conceptual alignment deep neural...

Journal of Intelligent & Fuzzy Systems 34 (2018) 1631–1642DOI:10.3233/JIFS-169457IOS Press

1631

Conceptual alignment deep neural networks

Yinglong Daia, Guojun Wangb,∗ and Kuan-Ching LicaSchool of Information Science and Engineering, Central South University, Changsha, ChinabSchool of Computer Science and Educational Software, Guangzhou University, Guangzhou, ChinacDepartment of Computer Science and Information Engineering, Providence University, Taichung,Taiwan and Hubei University of Education, Wuhan, China

Abstract. Deep Neural Networks (DNNs) have powerful recognition abilities to classify different objects. Although themodels of DNNs can reach very high accuracy even beyond human level, they are regarded as black boxes that are absentof interpretability. In the training process of DNNs, abstract features can be automatically extracted from high-dimensionaldata, such as images. However, the extracted features are usually mapped into a representation space that is not aligned withhuman knowledge. In some cases, the interpretability is necessary, e.g. medical diagnoses. For the purpose of aligning therepresentation space with human knowledge, this paper proposes a kind of DNNs, termed as Conceptual Alignment DeepNeural Networks (CADNNs), which can produce interpretable representations in the hidden layers. In CADNNs, some hiddenneurons are selected as conceptual neurons to extract the human-formed concepts, while other hidden neurons, called freeneurons, can be trained freely. All hidden neurons will contribute to the final classification results. Experiments demonstratethat the CADNNs can keep up with the accuracy of DNNs, even though CADNNs have extra constraints of conceptualneurons. Experiments also reveal that the free neurons could learn some concepts aligned with human knowledge in somecases.

Keywords: Deep neural networks, conceptual alignment, interpretability, supervised learning, representation learning

1. Introduction

Deep Neural Networks (DNNs) can be referredto large Artificial Neural Networks (ANNs) stackedwith many layers. DNNs has very good performancein reducing high-dimensional data into a compactrepresentation space [13]. In various recognitiontasks, such as computer vision [12, 15, 24, 25] andspeech recognition [9, 14], DNNs show powerfulrecognition ability to fit the high-dimensional data.Given enough training data, DNNs trained by anoptimization algorithm can automatically adjust theirparameters and reach to a very high classificationaccuracy. Generally, it is very difficult to explain themeanings of the numerous parameters and the outputs

∗Corresponding author. Guojun Wang, School of Com-puter Science and Educational Software, Guangzhou University,Guangzhou 510006, China. E-mail: [email protected].

of the hidden neurons under the cognitive competenceof human beings. Therefore, the models of DNNs areusually regarded as black boxes that cannot interprethow they classify the objects according to some effec-tive features. Similarly, human beings usually cannotexplain how they can identify some objects. Forexample, Traditional Chinese Medicine (TCM) prac-titioners are difficult to explain how they diagnose thepatients based on subtle observations. However, themodel interpretability is necessary for many appli-cations, especially in clinical diagnoses. People willfeel an interpretable predictive model is more depend-able than an unknown model that delivers resultswithout supportive reasoning. Therefore, the modelinterpretability is crucial for the wide adoption inmedical research and clinical decision-making.

In order to specify the recognition process, humanbeings form many effective abstract concepts to dis-tinguish the different classes of objects. For example,

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1632 Y. Dai et al. / Conceptual alignment deep neural networks

a patient who has pale facial, skinny body, pale tongueand thin tongue coating might be classified intoQi-deficiency body constitution type in TCM [8, 26].Before the advances in deep learning, a majority ofmachine learning methods are heavily dependent onfeature engineering, which is a way to take advantageof the human knowledge. Human beings usually candiscover the underlying explanatory factors hiddenin the observed sensory data, and form the abstractconcepts. In other words, human beings can mapthe observed sensory data into a representation spacedescribed by the abstract concepts, and reach a con-sensus on the recognition tasks. Compared with ablack-box model that provides results without anyreasoning, an accurate and interpretable model willbe more dependable and attractive. This motivatesmany deep learning researchers to explore the repre-sentations in deep models [3]. But why can not thedeep models learn some common sense along withhuman beings? Maybe a direct and effective way isto make the deep models learn the human-formedconcepts so as to form similar cognitions.

