The discovered concepts are not guaranteed to align with human deﬁned concepts.
This is a general challenge in learning explainable/interpretable models in an unsupervised setting.
We believe it is a reasonable assumption to employ a linear concept classiﬁer over pre-trained word embeddings such that it linear separates the word embedding space.
R ELATED WORK
Our work relates to topic models, especially to Latent Dirichlet Allocation (LDA) (Blei et al., 2003) where each document is modeled as a mixture of topics and each word relates to one or more topics.
While LDA has been recently combined with recurrent neural networks (Zaheer et al., 2017), the methodology remains different.
LDA learns the parameters of a probabilistic graphical model of text generation while our goal is to build an interpretable prediction model that relies on binary presence/absence of concepts.
Some existing works interpret an already trained model, typically using perturbation and gradientbased approach, (Ribeiro et al., 2016; Bach et al., 2015; Shrikumar et al., 2017; Simonyan et al., 2014; Sundararajan et al., 2017)
Alvarez-Melis & Jaakkola (2017) design a model that detects inputoutput pairs that are causally related.
Contrarily to these methods, our work falls in the domain of self-interpretable models, which produce an explanation simultaneously with their prediction.
Lei et al.
; Yu et al.
; Bastings et al.
(2019) develop interpretable models for NLP tasks by selecting rationales, i.e. parts of text, on which a consequent model bases its prediction.
A rationale acts as a justiﬁcation supporting the prediction and is different from our deﬁnition of excerpt.
In EDUCE, excerpts support the attribution of presence of concepts, and this attribution supports the prediction.
Goyal et al.
(2019) propose visual explanations of a classiﬁer’s decision and Alaniz & Akata (2019) use an observer-classiﬁer pair model, whose prediction can be exposed as a binary tree.
Contrarily to ours, their model does not provide a local explanation based on parts of the input.
Quint et al.
(2018) extend a classic variational auto-encoder architecture with a differentiable decision tree classiﬁer.
However, their methodology is different and they only experiment on image data.
Most related to our work are methods providing concept-based explanations.
Alvarez Melis &
Jaakkola (2018) learn a self-explainable classiﬁer that takes as input a set of concepts extracted from the original input.
They deﬁne a set of desiderata for what is an interpretable concept, but simply represent extracted concepts as an encoding of the input learned with an auto-encoding loss.
Kim et al.
(2018) learn concept activation vectors, and Zhou et al.
(2018) build on Bau et al.
(2017) to propose a method that generates visual explanations of a classiﬁer, in the form of semantically interpretable components with a corresponding label and heatmap.
However, in these models, the ﬁnal classiﬁer is already trained and ﬁxed while EDUCE is learned end-to-end.
More importantly, these works need concepts to be predeﬁned from human annotations, while EDUCE is unsupervised.
Ghorbani et al.
(2019) propose a method based on unsupervised concept discovery to explain a model a posteriori.
We differ from their work as EDUCE is trained end-to-end to classify solely based on the discovered concepts, which presence is discriminant, resulting in a fully interpretable model.
Finally, we focus on text data while the aforementioned works experiment on image data.
T EXT CLASSIFICATION EXPERIMENTS
We experiment on three text classiﬁcation datasets.
The DBpedia ontology classiﬁcation dataset (Zhang et al., 2015) was constructed by picking 14 non-overlapping categories from DBpedia(Lehmann et al., 2015).
There are 14 classes.
We use 56 , 000 examples of the train dataset for training, and 56 , 000 for validation.
For testing, we use 7 , 000 examples of the test dataset (using stratiﬁed sampling).
Also in Zhang et al.
, the AGNews topic classiﬁcation dataset was constructed from the AG dataset’s 4 largest categories.
There are 4 classes.
We separate the training set into 84 ,training samples and 24 , 000 validation samples and report results on the full test dataset.
We also experiment on the Stanford Sentiment Treebank ( SST )
(Socher et al., 2013) that includes 5 sentiment classes.
For DBPedia and AGNews we use ﬁxed word vectors trained on Common Crawl (Grave et al., 2018).
For SST, we use ﬁxed Glove word vectors (Pennington et al., 2014).
Comparative models.
Since we are concerned with building self-interpretable models, we do not compare with the methods presented in Section 3 that explain a model a posteriori.
Rather, for comparison, we report the performance of (i) using a Bidirectional LSTM on the full text and predict directly from its hidden state (Baseline) (ii) the No Concept Loss model that uses a binary discrete intermediate representation but no concept classiﬁer, it corresponds to λ = 0 and its training objective is simply L output and (iii) adding a L 1 -norm sparsity constraint to the No Concept Loss model (referred to as No Concept Loss + L 1 ), i.e. Equation 5 changes to:
[Equation]
Therefore both No Concept Loss and No Concept Loss + L 1 models extract excerpts and use a [Table] binary intermediate representation, but are trained [Table]
[Table]
Hyperparameters selection.
