1 Introduction
CAPTCHA, which stands for “Completely Automated Public Turing test to tell Computers and Humans Apart”, is a type of challengeresponse test used in computers to determine whether or not the user is a human [1]. Most CAPTCHA systems are based on reading text contained in an image as shown in Fig. 1. However, such systems can be easily cracked by deep learning since deep learning can achieve very high accuracy in recognizing text. To address this, this paper proposes a new CAPTCHA, which distinguishes a human from a computer by testing the capability of image captioning (which generates a caption for a given image) or video storytelling (which generates a story consisting of multiple sentences for a give video sequence). It is known that the performance of computerized image captioning or video storytelling is far from human performance [2]. Hence, image/visual captioning based CAPTCHAs can more reliably distinguish computers from humans.
Deep learning is an important tool in many current natural language processing (NLP) applications. However, language rules or structures cannot be explicitly represented in deep learning architectures. The tensor product representation developed in [3, 4] has the potential of integrating deep learning with explicit rules (such as logical rules, grammar rules, or rules that summarize realworld knowledge). This paper develops a TPR approach for image/visualcaptioningbased CAPTCHAs, introducing the Tensor Product Generation Network (TPGN) architecture.
A TPGN model generates natural language descriptions via learned representations. The representations learned in a crucial layer of the TPGN can be interpreted as encoding grammatical roles for the words being generated. This layer corresponds to the roleencoding component of a general, independentlydeveloped architecture for neural computation of symbolic functions, including the generation of linguistic structures. The key to this architecture is the notion of Tensor Product Representation (TPR), in which vectors embedding symbols (e.g., lives, frodo) are bound to vectors embedding structural roles (e.g., verb, subject) and combined to generate vectors embedding symbol structures ([frodo lives]). TPRs provide the representational foundations for a general computational architecture called Gradient Symbolic Computation (GSC)
, and applying GSC to the task of natural language generation yields the specialized architecture defining the model presented here. The generality of GSC means that the results reported here have implications well beyond the particular task we address here.
In our proposed image/visual captioning based CAPTCHA, a TPGN takes an image as input and generates a caption. Then, an evaluator will evaluate the TPGN’s captioning performance by calculating the metric of SPICE [5] by comparing to humangenerated goldstandard captions. If the SPICE value is less than a threshold, this input image can be used as a challenge in our CAPTCHA. In this way, we can obtain a set of images to be used as challenges in CAPTCHA.
In our CAPTCHA shown in Fig. 2, an image is randomly selected from the set and rendered as a challenge; a tester is asked to give a description of the image as an answer. An evaluator calculates a SPICE value for the answer. If the SPICE value is greater than a threshold, the answer is considered to be correct and the tester is deemed to be a human; otherwise, the tester is deemed to be a computer.
2 Design of imagecaptioningbased CAPTCHA
2.1 A TPRcapable generation architecture
In this work we propose an approach to network architecture design we call the TPRcapable method. The architecture we use (see Fig. 3) is designed so that TPRs could, in theory, be used within the architecture to perform the target task — here, generating a caption one word at a time. Unlike previous work where TPRs are handcrafted, in our work, endtoend deep learning will induce representations which the architecture can use to generate captions effectively.
As shown in Fig. 3, our proposed system is denoted by . The input of is an image feature vector and the output of is a caption. The image feature vector is extracted from a given image by a pretrained CNN. The first part of our system is a sentenceencoding subnetwork which maps to a representation which will drive the entire captiongeneration process; contains all the imagespecific information for producing the caption. (We will call a caption a “sentence” even though it may in fact be just a noun phrase.)
If were a TPR of the caption itself, it would be a matrix (or 2index tensor) which is a sum of matrices, each of which encodes the binding of one word to its role in the sentence constituting the caption. To serially read out the words encoded in , in iteration 1 we would unbind the first word from , then in iteration 2 the second, and so on. As each word is generated, could update itself, for example, by subtracting out the contribution made to it by the word just generated; denotes the value of when word is generated. At time step we would unbind the role occupied by word of the caption. So the second part of our system — the unbinding subnetwork — would generate, at iteration , the unbinding vector . Once produces the unbinding vector , this vector would then be applied to to extract the symbol that occupies word ’s role; the symbol represented by would then be decoded into word by the third part of , i.e., the lexical decoding subnetwork , which outputs , the 1hotvector encoding of .