This paper proposes a training method that canmake the DNNs map the sensory data into a repre-sentation space aligned with human concepts. Theadvantages to make the DNNs learn the human-formed concepts are twofold. The former one isto let the DNNs become interpretable with humanknowledge, and the latter one is to let the DNNsbecome easy to be trained by a small amount oftraining data with prior knowledge. Moreover, theDNNs will become easy to be debugged because theclassification results can be traced back to the concep-tual neurons. In the proposed Conceptual AlignmentDeep Neural Networks (CADNNs), some neurons inthe hidden layers are chosen as the conceptual neu-rons. These neurons are used to extract designatedfeatures related to the corresponding human-formedconcepts. By introducing the conceptual neurons,the classification results of CADNNs become inter-pretable. Furthermore, the explanatory factors thatcontribute to the classification results can be checked.The main contributions of this paper are highlightedas follows:

– A kind of new DNNs, called CADNNs, is pro-posed. CADNNs have the attractive property ofinterpretability, as well as keep the high accuracylike the DNNs.

– The framework and objective of CADNNs areformalized and analyzed based on DNNs. Thetraining procedure is also provided.

– Experiments are designed to test the differentarchitectures of CADNNs, which results demon-strate that the conceptual neurons can learn theeffective representations of abstract concepts.Furthermore, some experiments show that thefree neurons could also learn the representa-tions corresponding to human-formed concepts,in some cases.

The remainder of this paper is structured as fol-lows. Section 2 provides an overview of the relatedwork. Section 3 describes the methods including thegeneral framework, objective and training method.Section 4 depicts experimental results, whilst dis-cussions and comments are presented in Section 5.Finally, conclusions and directions for future workare presented in Section 6.

2. Related work

With the increasing popularity of Deep NeuralNetworks (DNNs), a number of researches haveattempted to explore the representations space ofhidden layers of DNNs. Zeiler et al. [29, 30] usedeconvolutional networks to explore the low-leveland mid-level image representations. Yu et al. [28]have shown successful studies at learning hierarchicalimage representations from the pixel level via hierar-chical sparse coding. Zhu et al. [31] propose a deepmodel, termed multi-view perceptron, for learningface identity and view representations. For learn-ing robust representations of human physiology, Cheet al. [5] propose to use prior knowledge to regular-ize parameters in the topmost layers. Recently, Cheet al. [6] propose an interpretable mimic learningmethod to distill knowledge from DNNs via Gra-dient Boosting Trees (GBT) to learn interpretablemodels and strong prediction rules. Bengio et al. [4]provide a comprehensive review of representationlearning about learning good representations. Despitemore researchers realize the relationship between therepresentations of DNNs and human-formed con-cepts, there is not a clear method to incorporate theprior knowledge of human-formed concepts into theDNNs.

Transfer learning, which is motivated by the factthat human beings can apply previously learnedknowledge to solve new problems faster even withbetter solutions [18], also confirms the DNNs canlearn effective representations to distinguish thedifferent objects, even in different classification

Y. Dai et al. / Conceptual alignment deep neural networks 1633

tasks [3]. Ahmed et al. [2] propose using trans-fer learning to improve the training of hierarchicalDNNs, and experiments show that transfer learningsubstantially improves the quality of ConvolutionalNeural Networks (CNNs) by incorporating usefulprior knowledge. Long et al. [16] propose a TransferSparse Coding (TSC) approach to construct robustsparse representations for images. Oquab et al. [17]design a method to reuse the layers of DNNs trainedon the ImageNet dataset to compute mid-level imagerepresentations for images in the PASCAL VOCdataset. They demonstrated that the transferable rep-resentations are useful in various kinds of tasks.However, the main difference of this work lies inthat our aim is to make the DNNs generate not onlyeffective but also interpretable representations.

Generative Adversarial Networks (GANs) [10] areused to learn to generate the observations from a com-pact low-dimensional representation space. Recently,GANs have shown promising results in learning hier-archical representations [19]. InfoGAN [7], which isa variant GAN, shows it can learn interpretable rep-resentations. In the experiments, it discovers visualconcepts, such as hair styles, presence of eyeglassesand emotions [7]. Reed et al. [20, 21] demonstratethat GANs can generate images from human visualconcepts. Reed et al. [22] also propose modelscombining CNNs and Long Short-Term Memories(LSTMs) to relate the images with fine-grained andcategory-specific language concepts. However, theinterpretable representations produced by GANs arestill very limited.