We tried different values of hyperparameters (details in supplementary
Section B.1) and for each set of hyperparameters, we run 5 different random seeds.
We choose the best hyperparameters set using its average validation performance over the 5 random seeds.
Metrics.
We report the test output accuracy (Output Acc.) over the task.
Evaluating the relevance of discovered concepts is a challenge in the unsupervised setting.
To measure how well the discovered concepts align with human deﬁned concepts one would need human experiments, which we consider as future work.
However, we evaluate how consistent and separable the discovered concepts are, as a proxy to measure how easy it would be for a user to interpret them.
For EDUCE, we can compute the accuracy of the concept classiﬁer on the test data.
However, this should be low for models No
Concept Loss and No Concept Loss + L 1 that do not train with a concept loss.
Therefore, to evaluate interpretability, we report an a posteriori concept accuracy: after training, for each model (including
EDUCE)
, we gather the excerpts extracted ( z c = 1 ) in the test data.
We separate these excerpts into two sets (training and testing, note that these are both generated from the test data).
We train a new, separate linear concept classiﬁer a posteriori on the extracted excerpts to evaluate and we report its performance as a posteriori concept accuracy (A Posteriori Concept Acc.).
Quantitative results on DBPedia and AGNews.
Table 1 reports test performance on the DBPedia and AGNews datasets for C
= 10 concepts.
We report results with values λ = 0 .
1 and λ L 1 =
.that give best trade-off performance between output and concept accuracies.
Complete results are available in supplementary Table 4.
For all metrics we report the mean and standard error of the mean (SEM) over the training random seeds.
Table 1 shows that the Baseline model outperforms the other models that all employ a binary discrete encoding of the input.
This is expected, and shows the trade-off between interpretability and output accuracy.
In terms of output accuracy, EDUCE is comparable with its counterpart that does not encourage concept consistency (No Concept Loss), loosing only 0 .
4% on DBPedia and 0 .
7% on AGNews, and as expected outperforms it in terms of concept accuracy.
Adding an L 1 constraint to the No Concept Loss model increases the consistency of the concepts (as per A posteriori Concept Accuracy values) yet is largely outperformed by EDUCE on that metric, and output accuracy is also lower than EDUCE’s.
Interpreting EDUCE on AGNews.
We turn to show how EDUCE’s output prediction is easily interpretable.
The following results were generated with λ = 0 .
1 and C = 10 concepts.
Figure 2a shows examples of the AGNews test set that were correctly classiﬁed by EDUCE.
The underlined words correspond to the excerpts extracted for different concepts.
Separately, in Figure 2b we show, for each concept detected in the examples of Figure 2a, examplar excerpts extracted from others test documents (excerpts are separated by “/").
We interpret the concepts’ meaning as follows: conceptmaps to informatics notions, concept 2 to corporations/petrol, concept 4 to the notions of investments and ﬁnance, concept 6 to sports events and concept 8 to governmental/state affaires.
Concept 1 is less clearly deﬁned.
Note that in Figure 2b excerpts are consistent yet are extracted in texts from multiple output classes.
The excerpts extracted in the examples of Figure 2a are consistent with these interpretations.
These results show how easily the classiﬁcation of any text can be explained by the detection of multiple, relevant, and intelligible concepts.
More qualitative examples are in supplementary Section C. Note that supplementary Table 10 shows the concepts extracted by the No
Concept Loss model, we see that they form less semantically consistent units and are hard to interpret.
Supplementary table 8 shows test examples where the ﬁnal classiﬁer’s prediction was incorrect.
In some of these, the predicted class could be considered as an appropriate label, and importantly the concepts that are identiﬁed as present in the text are relevant with the set of discovered concepts.
[Table]
SST dataset Figure 3d shows output accuracy versus a posteriori concept accuracy on the SST dataset, for different different number of concepts C and different values of λ : Each marker is a different value of λ , and values are (from left to right markers) { 0 , 0 . 01 , 0 . 1 , 0 . 5 } .
We do the same for the No Concept Loss + L 1 model.
Note that the left most markers in all curves correspond to λ
=and λ L 1 = 0 , therefore to the model referred to as No Concept Loss.
While our goal and model is very different than Lei et al.
; Bastings et al.
(2019), we report their test scores (obtained using 40% of the text on the SST dataset, we report directly from Bastings et al.
The a posteriori concept accuracy for Baseline, Lei et al.
(2016) and Bastings et al.
(2019) is not applicable.
Figure 3d conﬁrms our results: EDUCE (in blue, purple and red) overperforms the model
No Concept Loss + L(in green) on both output and a posteriori concept accuracies, and achieve output accuracy comparable to Lei et al.