Unbinding in TPR is achieved by the matrixvector product (see Appendix A). So the key operation in generating is thus the unbinding of within , which amounts to simply:
(1) 
This matrixvector product is denoted “” in Fig. 3.
Thus the system of Fig. 3 is TPRcapable. This is what we propose as the TensorProduct Generation Network (TPGN) architecture. The learned representation will not be proven to literally be a TPR, but by analyzing the unbinding vectors the network learns, we will gain insight into the process by which the learned matrix gives rise to the generated caption.
What type of roles might the unbinding vectors be unbinding? A TPR for a caption could in principle be built upon positional roles, syntactic/semantic roles, or some combination of the two. In the caption a man standing in a room with a suitcase, the initial a and man might respectively occupy the positional roles of and ; standing might occupy the syntactic role of verb; in the role of SpatialP(reposition); while a room with a suitcase might fill a 5role schema . In fact, there is evidence that our network learns just this kind of hybrid role decomposition.
What form of information does the sentenceencoding subnetwork need to encode in ? Continuing with the example of the previous paragraph, needs to be some approximation to the TPR summing several filler/role binding matrices. In one of these bindings, a filler vector — which the lexical subnetwork will map to the article a — is bound (via the outer product) to a role vector which is the dual of the first unbinding vector produced by the unbinding subnetwork : . In the first iteration of generation the model computes , which then maps to a. Analogously, another binding approximately contained in is . There are corresponding bindings for the remaining words of the caption; these employ syntactic/semantic roles. One example is . At iteration 3, decides the next word should be a verb, so it generates the unbinding vector which when multiplied by the current output of , the matrix , yields a filler vector which maps to the output standing. decided the caption should deploy standing as a verb and included in the binding . It similarly decided the caption should deploy in as a spatial preposition, including in the binding ; and so on for the other words in their respective roles in the caption.
2.2 CAPTCHA generation method
We first describe how to obtain a set of images as challenges in our CAPTCHA system. In our proposed image/visual captioning based CAPTCHA, a TPGN takes an image as input and generates a caption. Then, an evaluator will evaluate the TPGN’s captioning performance by calculating the metric of SPICE [5] by comparing to humangenerated goldstandard captions. If the SPICE value is less than a threshold , this input image can be used as a challenge in our CAPTCHA; otherwise, this input image will not be selected as a challenge and a new image will be examined. In this way, we can obtain a set of images used as challenges in CAPTCHA. All images in are difficult to be captioned by a computerized image captioning system due to their low SPICE values.
Now, we describe our CAPTCHA generation method. In our CAPTCHA, an image is randomly selected from the set and rendered as a challenge; a tester is asked to give a description of the image as an answer. An evaluator calculates a SPICE value for the answer. If the SPICE value is greater than a threshold , the answer is considered to be correct and the tester is deemed to be a human; otherwise, the answer is considered to be wrong and the tester is deemed to be a computer.
3 Experimental results
To evaluate the performance of our proposed architecture, we use the COCO dataset [2]. The COCO dataset contains 123,287 images, each of which is annotated with at least 5 captions. We use the same predefined splits as [6, 7]: 113,287 images for training, 5,000 images for validation, and 5,000 images for testing. We use the same vocabulary as that employed in [7], which consists of 8,791 words.
For the CNN of Fig. 3, we used ResNet152 [8]
, pretrained on the ImageNet dataset. The feature vector
has 2048 dimensions. Word embedding vectors in are downloaded from the web [9]. The model is implemented in TensorFlow
[10]with the default settings for random initialization and optimization by backpropagation.
In our experiments, we choose (where is the dimension of vector ). The dimension of is ; the vocabulary size ; the dimension of and is .