3. Methods

The information process of Deep Neural Networks(DNNs) is transmitting key information layer by layerfrom the input layer to the output layer. It can alsobe regarded as a representation space transforma-tion when the activation codes of the neurons ina layer activate the neurons in the next layer. Forthe recognition tasks, the layers of DNNs trend tohave smaller neurons from the input layer to the out-put layer. Therefore, these DNNs are to make theinput high-dimensional data reduce to a compact low-dimensional representation space. Generally, only therepresentation space of the output layer is meaningfulto human beings. The output neurons are trained tobe aligned with the category labels, which are usu-ally high-level abstract concepts. It is worth notingthat the categories are also human-formed concepts.

Generally, human-formed concepts can be organizedhierarchically. The fine-grained concepts form thehigh-level abstract concepts. In this way, the human-formed concepts should be hierarchically distributedin a DNN. Based on this conception, a framework isdevised as follows.

3.1. General framework

The general DNNs are illustrated as Fig. 1, wherethey are trained to fit the input and output variables,whilst the variables represented by the neurons in hid-den layers are not concerned. This paper proposesto train the DNNs having hierarchical interpretablehidden neurons aligned with human-formed con-cepts, termed Conceptual Alignment Deep NeuralNetworks (CADNNs), as illustrated in Fig. 2. Themethod is to assign some effective meanings to someselected hidden neurons, called conceptual neurons.

Fig. 1. The illustration of a general DNN. The circles representthe neurons of DNN. Only the neurons of input layer and outputlayer are assigned meanings, and they are drawn as shaded circles.

Fig. 2. The illustration of a CADNN. The circles represent theneurons. The shaded circles in hidden layers are conceptual neu-rons, and the hollow circles are free neurons, which can be trainedfreely.


In addition, there are still hidden neurons, calledfree neurons, used to be trained in their own way.The number of conceptual neurons in each hiddenlayer depends on specific applications. It can be zeroconceptual neuron or full of conceptual neurons ina hidden layer. The conceptual neurons need to bemanually assigned according to human knowledge.In shallow hidden layers, conceptual neurons shouldbe assigned to represent low-level abstract concepts.And high-level abstract concepts should be repre-sented by conceptual neurons in deep hidden layers.

A m-layer CADNN can be defined as Net(W, b),where W and b denote the model parameters. Assumethe neurons of the input layer are represented by avector x. The non-linear transformation in the firsthidden layer is

h1 = (h1f , h1c) = f (x), (1)

where h1 is a vector that represents the free neuronsand conceptual neurons in the first hidden layer, h1f

denotes the free neurons, h1c denotes the conceptualneurons, and f (·) is the non-linear transformationfunction. The typical function is a linear weightedsum with a non-linear activation function as

f (x) = σ(W1x+ b1), (2)

where W1 is the weight matrix for the first hiddenlayer, b1 is the bias scalar for the first hidden layer,and σ(·) is the activation function, which can besigmoid function, tanh function, softmax, RectifiedLinear Unit (ReLU), or any other variants [11]. In asimilar way, the non-linear transformation in the ithhidden layer can be formulated as

h(i) = (h(i)f , h(i)c) = f (h(i−1)). (3)

The parameters of f (h(i−1)) are denoted as W i andbi. Finally, the result of the output layer is

o = f (h(m−2)), (4)

where o is a vector that represents the neurons in theoutput layer, the parameters of f (h(m−2)) are W (m−1)and b(m−1).