(orange line) while having 60% a posteriori concept accuracy.
Regarding the effect of the number of concept C , for a ﬁxed C , choosing the adequate value of λ allows the user to balance between ﬁnal accuracy and concepts’ accuracy.
Similar performances can be achieved by different number of concepts: C = 20 , λ = 0 .
1 (dotted purple line, squared marker) achieves ∼ 41 .
5% ﬁnal accuracy and ∼ 70% concept accuracy, while C = 5 , λ = 0 .
01 (plain blue line, diamond marker) achieves ∼ 42 .
0% ﬁnal accuracy and ∼ 60% concept accuracy.
The smaller the number of concepts, the smaller the value of λ which is expected as with less concepts the task of the concept classiﬁer is easier.
Figure 3a shows the empirical frequency of presence of each concept, per output class in the SST dataset, using λ = 0 .
1 and C = 10 concepts.
We see that concepts 3, 5 and 7 are often triggered when a sample is positive or very positive, and on the opposite concept 8 is present in negative/very negative texts.
The values of weight matrix δ of the output classiﬁer in Figure 3b proves that the presence of these concepts is responsible for the output classiﬁer’s prediction.
We can further analyze the concepts: Each word in SST sentences is annotated with a label for the sentiment it expresses, referred to as word label .
We do not use them during training or validation, but at test-time this allows us to analyze the repartition of words labels in the set of excerpts extracted for each concept.
Figure 3c shows that indeed the excerpts selected for concepts 3, 5 and 7 are mostly composed of positive or very positive words, and the excerpts extracted when concept 8 is triggered are mostly composed of negative or very negative words 2 .
[Figure]
M ULTI ASPECT S ENTIMENT A NALYSIS EXPERIMENT
BeerAdvocate dataset While our paradigm is different than Lei et al.
; Bastings et al.
(2019), we also perform a multi-aspect sentiment regression experiment on the pre-processed subset of the
BeerAdvocate 3 dataset (McAuley et al., 2012).
It consists of 260 , 000 beer reviews where ratings for four aspects (look, smell, palate and taste) are given, as well as an overall rating.
The reviews are separated into training/validation sets speciﬁc to each aspect, and ratings are mapped to scalars in [0 , 1] .
This is a regression task, so we modify the Baseline model and EDUCE in the last layer of the prediction with a sigmoid activation function, and use Mean Squared Error (MSE) instead of cross-entropy for L output ( y, z ( x ) , δ ) .
McAuley et al.
(2012) provided a test set ( 994 reviews) with sentence-level rationale annotations: different parts of each review are annotated with one (or multiple) aspect label, indicating what aspect it covers (referred to as gold rationales).
Importantly, we do not use these gold rationales during training or validation, but use to evaluate our model.
Hyperparameters selection is similar to our classiﬁcation experiments.
We train EDUCE on the prediction of the 5-values vector at once (4 aspects and the overall score, there are therefore 5 scalar ratings to predict) using the 260 , 000 reviews.
We compare EDUCE’s performance with the Baseline that accesses the full text.
The test MSE is 0 .
0089 ± 0 .
(mean and
SEM accross training seeds) for the Baseline model and 0 .
0119 ± 0 .
for EDUCE using λ = 0 .and
C =
10 concepts, with a corresponding concept accuracy of 92 .
8 ± 0 .
Of speciﬁc interest to us is the per-concept precision of gold rationales and the total percentage of selected words.
Indeed,
Table 3 shows that when predicting the 4 aspects and the overall score, some concepts are capturing a speciﬁc aspect: for example, the precision of Concept 7 on the Appearance aspect is 97 .
This is conﬁrmed by Table 2 that shows that excerpts extracted for Concept 7 are mostly related to the color and head (the frothy foam on top of beer) of the beer 4 .
Supplementary Table 5 reports examplar excerpts for all concepts.
As in Lei et al.
; Bastings et al.
we also train EDUCE on the prediction of each of the ﬁrst three aspects separately.
Supplementary Table 6 reports the precision of gold rationales for each aspect.
While the results are less convincing than the models speciﬁcally designed for rationales extraction, extracted excerpts match gold rationales to a certain extent.
Tables 3 and 2 reports
[Table] [Table]
D ISCUSSION AND PERSPECTIVES
We propose a new self-interpretable model, EDUCE, that maps inputs to an easy-to-interpret representation on which the output prediction relies.
We experimentally demonstrate its ability (i) to extract semantically meaningful concepts described by consistent excerpts, and (ii) to ground its output prediction on the presence/absence of these concepts in each input.
EDUCE generates relevant explanations while retaining high predictive performance.
As future direction for research, we contemplate using hierarchical representations, as human notions can often be represented with hierarchical structures, for example as in WordNet (Miller, 1995).