Methods  METEOR  BLEU1  BLEU2  BLEU3  BLEU4  CIDEr  SPICE 

NIC [11]  –  0.666  0.451  0.304  0.203  –  – 
CNNLSTM  0.238  0.698  0.525  0.390  0.292  0.889  – 
TPGN  0.243  0.709  0.539  0.406  0.305  0.909  0.18 
The main evaluation results on the MS COCO dataset are reported in Table 1. The widelyused BLEU [12], METEOR [13], CIDEr [14], and SPICE [5] metrics are reported in our quantitative evaluation of the performance of the proposed schemes. In evaluation, our baseline is the widely used CNNLSTM captioning method originally proposed in [11]. For comparison, we include results in that paper in the first line of Table 1. We also reimplemented the model using the latest ResNet feature and report the results in the second line of Table 1. Our reimplementation of the CNNLSTM method matches the performance reported in [7], showing that the baseline is a stateoftheart implementation. As shown in Table 1, compared to the CNNLSTM baseline, the proposed TPGN significantly outperforms the benchmark schemes in all metrics across the board. The improvement in BLEU is greater for greater ; TPGN particularly improves generation of longer subsequences. The results clearly attest to the effectiveness of the TPGN architecture.
Now, we address the issue of how to determine the two thresholds and in our CAPTCHA system. We set , which is about 80% less than the SPICE metric obtained by TPGN. In this way, the image set only contains images that are most difficult to be captioned by a computer.
We run a trained TPGN with input images from COCO test dataset, and select ten images from COCO test dataset, whose SPICE metrics are less than . Then we use Amazon Mechanical Turk system to generate captions for these ten images by humans. We observe that the SPICE metric obtained by a caption generated by a human is always larger than 0.3; hence, we set , which is much larger than the SPICE metric achievable by any existing computerized image captioning system [2].
4 Conclusion
In this paper, we proposed a new Tensor Product Generation Network (TPGN) for image/visualcaptioningbased CAPTCHAs. The model has a novel architecture based on a rationale derived from the use of Tensor Product Representations for encoding and processing symbolic structure through neural network computation. In evaluation, we tested the proposed model on captioning with the MS COCO dataset, a largescale imagecaptioning benchmark. Compared to widely adopted LSTMbased models, the proposed TPGN gives significant improvements on all major metrics including METEOR, BLEU, CIDEr, and SPICE. Our findings in this paper show great promise of TPRs in CAPTCHA. In the future, we will explore extending TPR to a variety of other NLP tasks and spam email detection.
Appendix
Appendix A Review of tensor product representation
Tensor product representation (TPR) is a general framework for embedding a space of symbol structures into a vector space. This embedding enables neural network operations to perform symbolic computation, including computations that provide considerable power to symbolic NLP systems [4, 15]. Motivated by these successful examples, we are inspired to extend the TPR to the challenging task of learning image captioning. And as a byproduct, the symbolic character of TPRs makes them amenable to conceptual interpretation in a way that standard learned neural network representations are not.
A particular TPR embedding is based in a filler/role decomposition of . A relevant example is when is the set of strings over an alphabet . One filler/role decomposition deploys the positional roles , where the filler/role binding assigns the ‘filler’ (symbol) to the position in the string. A string such as is uniquely determined by its filler/role bindings, which comprise the (unordered) set . Reifying the notion role in this way is key to TPR’s ability to encode complex symbol structures.
Given a selected filler/role decomposition of the symbol space, a particular TPR is determined by an embedding that assigns to each filler a vector in a vector space , and a second embedding that assigns to each role a vector in a space . The vector embedding a symbol is denoted by and is called a filler vector; the vector embedding a role is and called a role vector. The TPR for is then the following 2index tensor in :
(2) 
where
denotes the tensor product. The tensor product is a generalization of the vector outer product that is recursive; recursion is exploited in TPRs for, e.g., the distributed representation of trees, the neural encoding of formal grammars in connection weights, and the theory of neural computation of recursive symbolic functions. Here, however, it suffices to use the outer product; using matrix notation we can write (
2) as:(3) 
Generally, the embedding of any symbol structure is ; here: [3, 4].
A key operation on TPRs, central to the work presented here, is unbinding, which undoes binding. Given the TPR in (3), for example, we can unbind to get ; this is achieved simply by . Here is the unbinding vector dual to the binding vector . To make such exact unbinding possible, the role vectors should be chosen to be linearly independent. (In that case the unbinding vectors are the rows of the inverse of the matrix containing the binding vectors as columns, so that while for all other role vectors ; this entails that , the filler vector bound to . Replacing the matrix inverse with the pseudoinverse allows approximate unbinding when the role vectors are not linearly independent).