3.2. Cost function

Given a training sample x, and the correspondingconceptual label y = {y1, ..., yi, ..., y(m−1)} wherey1 is a vector that is used to label the conceptual neu-rons in the first hidden layer and has the same sizewith them, yi is used to label the conceptual neuronsin the ith hidden layer and has the same size with

them, and y(m−1) is the label for the output layer. Thecost of first hidden layer can be measured by �2-norm,written as

J1(x) = 1

2‖y1 − h1c‖22, (5)

where the h1c is calculated according to Equation (1).In a similar way, the cost of ith hidden layer can bewritten as

Ji(x) = 1

2‖yi − h(i)c‖22, (6)

where the h(i)c is calculated using the forward prop-agation method according to Equation (3). The costof the output layer can be written as

J(m−1)(x) = 1

2‖y(m−1) − o‖22. (7)

where the o is calculated using the forward propaga-tion method according to Equation (4). And the totalcost is the accumulated cost of each layer adding aregularization term, written as

J(x) =m−1∑

i=1

(βiJi(x)+ λ

2‖W i‖22), (8)

where λ is a hyper-parameter, which is used to avoidover-fitting by controlling scale of the weights. Thehyper-parameters β = {β1, . . . , βm−1} are used totrade off the objectives of each one of layers.

For a training data set (X, Y ) containing n sam-ples {x(j), y(j)}, (1 � j � n), the batch cost can beevaluated using the average cost, as

J(X) = 1

n

n∑

j=1

m−1∑

i=1

(βiJi(x(j))+ λ

2‖W i‖22). (9)

3.3. Training procedure

Once an objective function as Equation (9) is cho-sen, the parameters of a CADNN model can be trainedby optimization methods, such as Stochastic Gradi-ent Descend (SGD). In order to use the optimizationmethods, the partial derivatives of the objective func-tion with respect to parameters need to be calculated.Back-Propagation (BP) algorithm [23], which is acommon method to train the multi-layer artificial neu-ral networks, also can be used to train the CADNNs.BP algorithm uses a chain rule to calculate the partialderivatives. At the start, a feedforward pass compu-tation runs from the input layer to the output layer,and the loss values of the output neurons can be


calculated. Then, the loss values can be propagatedbackwards and be used to calculate the partial deriva-tives with respect to the parameters of each layer.The partial derivatives of the weights W (m−1) andthe biases b(m−1) with respect to the output layer ofCADNNs can be obtained as follows,

∂J(x)

∂W (m−1)= ∂J(m−1)(x)

∂W (m−1)+ λ‖W (m−1)‖2, (10)

∂J(x)

∂b(m−1)= ∂J(m−1)(x)

∂b(m−1). (11)

And they can directly compute the results accord-ing to Equation (7). The partial derivatives of theweights W i and the biases bi with respect to the ithlayer of CADNNs can be obtained as follows,

∂J(x)

∂W i

=m−1∑

t=i

∂Jt(x)

∂W i

+ λ‖W i‖2, (12)

∂J(x)

∂bi

=m−1∑

t=i

∂Jt(x)

∂bi

. (13)

Each ∂Jt (x)∂W i

and ∂Jt (x)∂bi

in Equations (12) and (13)can be calculated according to the chain rule of BPalgorithm. The partial derivatives of all the layers canbe calculated from the output layer to the input layer.The training procedure for CADNNs is described asAlgorithm 1. First of all, the specific architecture ofa CADNN Net(W, b) needs to be defined. At thestart of training, the parameters (W, b) of the definedCADNN are set randomly. For each training epoch, amini-batch of training data (Xm, Ym) is sampled fromthe entire training dataset (X, Y ). Based on BP algo-rithm and Equations (12) and (13), the mini-batch canbe used to calculate the partial derivatives (gw, gb)with respect to the weights and biases, which arethen used for updating the parameters according toa learning rate α. A training epoch contains a numberof iterations of the parameter updates so as to traversethe entire training dataset. And a number of trainingepoches are needed to optimize the parameters to fitthe data. When the training loss J(X) is converged,the parameters (W, b) of the network Net(W, b) areobtained.

In addition, the conceptual neurons of CADNNscan be pre-trained from the input layer to the outputlayer. Once the training for a layer is finished, thelearning rate for the parameters related to the alignedconceptual neurons need to be decreased in the fol-lowing training process, and the complete CADNNsshould be fine-tuned in the end.

Algorithm 1 CADNN training algorithm, the train-ing procedure of Conceptual Alignment Deep NeuralNetworks (CADNNs)Input:

Training dataset (X, Y ), network definitionNet(W, b), objective functionJ(X), learning rateα, regularization hype-parameter λ, and layer-wise hype-parameters β.

Output:Parameters (W, b), loss value J(X).

1: Randomly set the initial parameters (W, b) of thenetworks.