Furthemore, our principles can be applied on different types of inputs like images, and we provide initial experiment in Supplementary
Section D
A D ETAILS ON THE LEARNING ALGORITHM
As mentioned in our main paper, when computing Equation 5 the cross-entropy losses of the output classiﬁer and concept classiﬁer are differentiable, therefore the gradients with respect to the weights δ and θ can be computed.
However, the gradients with respect to the parameters of the LSTM ( γ ) and the Bernouilli distribution over presence of concepts ( α ) pose a difﬁculty because we sample ∀ c s c ( x ) ∼ p γ ( s | x, c ) and
∀ c
z c ∼ p
α
( z c | s c ( x ) , c ) .
We use straight-through estimator (Bengio et al., 2013b) in the backward pass for the parameters α , and resort to Monte-Carlo approximations of the gradient employed in Reinforcement Learning (Sutton & Barto, 1998) for the parameters γ .
The loss L ( x ) serves as reinforcement signal.
We weight the two terms of the gradient using a parameter r as follows:
[Equation]
(7) where r controls the strength of the Reinforcement Learning term and b is the average of the loss, used as control variate.
B E XPERIMENTAL DETAILS AND DETAILED RESULTS .
We monitor validation performance and use early stopping.
For the comparative models we monitor the output prediction accuracy.
For EDUCE we monitor the sum of the output prediction accuracy and the concept classiﬁer accuracy (weighted by the parameter λ ).
B. H YPERPARAMETERS CONSIDERED
In all experiment, we increase the value of λ by 1 0% every epoch.
In order to choose the best set of hyperparameters, we take the average value on the 5 random seeds.
DBPedia and AGNews We try the following ranges of hyperparameters λ ∈ { 0 . 0 , 0 .
001 , 0 . 01 , 0 . 1 } , λ L 1 = { 0 . 0 , 0 .
001 , 0 . 01 , 0 . 1 , 1 } , r ∈ { 0 . 01 , 0 . 1 } , learning rate lr = { 0 . 0005 , 0 . 001 } .
The hidden state of the LSTM is of size 200 .
We use Adam optimizer (Kingma & Ba, 2014), batches of size 64 .
For the Baseline model, we try adding weight decay in { 0 . 0 , 1 e − 6 } and dropout in { 0 . 0 , 0 . 1 , 0 . 2 } .
SST
We try the following ranges of hyperparameters λ ∈ { 0 . 0 , 0 .
001 , 0 . 01 , 0 . 1 } , λ L 1 = { 0 . 0 , 0 .
001 , 0 . 01 , 0 . 1 , 1 } , r ∈ { 0 . 01 , 0 . 1 } , learning rate lr = { 0 . 0002 , 0 .
001 } and weight decay in { 0 . 0 , 1 e − 6 } .
The hidden state of the LSTM is of size 150 .
We use Adam optimizer (Kingma & Ba, 2014), batches of size 25 .
For the Baseline model, we follow Bastings et al.
and use weight decay 1 e − 6 and dropout { 0 . 5 } .
BEER
We try the following ranges of hyperparameters λ ∈ { 0 . 001 , 0 . 01 , 0 . 1 } , r ∈ { 0 .
001 , 0 . 01 , 0 . 1 } , learning rate lr = { 0 . 0005 , 0 . 001 } .
The hidden state of the LSTM is of size 200 .
We use Adam optimizer (Kingma & Ba, 2014), batches of size 256 .
We also clip the gradient to the value of 1 and employ an entropy maximization regularization on mean of the Bernoulli distributions ∀ c, p α ( z c | s c ( x ) , c ) , weighted by 0 .
We train all models for 250 epochs and use early stopping on the validation set.
For the Baseline model on the BEER dataset, we use the same hyperparameters as in Bastings et al.
( lr = 0 .
0004 , hidden dimension 200 , dropout in { 0 . 1 , 0 . 2 } and weight decay 1 e − 6 ) and train for 100 epochs.
B.1. D ETAILED RESULTS ON AGN EWS AND DBP EDIA
[Table]
B. A DDITIONAL RESULTS ON B EER
As in Lei et al.
; Bastings et al.
[Table]
we also train EDUCE on the prediction of each of the ﬁrst three aspects (the 4th aspect they do not experiment on) 5 .
Table 6 reports the precision of gold rationales for that aspect and the total percentage of selected words, values for Lei et al.
; Bastings et al.
(2019) are taken from Bastings et al.
We use C = 10 and λ = 0 . 1 .
Concept0 fruity esters , and/ fruits , caramelized pecans , and/ toffee and caramel accents ,/ coffee and chocolate ﬂavors/ earthy hop resin .