Appendix B System Description
The unbinding subnetwork and the sentenceencoding network of Fig. 3 are each implemented as (1layer, 1directional) LSTMs (see Fig. 4); the lexical subnetwork
is implemented as a linear transformation followed by a softmax operation. In the equations below, the LSTM variables internal to the
subnet are indexed by 1 (e.g., the forget, input, and outputgates are respectively ) while those of the unbinding subnet are indexed by 2.Thus the state updating equations for are, for = caption length:
(4)  
(5)  
(6)  
(7)  
(8)  
(9) 
where , , , , , , ,
is the (elementwise) logistic sigmoid function;
is the hyperbolic tangent function; the operator denotes the Hadamard (elementwise) product; , , , , , , , , . For clarity, biases — included throughout the model — are omitted from all equations in this paper. The initial state is initialized by:(10) 
where
is the vector of visual features extracted from the current image by ResNet
[7] and is the mean of all such vectors; . On the output side, is a 1hot vector with dimension equal to the size of the caption vocabulary, , and is a word embedding matrix, the th column of which is the embedding vector of the th word in the vocabulary; it is obtained by the Stanford GLoVe algorithm with zero mean [9]. is initialized as the onehot vector corresponding to a “startofsentence” symbol.For in Fig. 3, the state updating equations are:
(11)  
(12)  
(13)  
(14)  
(15)  
(16) 
where , , and . The initial state is the zero vector.
The dimensionality of the crucial vectors shown in Fig. 3, and , is increased from to as follows. A blockdiagonal matrix is created by placing copies of the matrix as blocks along the principal diagonal. This matrix is the output of the sentenceencoding subnetwork . Now, following Eq. (1), the ‘filler vector’ — ‘unbound’ from the sentence representation with the ‘unbinding vector’ — is obtained by Eq. (17).
(17) 
Here , the output of the unbinding subnetwork , is computed as in Eq. (18), where is ’s output weight matrix.
(18) 
Finally, the lexical subnetwork produces a decoded word by
(19) 
where is the softmax function and is the overall output weight matrix. Since plays the role of a word deembedding matrix, we can set
(20) 
where is the wordembedding matrix. Since is predefined, we directly set by Eq. (20) without training through Eq. (19). Note that and are learned jointly through the endtoend training.
Fig. 5 shows a pretraining method for initializing TPGN. During the pretraining phase, there is no image input, i.e., image feature vector . In Fig. 5, at time , the LSTM module takes a sentence of length as input and outputs a vector () at time . That is, the LSTM converts a sentence into , which is the input of TPGN. We use endtoend training to train the whole system shown in Fig. 5. After finishing pretraining, we let and use images as input to train the TPGN in Fig. 3, initialized by the pretrained parameter values.
Appendix C Related work
Most existing DLbased image captioning methods [16, 11, 17, 18, 19, 6, 20, 21]
involve two phases/modules: 1) image analysis, typically by a Convolutional Neural Network (CNN), and 2) a language model for caption generation (
[22]). The CNN module takes an image as input and outputs an image feature vector or a list of detected words with their probabilities. The language model is used to create a sentence (caption) out of the detected words or the image feature vector produced by the CNN.
There are mainly two approaches to natural language generation in image captioning. The first approach takes the words detected by a CNN as input, and uses a probabilistic model, such as a maximum entropy (ME) language model, to arrange the detected words into a sentence. The second approach takes the penultimate activation layer of the CNN as input to a Recurrent Neural Network (RNN), which generates a sequence of words (the caption)
[11].The work reported here follows the latter approach, adopting a CNN + RNNgenerator architecture. Specifically, instead of using a conventional RNN, we propose a recurrent network that has substructure derived from the general GSC architecture: one recurrent subnetwork holds an encoding — which is treated as an approximation of a TPR — of the words yet to be produced, while another recurrent subnetwork generates a sequence of vectors that is treated as a sequence of roles to be unbound from , in effect, reading out a word at a time from . Examining how the model deploys these roles allows us to interpret them in terms of grammatical categories; roughly speaking, a sequence of categories is generated and the words stored in are retrieved and spelled out via their categories.
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