2: for t = 1, . . . , T do3: for k = 1, . . . , K do4: Sample a mini-batch (Xm, Ym) from train-

ing data set (X, Y )5: Use BP algorithm to compute the partial

derivatives according to Equations (12) and (13):

gw← ∇wJ(Xm),gb ← ∇bJ(Xm).

6: Update the corresponding parameters:

w← w− α · gw, b← b− α · gb.

7: end for8: end for9: return (W, b) and J(X).

4. Experiments

4.1. Dataset

Fashion-MNIST dataset [27] is used in the exper-iments. It is a dataset that has the same format asthe popular and overused MNIST dataset consist-ing of a training set of 60,000 examples and a testset of 10,000 examples. Each example is a 28× 28grayscale image, associated with a label from 10classes. In contrast with the simple handwritten digitsin MNIST dataset, the examples in Fashion-MNISTdataset are images about different clothes, trousers,shoes and bags, as shown in Table 1.

4.2. Experimental design

4.2.1. Hierarchical label generationIn order to obtain the hierarchical labels, we further

reduce ten classes of examples into four classes. Theyare top, bottom, shoe and bag, as shown in Table 2.The top class includes T-shirt, pullover, dress, coatand shirt corresponding to the original label 0, 2,4 and 6 respectively. The bottom class includes the


Table 1The labels and the examples of Fashion-MNIST dataset

Table 2The high-level concepts and the label definition

Label Concept Original labels

0 Top 0 (T-shirt), 2 (Pullover), 3 (Dress),4 (Coat), 6 (Shirt)

1 Bottom 1 (Trouser)2 Shoe 5 (Sandal), 7 (Sneaker), 9 (Ankle boot)3 Bag 8 (Bag)

trouser corresponding to the original label 1. The shoeclass includes sandal, sneaker and ankle boot corre-sponding to the original label 5, 7 and 9 respectively.The bag class includes bag corresponding to the orig-inal label 8. Therefore, a training dataset of two-layerlabels is obtained. The original labels can be used fortraining the conceptual neurons in the hidden layer,while the four new labels are used for training theneurons in the output layer.

4.2.2. Experimental architecturesThe neurons in the input layer and the output layer

are prescribed in the experiments. The size of theinput layer neurons is 784, which is the number ofpixels of an input image (28× 28). The output layerhas 4 neurons for four generated labels as shown inTable 2. And the activation function for output layeris softmax. A simple CADNN architecture A1, whichhas three fully-connected layers, is defined for explo-ration at start. As illustrated in Fig. 3, there are a totalof 100 hidden neurons, 10 conceptual neurons andother 90 free neurons in the hidden layer. The activa-tion function is sigmoid function. In order to checkthe performance of the conceptual neurons, there isalso an extreme architecture A2. It has only ten con-ceptual neurons and no free neuron, as illustrated inFig. 4. The activation functions and the connectiontypes are the same with architecture A1.

Fig. 3. The illustration of architecture A1. The input layer has784 neurons, the output layer has 4 neurons, and its activationfunction is softmax. The hidden layer has 100 neurons including 10conceptual neurons and 90 free neurons. The activation functionof hidden layer is sigmoid function. The two connection typesbetween the three layers are fully-connected.

As shown in Table 2, if there are ten concep-tual neurons corresponding to ten original labels, thenew defined labels are completely represented byten conceptual neurons. In order to test the incom-plete representation situation, another architectureA3, which cuts down the conceptual neurons, is alsoexplored. As illustrated in Fig. 5, architecture A3 alsodeploy 10 neurons in the hidden layer, but there arejust 9 conceptual neurons aligned with nine originallabels, which do not contain the last conceptual label“ankle boot”. In addition, there is one free neuron thatcan be trained freely. The activation function for thehidden layer is also sigmoid function, and the layers


Fig. 4. The illustration of architecture A2. It is an extreme casethat all 10 conceptual neurons and no free neuron are found in thehidden layer. The 10 conceptual neurons are used to be aligned withthe ten original labels. The activation functions and connectiontypes are the same with A1.

Fig. 5. The illustration of architecture A3. There are 9 conceptualneurons and one free neuron in the hidden layer. The 9 conceptualneurons are aligned with nine labels in the ten original labels, andthe free neurons can be trained freely. The activation functions andconnection types are the same with A1.

are fully connected. In case of incomplete representa-tions of 9 conceptual neurons, an interesting questionis that whether the free neuron can learn an effectiverepresentation aligned with the veiled label “ankleboot”.