Concept1 delicious and with/ enjoyed this beer/
damn good beer/ nice stout that/ good beer to
Concept2 creamy and a/ chewy and rich and drinkability/ creamy mouthfeel that/
smooth and just velvety on the/ thick , and
Concept3 rich malt scents/ aroma is quite hoppy with big citrus/ tons of different sweet malts , toffe/ smells extremely roasty/ boom of grapefruity
Concept4 octoberfest : say the word and you probably/
2004 vintage : pours/ 12 ounce bottle acquired in a trade/ i hate to be the guy/ 12oz bottle , best before 9/09 , sampled 5/16/
Concept5 which is fantastic/ it is delicious/ is intensely packed/ and a lovely/ builds a wonderful
Concept6 ’m really digging/ a damn good/ a super fresh growler/ the better abitas/ a great traditional
Concept7 good head and lacing/ beautiful golden-amber color/ creamy tan head/ nice deep brown color/ proud head has settled .
nothing
Concept easy to drink/ hot summer day/ drinkability easy/ easy to down/ can easily turn this ’strong ale ’ into a session
[Table]
carbonation is graceful/ drinkability is excellent/ mouthfeel is wonderful/ mouthfeel is exemplary/ drinkability : excellent
[Table]
trained separately on each aspect.
We consider a word as selected if any of the concept selects it, and count it as one selected even if it is selected by multiple concepts.
While the results are less convincing than the aforementioned rationales models that are speciﬁcally designed for this task, we see that extracted excerpts match gold rationales to a certain extent, especially for the aspects Appearance and Smell.
For the Palate aspect, manual inspection shows us that for some seeds, the model deﬁnes a concept dedicated to the notion of numbers (e.g. corresponding to excerpts “12 ounce bottle”) that is consistent, yet not part of the gold rationale.
C A DDITIONAL QUALITATIVE EXAMPLES ON DBP EDIA AND AGN EWS
Class Sports: just imagine what david ortiz could do on a good night ’ s rest .
ortiz spent the night before last with his baby boy , d ’ angelo , who is barely 1 month old .
he had planned on attending the red sox ’ family day at fenway park yesterday morning , but he had to sleep in .
after all , ortiz had a son at home , and he . . .
Class Sports: foxborough – looking at his ridiculously developed upper body , with huge biceps and hardly an ounce of fat , it ’ s easy to see why ty law , arguably the best cornerback in football , chooses physical play over ﬁnesse .
that ’ s not to imply that he ’ s lacking a ﬁnesse component , because he can shut down his side of the ﬁeld much as deion sanders . . .
Class Sports: ap - american natalie coughlin won olympic gold in the 100-meter backstroke monday night .
coughlin , the only woman ever to swim under 1 minute in the event , ﬁnished ﬁrst in 1 minute , 0 .
37 seconds .
kirsty coventry of zimbabwe , who swims at auburn university in alabama , earned the silver in 1 00 .
laure manaudou of france took bronze in 1 00 .
Class World: lourdes , france - a frail pope john paul ii , breathing heavily and gasping at times , celebrated an open-air mass on sunday for several hundred thousand pilgrims , many in wheelchairs , at a shrine to the virgin mary that is associated with miraculous cures .
at one point he said help me in polish while struggling through his homily in french . . .
Class World: najaf , iraq - explosions and gunﬁre rattled through the city of najaf as u . s .
troops in armored vehicles and tanks rolled back into the streets here sunday , a day after the collapse of talks - and with them a temporary cease-ﬁre - intended to end the ﬁghting in this holy city . . .
Class World: kabul , afghanistan - government troops intervened in afghanistan ’ s latest outbreak of deadly ﬁghting between warlords , ﬂying from the capital to the far west on u . s .
and nato airplanes to retake an air base contested in the violence , ofﬁcials said sunday . . .
Class Business: london ( reuters ) - the dollar dipped to a four-week low against the euro on monday before rising slightly on proﬁt-taking , but steep oil prices and weak u . s .
data continued to fan worries about the health of the world ’ s largest economy .
Class Business: new york ( reuters ) - the dollar extended gains against the euro on monday after a report on ﬂows into u . s .
assets showed enough of a rise in foreign investments to offset the current account gap for the month .
Class Business: reuters - apparel retailers are hoping theirback-to-school fashions will make the grade amongstyle-conscious teens and young adults this fall , but it couldbe a tough sell , with students and parents keeping a tighterhold on their wallets .
Predicted: Business, True Class: Sci/Tech hong kong ( reuters ) - dell inc . &lt dell .
o&gt , the world ’ s largest pc maker , said on monday it has left the low-end consumer pc market in china and cut its overall growth target for the country this year due to stiff competition in the segment .
Predicted: Business, True Class: World supporters and rivals warn of possible fraud government says chavez ’ s defeat could produce turmoil in world oil market .
