Solving algebraic word problems has recently emerged as an important natural language processing task . To solve algebraic word problems , recent studies suggested neural models that generate solution equations by using ' Op ( operator / operand ) ' tokens as a unit of input / output . However , such a neural model suffered two issues : expression fragmentation and operand-context separation . To address each of these two issues , we propose a pure neural model , Expression-Pointer Transformer ( EPT ) , which uses ( 1 ) ' Expression ' token and ( 2 ) operand-context pointers when generating solution equations . The performance of the EPT model is tested on three datasets : ALG514 , DRAW-1 K , and MAWPS . Compared to the state-of-the-art ( SoTA ) models , the EPT model achieved a comparable performance accuracy in each of the three datasets ; 81.3 % on ALG514 , 59.5 % on DRAW-1 K , and 84.5 % on MAWPS . The contribution of this paper is two-fold ; ( 1 ) We propose a pure neural model , EPT , which can address the expression fragmentation and the operandcontext separation . ( 2 ) The fully automatic EPT model , which does not use hand-crafted features , yields comparable performance to existing models using hand-crafted features , and achieves better performance than existing pure neural models by at most 40 % . Solving algebraic word problems has recently become an important research task in that automatically generating solution equations requires understanding natural language . Table 1 shows a sample algebraic word problem , along with corresponding solution equations that are used to generate answers for the problem . To solve such problems with deep learning technology , researchers recently suggested neural models that generate solution equations automatically ( Huang Problem One number is eight more than twice another and their sum is 20 . What are their numbers ? Numbers 1('one ' ) , 8('eight ' ) , 2('twice ' ) , 20 . Equations x 0 -2x 1 = 8 , x 0 + x 1 = 20 Answers ( 16 , 4 ) et al . , 2018 ; Amini et al . , 2019 ; Chiang and Chen , 2019 ; Wang et al . , 2019 ) . However , suggested neural models showed a fairly large performance gap compared to existing state-of-the-art models based on hand-crafted features in popular algebraic word problem datasets , such as ALG514 ( 44.5 % for pure neural model vs. 83.0 % for using hand-crafted features ) ( Huang et al . , 2018 ; Upadhyay and Chang , 2016 ) . To address the large performance gap in this study , we propose a larger unit of input / output ( I / O ) token called " Expressions " for a pure neural model . Figure 1 illustrates conventionally used " Op ( operator / operands ) " versus our newly proposed " Expression " token . To improve the performance of pure neural models that can solve algebraic word problems , we identified two issues that can be addressed using Expression tokens , which are shown in Figure 1 : ( 1 ) expression fragmentation and ( 2 ) operandcontext separation . First , the expression fragmentation issue is a segmentation of an expression tree , which represents a computational structure of equations that are used to generate a solution . This issue arises when Op , rather than the whole expression tree , is used as an input / output unit of a problem-solving model . For example , as shown in Figure 1 ( a ) , using Op tokens as an input to a problem-solving model disassembles a tree structure into operators ( " × " ) and operands ( " x 1 " and " 2 " ) . Meanwhile , we propose using the Figure 1 : Illustration using the word problem in Table 1 for the ( a ) expression fragmentation issue , ( b ) operandcontext separation issue , and ( c ) our solution for these two issues . " Expression " ( ×(x 1 , 2 ) ) token , which can explicitly capture a tree structure as a whole , as shown in Figure 1 ( c ) . The second issue of operand-context separation is the disconnection between an operand and a number that is associated with the operand . This issue arises when a problem-solving model substitutes a number stated in an algebraic word problem into an abstract symbol for generalization . As shown in Figure 1 ( b ) , when using an Op token , the number 8 is changed into an abstract symbol ' N 1 ' . Meanwhile , when using an Expression token , the number 8 is not transformed into a symbol . Rather a pointer is made to the location where the number 8 occurred in an algebraic word problem . Therefore , using such an " operand-context pointer " enables a model to access contextual information about the number directly , as shown in Figure 1 ( c ) ; thus , the operand-context separation issue can be addressed . In this paper , we propose a pure neural model called Expression-Pointer Transformer ( EPT ) to address the two issues above . The contribution of this paper is two-fold ; 1 . We propose a pure neural model , Expression-Pointer Transformer ( EPT ) , which can address the expression fragmentation and operandcontext separation issues . 2 . The EPT model is the first pure neural model that showed comparable accuracy to the existing state-of-the-art models , which used handcrafted features . Compared to the state-ofthe-art pure neural models , the EPT achieves better performance by about 40 % . In the rest of the paper , we introduce existing approaches to solve algebraic word problems in Section 2 . Next , Section 3 introduces our proposed model , EPT , and Section 4 reports the experimental settings . Then in Section 5 , results of two studies are presented . Section 5.1 presents a performance comparison between EPT and existing SoTA models . Section 5.2 presents an ablation study examining the effects of Expression tokens and applying operand-context pointers . Finally , in Section 6 , a conclusion is presented with possible future directions for our work . In this study , we proposed a neural algebraic word problem solver , Expression-Pointer Transformer ( EPT ) , and examined its characteristics . We designed EPT to address two issues : expression fragmentation and operand-context separation . The EPT resolves the expression fragmentation issue by generating ' Expression ' tokens , which simultaneously generate an operator and required operands . In addition , the EPT resolves the operand-context separation issue by applying operand-context pointers . Our work is meaningful in that we demonstrated a possibility for alleviating the costly procedure of devising hand-crafted features in the domain of solving algebraic word problems . As future work , we plan to generalize the EPT to other datasets , including non-English word problems or non-algebraic domains in math , to extend our model .
Neural models largely underperform hand-crafted feature-based models on algebraic word datasets such as ALG514 because of two issues namely expression fragmentation and operand-context separation.
They propose a model which generates an operator and required operands and applies operand-context pointers to resolve the expression fragmentation and operand-context separation issues respectively.
The proposed model performs comparable results to the state-of-the-art models with hand-crafted features and outperforms neural models by 40% on three datasets.