The deeper architectures A4 and A5 are designed.Architecture A4 is an extension of A2. Four layers

are interpolated between the input layer and the hid-den layer of A2. They are two convolutional layersfollowed two max-pooling layers respectively. In thesame way, architecture A5 extends the architecture A3by adding more hidden layers, as illustrated in Fig. 6.Architecture A4 has almost the same structure withA5 except that the last hidden layer are filled with10 conceptual neurons, so the illustration of architec-ture A4 is omitted. The kernel sizes of convolutionsare all 5× 5 using the SAME mode, and the kernelsizes of the max-poolings are all 2× 2. There are 8kernels for first convolutional layer, and 16 kernelsfor second convolutional layer. ReLU is specified asactivation function for two convolutional layers. Theactivation functions for last hidden layer and outputlayer are still sigmoid and softmax respectively. Theinput layer is resized to a 28× 28 map. Through firstconvolutional computations, the input data will mapto 8 feature maps. The size of each feature map is28× 28. Therefore, there are 6272 neurons in thefirst hidden layer. After max-pooling computations,the sizes of feature maps are reduced to 8× 14× 14.The number of neurons in second hidden layer isreduced to 1568. Second convolutional computationsmap the outputs of first max-pooling layer into 16 fea-ture maps of size 14× 14. Then second max-poolingcomputations reduce them into 16 feature maps ofsize 7× 7. So there are 3136 neurons in the thirdhidden layer and 784 neurons in the fourth hiddenlayer. The 784 neurons are fully connected to the 10neurons in last hidden layer. Finally, the neurons oflast hidden layer are fully connected to the 4 neuronsin output layer.

4.3. Experimental results

The designed architectures are implemented andtested using TensorFlow [1]. The TensorFlow (ver-sion 1.0) is installed on Python 3.5 (64-bit), andthe computing environment is based on Windows 10(64-bit), 2.30 GHz CPU (Intel i3-2350M) and 4 GBmemory. A training process of A1 compared with asame structure with all free neurons is illustrated inFig. 7. The gradient descent optimizer is used, and thelearning rate is set to 1. The hyper-parameters β1 andβ2 are all set to 1. Architecture A1 quickly reaches ahigh accuracy after about 10 training epoches andacquires an accuracy near 99% at the end of 100training epoches. The performance of architectureA1 is almost the same with the corresponding DNNarchitecture. Then, several comparative architectures,which have almost the same structure with A1 except


Fig. 6. The illustration of the architecture A5. Architecture A4 has almost the same structure except that there are full of 10 conceptualneurons in the last hidden layer. The convolutions use the SAME mode. The activation functions for the convolutional layers, the last hiddenlayer, and the output layer are ReLU, sigmoid and softmax respectively. The numbers of neurons from the first hidden layer to the fifthhidden layer are 6272, 1568, 3136, 784 and 10 respectively.

Fig. 7. The illustration of the training processes of architectureA1 (CADNN) and architecture A1 with all free neurons (DNN).The horizontal axis indicates the training epoch and the verticalaxis indicates the accuracy. It shows that A1 has almost the sameperformance with the corresponding DNN architecture.

that the number of its free neurons were reduced to 10,5 and 2, have been tested. The experimental resultsare almost the same with A1.

To the extreme case, another architecture A2 withonly 10 conceptual neurons in the hidden layer alsohas been tested. The gradient descent optimizer isused again, and the learning rate is set to 1 too.The hyper-parameters β1 and β2 are also set to 1.As expected, the experimental results are almost thesame with A1 except for a tiny accuracy reductionto about 98.5%, because the ten conceptual neuronsconstruct a complete representation space for the fourgenerated labels. On the other hand, the accuracy ofthe conceptual neurons used in identifying the ten

Fig. 8. The illustration of the performance of conceptual neuronsin the architecture A2. This figure shows the accuracies of con-ceptual neurons in identifying ten original labels in 100 trainingepoches. As a comparison, the accuracies of ten hidden neuronstrained freely in a DNN framework are also plotted. It shows thatconceptual neurons are trained to be aligned with ten original labelsrather than unaccountable representations.

original labels is checked in order to observe the per-formance of conceptual neurons. Figure 8 illustratesthe performance of conceptual neurons in the archi-tecture A2. In the training framework of CADNNs,the conceptual neurons demonstrate that they havelearnt the representations aligned with the concep-tual labels. The free neurons in DNN framework canlearn some representations that contribute to a highaccuracy in the end, but they have just learnt someinexplicable representations, which make no sensefor human beings.