Predicted: Sports, True Class: World athens , greece - top american sprinters jason lezak and ian crocker missed the cut in the olympic 100-meter freestyle preliminaries tuesday , a stunning blow for a country that had always done well in the event .
pieter van den hoogenband of the netherlands and australian ian thorpe advanced to the evening semiﬁnal a day after dueling teenager michael phelps in the 200 freestyle , won by thorpe . . .
Predicted: Sci/Tech, True Class: Business san francisco – in the latest of a series of product delays , intel corp . has postponed the launch of a video display chip it had previously planned to introduce by year end , putting off a showdown with texas instruments inc . in the fast-growing market for high-deﬁnition television displays .
Predicted: World, True Class: Sports athens – the mistakes were so minor .
carly patterson ’ s foot scraping the lower of the uneven bars .
courtney kupets ’ tumbling pass that ended here instead of there .
mohini bhardwaj ’ s slight stumble on the beam .
Predicted: World, True Class: Sports thens , aug . 17 - so michael phelps is not going to match the seven gold medals won by mark spitz .
and it is too early to tell if he will match aleksandr dityatin , the soviet gymnast who won eight total medals in 1980 .
but those were not the . . .
[Table]
software services giant / moonwalk to home / video display chip / downloading music .
[Table]
upcoming my prerogative video / his ever-growing swimming / launch of a video display chip / illegality of downloading
[Table]
oil market .
/ oil giant sibneft / oil prices and / ipos .
public
Concept 100-meter freestyle preliminaries tuesday , a stunning blow for a / the red sox ’ family day at / the winner .
/ entire era .
[Table]
cash settlement of up to #36 50 million / six-year deal worth about $40 million / the dollar dipped to a four-week low against the euro / ﬁve shares ,
[Table]
york , light / boston and texas / london ( reuters / newsday #146 s
Concept olympic 100-meter freestyle / sox ’ family / olympics should help / athletes were already
[Table]
gunﬁre rattled through the / election .
on / democratic coordination or cd as the / wiretapping internet phones to monitor criminals and terrorists is
[Table]
frail pope john paul / indian army major shot / unions representing workers / goverment representatives .
[Table]
natalie / new york - /
[Table]
[Table] [Table]
who
[Table] [Table]
shutters outside
[Table]
windows /
[Table] [Table]
najaf , iraq - explosions and gunﬁre / latest veterans committee
[Table] [Table]
prices / billed its ipo
[Table]
google inc . ’ / the pollution , the daylight , the noise / video display chip / downloading music .
the ignorance
[Table]
, france / veterans committee ballot / intel corp . has / downloading music .
the ignorance
[Table]
sprinters jason
lezak
and ian crocker missed / david ortiz could / the season .
/ wireless networking standard up to 10 times the speed
[Table]
oil market .
/ david ortiz could do on a good night ’ / proﬁt-taking , but steep oil prices / boston the jury is still out on whether a computer
Concept pilgrims , many in wheelchairs / david ortiz could / factory is never / nobel laureate in medicine
Concept , france - a frail pope / new york ( / world ’ s largest economy / maps , ﬁgures and endless charts
Concept afp - india ’ s tata iron and steel company / quot it hurt / proﬁt-taking , but steep oil / goverment representatives .
but i hope you ﬁnd it
Class Company: transurban
manages and develops urban toll road networks in
australia
and
north america
it
is a top
company
on the
australian
securities exchange (
asx
) and
has been
in
business
since 1996 .
in
australia transurban
has a stake in
ﬁve
of sydney
’ s nine
motorways
and
in
melbourne it
is the full owner
of citylink
which connects
three of
the city
’ s major freeways .
in
the usa transurban has ownership interests in
the 495 express lanes on a section
of
the capital
beltway
around washington
dc .
Class Animal: the red-necked falcon or red-headed merlin ( falco chicquera
is a bird of prey in the falcon family .
this bird is a widespread resident in india and adjacent regions as well as sub-saharan africa .
it is sometimes called turumti locally .
the red-necked falcon is a medium-sized long-winged species with a bright rufous crown and nape .
it is on average 30–36 cm in length with a wingspan of 85 cm .
the sexes are similar except in size males are smaller than females as is usual in falcons .
[Table]
: astroloma is an endemic australian genus of around 20 species of ﬂowering plants in the family ericaceae .
the majority of the species are endemic in western australia but a few species occur in new south wales victoria tasmania and south australia .
species include
[Table]
baxteri
[Table]
cunn .
ex
[Table] [Table]
[Table] [Table]
wilson ms
[Table]
lindl . )
druce
[Table]
compactum
[Table]
[Table] [Table]
conostephioides
[Table]
sond . )
[Table] [Table]
ex benth .
Class Album: stars and hank forever was the second ( and last ) release in the american composers series by the avant garde band the residents .
the album was released in 1986 .
this particular release featured a side of hank williams songs and a medley of john philip sousa marches .
this was also the last studio album to feature snakeﬁnger .
kaw-liga samples the rhythm to michael jackson ’ s billie jean and did well in europe it is as close as the residents ever got to a bona
ﬁde
commercial hit .
Class Written Work:
ﬁre
ice is the
third
book in the numa
ﬁles series of
books
co
-written by
best
-selling author
clive cussler and paul kemprecos and was published in 2002 .
the main character of this series is kurt austin .
in this novel a russian businessman with tsarist ambitions masterminds a plot against america which involves triggering a set of earthquakes on the ocean ﬂoor creating a number of tsunami to hit the usa coastline .
it is up to kurt and his team and some new allies to stop his plans .
Class Educational Inst.: avon high school is a secondary school for grades 9-12 located in avon ohio .
its enrollment neared 1000 as of the 2008-2009 school year with a 2008 graduating class of 215 .
the school colors are purple and gold .
the school mascot is an eagle .
the avon eagles are part of the west shore conference .
they will be moving to the southwestern conference beginning in the 2015-2016 school year .
Class Artist: vicky hamilton ( born april 1 1958 ) is an american record executive personal manager promoter and club booker writer ( journalist playwright and screenwriter ) documentary ﬁlm maker and artist .
hamilton is noted for managing the early careers of guns n ’ roses poison and faster pussycat for being a management consultant for mötley crüe and stryper a 1980s concert promoter on the sunset strip and a club booker at bar sinister from 2001 to 2010 .
Class Athlete: james jim arthur bacon ( birth registered october–december 1896 in newport district — death unknown ) was a welsh rugby union and professional rugby league footballer of the 1910s and ’ 20s and coach of the 1920s playing club level rugby union ( ru ) for cross keys rfc and representative level rugby league ( rl ) for great britain and wales and at club level for leeds as a wing or centre i .
e .
number 2 or 5 or 3 or 4 and coaching club level rugby league ( rl ) for castleford .
Class Ofﬁce Holder: jonathan david morris ( october 8 1804 - may 16 1875 ) was a u .
s .
representative from ohio son of thomas morris and brother of isaac n .
morris .
born in columbia hamilton county ohio morris attended the public schools .
he studied law .
he was admitted to the bar and commenced practice in batavia ohio .
he served as clerk of the courts of clermont county .
morris was elected as a democrat to the thirtieth congress to ﬁll the vacancy caused by the death of thomas l .
Class Mean Of Transp.
: german submarine u-32 was a type viia u-boat of nazi germany ’ s kriegsmarine during world war ii .
her keel was laid down on 15 march 1936 by ag weser of bremen as werk 913 .
she was launched on 25 february 1937 and commissioned on 15 april with kapitänleutnant ( kptlt . )
werner lott in command .
on 15 august 1937 lott was relieved by korvettenkapitän ( krv .
kpt . )
paul büchel and on 12 february 1940 oberleutnant zur see ( oblt .
z .
s . )
hans jenisch took over he was in charge of the boat until her loss .
Class Building: the tootell house ( also called king ’ s row or hedgerow ) is a house at 1747 mooresﬁeld road in kingston rhode island that is listed on the national register of historic places .
the two-story wood-shingled colonial revival house on a 3-acre ( 12000 m2 ) tract was designed by gunther and beamis associates of boston for mr . & mrs . f .
delmont tootell and was built in 1932-1933 .
house design was by john j .
g .
gunther and elizabeth clark gunther was the landscape architect for the grounds .
Class Village: angamoozhi is a village in pathanamthitta district located in kerala state india .
angamoozhi is near seethathodu town .
geographically angamoozhi is a high-range area .
it is mainly a plantation township .
both state run ksrtc and private operated buses connect angamoozhi to pathanamthitta city .
tourist can avail the travelling facility by ksrtc service ( morning 5 30 from kumili and 11 30 from pathanamthitta ) in between kumili and pathanamthitta via vallakkadavu angamoozhi kakki dam and vadaserikkara and can enjoy the beauty of the forest .
[ citation needed ]
Concept a top 50 company / the regular seasonal movement / the production of port wine / the american composers / a bollywood ﬁlm / the third book / a secondary school / an american record executive personal manager promoter / a well-known v8 supercars presenter and commentator / a merchant and public ofﬁcial / a type viia u-boat / a house at / the main fort / a major poet
Concept born in philadelphia / tranquil star ( foaled / instructional documentary produced / bollywood ﬁlm released in / nineteenth instalment in / secondary school for / born april 1 1958 / birth registered october–december 1896 / october 8 1804 - may 16/ academy is the volleyball academy of / village in pathanamthitta
Concept ( 1800–1870 ) probably born in / ( 12 april / ) release in / is a bollywood ﬁlm released in / an omnibus release from / a studio school located in / ( born april / gunji 8 july / ( october 8 1804 - may 16 / an iron collier in / of historic places .