Fig. 9. The illustration of the training result of the architecture A3,β1 = 1 and β2 = 1. It is a trade off that sacrifices the accuracy ofthe hidden layer for a high accuracy of output layer. The outputlayer remains a high accuracy in recognizing four newly gener-ated labels. However, the hidden layer achieves a low accuracy inidentifying ten original labels.

In order to answer that whether a free neuroncan learn the representation aligned with the veiledconcept of “ankle boot”, some experiments on archi-tecture A3 are explored. Figure 9 shows a trainingresult using the hyper-parameters β1 = 1 and β2 = 1.Although the accuracy of the output layer remainshigh, the accuracy of the hidden layer drops sharply.This result shows that the hidden layer is adjustedto another representation space. There is a trade offthat the training algorithm has to keep the accuracy ofoutput layer according to the objective function, referto Equation (9). Generally, a complex objective func-tion has numerous local minimums, and optimizationalgorithms usually fall into a local optimal solution.Therefore, the result of Fig. 9 is just an undesiredlocal optimal solution. It is possible to increase thevalue of parameter β1 to promote the conceptual neu-rons be aligned with conceptual labels. Figure 10shows a training result using the hyper-parametersβ1 = 10 and β2 = 1. In this case, Stochastic Gradi-ent Descent (SGD) algorithm adjusts the parametersof A3 to converge into a local optimal solution thatthe hidden layer achieves an accuracy of about 82%,which is close to the results of architecture A2. Itdemonstrates that the representation space of hiddenlayer has aligned with ten original labels. That is tosay, the free neuron has learnt the representation oflabel “ankle boot”.

As a comparison with architecture A2, a result ofthe deeper architecture A4 is illustrated in Fig. 11,

Fig. 10. The illustration of the training result of the architecture A3,β1 = 10 and β2 = 1. The output layer remains a high accuracy inrecognizing the four generated labels. Moreover, the hidden layerachieves almost the same accuracy as architecture A2 in identifyingten original labels.

Fig. 11. The illustration of the training result of the architecture A4,β5 = 1 and β6 = 1 (β1, β2, β3 and β4 are not cared). The accuracyof last hidden layer is above 90%, and the accuracy of output layeris above 99%. Compared with the experimental results of previousshallow architectures, it shows an accuracy boost.

where β5 = 1 and β6 = 1. It is worth noting that thereis no conceptual neuron in the preceding four hiddenlayers, so the corresponding costs of these layers areall zero. Hence, the values of β1, β2, β3 and β4 are notcared according to Equation (8). The result shows thatthe deeper architecture A4 boosts the accuracy of thehidden layer to exceed 90% in identifying the 10 orig-inal concepts. And the accuracy of the output layeris reached above 99%. As a comparison with archi-tecture A3, the deeper architecture A5 is also tried.The conceptual label “ankle boot” is also eliminated


Fig. 12. The illustration of the training result of architecture A5,β5 = 10 and β6 = 1 (β1, β2, β3 and β4 are not cared). The outputlayer has a high accuracy above 99%, while the last hidden layerjust achieves an accuracy just about 80%. The accuracy reduc-tion of last hidden layer demonstrates that the free neuron has notconverged to an effective representation of “ankle boot”.