/ fort ( also called
Concept top 50 company / medium-sized long-winged species with a bright rufous crown / endemic australian genus / album was released / bollywood ﬁlm released / paul kemprecos and was published / inns of court exclusively entitled / debut album explores / lagarto ( lizard / hong kong cross-media creator / bird park in / wild blackwater river
Concept beltway around washington dc .
/ democratic republic of / plants in the / party live in / my texas .
/ asheville north carolina .
/ ohio .
its / executive .
he / democrat to the / south africa .
/ mooresﬁeld road in kingston rhode island that / north to south .
/ kerala state india .
Concept is a top 50 company / is a genus of crane ﬂy / is a red portuguese wine grape / is the debut studio record / is an abc family original movie / was a regional fashion entertainment and lifestyle publication / interactive technologies institute / is a beirutbased lebanese haute couture fashion designer / was a montenegrin serb boxer / is the chief technology ofﬁcer / was a type viia u-boat / of historic places .
the two-story wood-shingled / fort ( also / is a village
Concept company on the / bird of prey in / apple .
in / documentary produced by / ﬁlm released in / sequel to the / school for grades / animator .
he / catcher .
he / cross-media creator who / aircraft corporation to / museum was made in Concept the brands club mahindra holidays club mahindra travel club / a bird of prey in / an endemic australian genus of around / snooker world rankings 1978/1979 the professional world rankings for / a black and white chinese animation short made in / a british rugby league periodical that / a russian youth football academy based in / a turkish cypriot singer and athlete .
/ a welsh rugby union and professional rugby league footballer of / a planter a confederate cavalry general in / a type viia u-boat of / a volleyball academy .
/ an uninhabited steep rocky island west of
Concept street sounds was / medium-sized long-winged species with a bright rufous / rataj places it / ep by linkin park / white chinese animation / british schools ( / secondary school for grades / argentine painter of the concretist and cubist schools / eminent anglican priest / hospital ships was built / national register of historic places / uninhabited steep rocky island west /
village
in pathanamthitta district
Concept translation pension fund for / adaptation which enables / mopeds produced by / instructional documentary produced by / bollywood ﬁlm released in / book in the / river in kwazulu-natal / memoir of her / boxer in the / presidency of dmitry medvedev began / u-boat of nazi / harbour of helsingør dedicated to / uninhabited steep rocky island
west
of
[Figure]
D A PPLYING EDUCE PRINCIPLES FOR I MAGE C LASSIFICATION
Having assessed the relevance of our model on text data, we now turn to image data and explore if
EDUCE is also able to extract meaningful concepts.
In that case, the excerpts extracted in textual data are replaced by regions (or patches) in an image, and the recurrent neural architecture processing text is replaced by a classical convolutional neural network.
Principles:
Each image x is ﬁrst encoded through a convolutional neural network that output a representation in h ( x ) =
R W × H × D where D is the number of output ﬁlters.
Each vector h
i,j,.
( x ) ∈
R D corresponds to a particular region s of the input image (i.e the receptive ﬁeld of the convolutional neural network).
Then each h i,j,.
is used to compute p γ ( s | x, c ) through a linear model and a softmax activation as in Section 2.1 (step 1), and to compute p α ( z c = 1 | s c ( x ) , c ) (Section 2.1, step 2) here again with a linear model and a Bernoulli distribution.
The semantics homogeneity is ensured by using an image classiﬁcation network over the region captured by the receptive ﬁeld in the previous convolutional neural networks that ensure that all regions captured from a particular concept ”look the same” and look differently from the regions captured for other concepts.
Experiments:
To ensure the validity of our adaptation of EDUCE to images, we conduct very simple experiments on a dataset composed of 224 × 224 RGB images split in 3 categories: dogs, cats, and birds 6 in equal proportion.
We train on 3 , 000 images and test on 3 , 000 images.
We build our model on top of a pretrained VGG-11 model Simonyan & Zisserman (2014) which is used for computing the intermediate representations h ( x ) .
Said otherwise, the output of the VGG-11 model is used for both detecting relevant regions and thus building the binary representation z , but also to ensure the homogeneity of extracted regions during training.
Figure 4 shows extracted patterns and associated categories.
Final classiﬁcation performance is 91 .
6% with 10 concepts.
In Figure 4 we plot extracted patterns for the 10 concepts and report in Figure 5a the weights of the ﬁnal classiﬁer.
From these two ﬁgures, we can interpret the model’s behavior: concept 8 and concept 9 show what differentiates a dog from a cat or a bird , and support the classiﬁer’s prediction of the dog category.
Moreover, by looking at which regions are extracted by our model (Figure 5b ), we can see that
EDUCE can focus its attention to discriminative regions of the images.
[Figure]
[Figure] [Figure]