Fig. 13. The illustration of a training result of the architecture A5replaced the activation function of last hidden layer by softmax,β5 = 10 and β6 = 1 (β1, β2, β3 and β4 are not cared). The accu-racy of last hidden layer is still above 90%, whilst the accuracyof output layer is still above 99%. There is a trade off that theaccuracy of output layer is decreasing while the accuracy of hid-den layer is increasing in the first 10 training epoches. After 10training epoches, the accuracy of hidden layer and the accuracy ofoutput layer are increasing simultaneously.

in the conceptual neurons of A5. Several experimentsdemonstrate that the architecture A5 easily falls intoa local optimal solution that has a high accuracy ofoutput layer but a low accuracy of the hidden layerif it uses the parameters of β5 = 1 and β6 = 1, justlike the case of A3, see Fig. 9. Under the parametersof β5 = 10 and β6 = 1, architecture A5 improves the

situation to a certain degree. Nevertheless, it is stillnot very stable as A3, which result is illustrated inFig. 12. Maybe it is due to the deeper layers andmore parameters of A5. In order to achieve a morestable solution, a tricky method is to replace the sig-moid activation function with the softmax in the lasthidden layer of A5. In this case, A5 also has simi-lar performance with A4 that boosts the accuracy ofthe hidden layer and the accuracy of the output layerabove 90% and 99% respectively. A trade off happensin the first 10 training epoches that the accuracy of thehidden layer is increasing while the accuracy of theoutput layer is decreasing, as illustrated in Fig. 13. Itdemonstrates that architecture A5 has also learnt theeffective representation of “ankle boot” through thefree neuron.

5. Discussion

There are numerous different representation spacesfor an object, which can be recognized in many ways.The purpose of CADNNs is to align the representa-tion space of DNNs with some human concepts, soas to enhance the interpretability. Optimization algo-rithms cannot always find an effective representationspace, particularly in the case of lacking trainingdataset. The introduction of conceptual neurons inCADNNs can promote the architectures converged toa desired representation space. On the other hand, thefree neurons can learn the representations that are notcontained in the conceptual neurons, so as to keep theaccuracy of the output layer. Moreover, the architec-tures of CADNNs can be used to explore the latentrepresentations for the recognition tasks. It is easyto check the effectiveness of some concepts used forrecognition of certain objects in CADNNs. The inter-pretable CADNNs is very appropriate for the transferlearning tasks that learn some representations fromone task and use the representations to other tasks.However, there is a problem that few existing train-ing data sets have hierarchical labels used for trainingthe CADNNs. One solution is to directly build newdata sets that contain hierarchical labels, while theother solution is to utilize a number of correlativeexisting data sets to form hierarchical labels to trainCADNNs.

The valuable human knowledge, formed by a longevolutional history, is constructed by a complex net-work of numerous effective concepts. It should bepromising that infusing the effective human-formedconcepts into computer systems to boost artificial


intelligence. Moreover, maybe there is a key toanswering what is the essence of human conscious-ness. However, the way of organizing the numerousconcepts into a dynamical network is still unclear sothat it needs more explorations. Although the workof CADNNs may be a primitive exploration, there isno harm in proposing the perspective that serves asa modest spur to induce someone to come forwardwith his or her valuable contributions.

6. Conclusion

This paper proposes a kind of Deep Neural Net-works (DNNs), termed as Conceptual AlignmentDeep Neural Networks (CADNNs). There are con-ceptual neurons used for learning representationsof human-formed concepts in the hidden layersof CADNNs. Although added the extra constrainsof some conceptual neurons, CADNNs can guar-antee the performance compared with the DNNs.Meanwhile, the conceptual neurons can align therepresentation space with human-formed concepts inCADNNs, as shown in the experiments. Experimentsalso demonstrate that the free neurons of CADNNscould learn effective representations aligned withhuman-formed concepts in some cases. Moreover,hyper-parameters could be used to trade off the inter-pretability of the hidden layers and the accuracy ofthe output layer. However, the results are not alwaysconverged to expected solutions that have both goodinterpretability and high accuracy. The method ofchoosing appropriate hyper-parameters and activa-tion functions is still need to be researched. Thereis also a challenge to make the free neurons formsome new effective concepts based on known con-cepts that people can understand. Constraints andimproved training methods for free neurons will bethe future work. Furthermore, the CADNN frame-work could also extend to other structures, suchas Recurrent Neural Networks (RNN). More explo-rations are needed to make CADNNs become morecomprehensive and dynamical.

Acknowledgments

This work is supported in part by the NationalNatural Science Foundation of China under GrantNumbers 61632009 and 61472451, the GuangdongProvincial Natural Science Foundation under GrantNumber 2017A030308006, and the High Level

Talents Program of Higher Education in GuangdongProvince under Funding Support Number 2016ZJ01.

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