Ai-based system for classifying sub-types of mathematical problems

Abstract

The present invention relates to an artificial intelligence-based mathematical problem assistance type classification system comprising: a user terminal; an input unit that receives a mathematical problem containing a formula from the user terminal and extracts the formula from the mathematical problem; a conversion unit that converts the extracted formula into a Sympy format according to the operation structure of an operator and an operand to generate feature information and converts the feature information into natural language text; and a classification unit that classifies the main type of the mathematical problem through an artificial intelligence-based classification model based on the feature information converted into natural language text and classifies a plurality of sub-types that complement the main type. The invention includes an output unit that transmits the main type and the sub type to the user terminal, and the classification unit includes a first classification module that classifies the main type through an artificial intelligence-based classification model based on the feature information, and a second classification module that sequentially classifies a plurality of the sub types according to a hierarchical classification structure based on the main type. According to the present invention, by precisely classifying the main type and sub type of a mathematical problem, customized learning materials reflecting the concept and structure of the problem are provided to the learner. This effectively improves the learner's problem-solving ability and mathematical thinking skills, and allows for the design of an optimal learning path tailored to the individual level by accurately diagnosing deficient concepts. Furthermore, by systematically analyzing the complex structure of mathematical problems and clearly distinguishing the relationship between the main type and the sub type, sophisticated learning analysis and feedback are provided in the educational field. Additionally, by automatically categorizing and systematically managing large-scale mathematical problem data, it can be efficiently utilized in various educational environments such as question bank systems, online learning platforms, and college entrance exam preparation services.

Description

Technology Field

[0001] The present invention relates to a system that utilizes artificial intelligence technology to analyze complex thought flows and computational structures included in mathematical problems and precisely classifies auxiliary subtypes that play a key role in the problem-solving process. Background Technology

[0002] Mathematics education aims to improve problem-solving skills and mathematical thinking by repeatedly solving various problem types based on a deep understanding of concepts and principles. To this end, there has been a steady demand in educational settings for problem type classification systems capable of precisely identifying which problem types students are familiar with and in which types they exhibit conceptual and structural weaknesses.

[0003] However, most existing problem type classification systems classify types based on keywords included in the problem, wording of the passage, and surface text structure. This approach has a significant limitation in that it fails to distinguish between problems with completely different computational flows or thought processes, even if they contain the same keywords, as it does not consider essential elements such as the problem's computational structure or solution strategies. For example, even if a problem contains the keyword "equation," single-variable linear equations and multivariable nonlinear equations differ fundamentally in their structural complexity and solution strategies, yet existing systems frequently misclassify them as the same type.

[0004] In particular, conventional single-type classification systems are designed to predict only the single most likely type for a problem, failing to reflect the multi-layered concepts and complex computational flows inherent in the problem. This represents a technical limitation that seriously overlooks the essence of mathematical problems; for instance, if a problem involving the differentiation of a cubic function is simply classified as a "differentiation" type, the computational flow combining the properties of a quadratic function (middle school 3rd grade level) and the characteristics of a cubic function (high school 2nd grade level) is missed. Consequently, if a student has a weakness in a specific concept, the learning effect may be limited even if they repeatedly study superficially similar problems, as they fail to understand the structural differences.

[0005] Furthermore, while some systems attempt multi-type prediction, they exhibit problems such as including subtypes lacking semantic connection to the main type or repeatedly listing subtypes that are excessively similar to the main type. This fails to provide practical assistance in diagnosing learners' misconceptions or designing educational feedback. For example, in a problem analyzing the differentiability of a function, learning diagnosis is more effective if subtypes reflecting the flow of operations—such as the derivation of the equation and the order of application of differentiation—are identified, rather than simply listing "equation" and "differentiation."

[0006] As such, conventional problem type classification systems have several limitations. Most systems fail to identify auxiliary types at all, thus failing to reflect the multi-layered computational structure of problems; even when they do predict auxiliary types, their educational utility is diminished because they include types that are excessively similar to the main type or irrelevant to the solution flow. Furthermore, they undermine the clarity and validity of learning diagnostics by failing to quantitatively control semantic differences or redundancy among sub-types. Moreover, because they rely on qualitative analysis or rule-based logic and cannot quantitatively analyze the computational patterns or hierarchical structures of problems, classification based on conceptual similarity or solution strategies is impossible.

[0007] Therefore, a new approach is required that structurally analyzes mathematical formulas to transform them into operator-centered hierarchical structures, quantitatively extracts the types, order, depth, and structural characteristics of operators, converts this data into natural language text, and inputs it into an artificial intelligence classification model. Through this, there is a need to develop problem type classification technology that accurately predicts auxiliary types semantically linked to main types, suppresses redundancy, and precisely reflects the computational flow and thought processes of the problem. The problem to be solved

[0008] The objective of the present invention is to solve the problems of the aforementioned prior art by providing an AI-based mathematical problem auxiliary type classification system that accurately classifies main types by structurally analyzing mathematical formulas to generate feature information, converting it into natural language text, and inputting it into an AI classification model, and effectively classifies sub-types by adjusting the distance between main types and sub-types and applying a loss function that reflects GNN-based relationships. means of solving the problem

[0009] The above objective is achieved, according to the present invention, by: a user terminal; an input unit that receives a mathematical problem containing a formula from the user terminal and extracts the formula from the mathematical problem; a conversion unit that converts the extracted formula into a Sympy format according to the operation structure of an operator and an operand to generate feature information and converts the feature information into natural language text; and a classification unit that classifies the main type of the mathematical problem through an artificial intelligence-based classification model based on the feature information converted into natural language text and classifies a plurality of sub-types that complement the main type. The system is achieved by an AI-based mathematical problem assistance type classification system that includes an output unit for transmitting the main type and the sub type to the user terminal, and the classification unit includes a first classification module that classifies the main type through an AI-based classification model based on the feature information, and a second classification module that sequentially classifies a plurality of the sub types according to a hierarchical classification structure based on the main type. Additionally, the conversion unit includes a preprocessing module that converts the mathematical formula into a Sympy format according to the operation structure of the operator and operand, a feature extraction module that generates feature information by extracting operator type information, operation order information, and tree depth information from the Sympy format, and a natural language processing module that analyzes the structure of the mathematical formula based on the feature information and converts it into natural language text. Additionally, the second classification module predicts the sub type by applying a loss function that reflects the structural correlation between the main type and the sub type, and the loss function includes a non-linear similarity-based loss term for the prediction probability distribution between the main type and the sub type and a Graph Neural Network (GNN)-based correlation correction term.In addition, the feature extraction module is characterized by generating operator attribute information including the number of terms of the operator, associativity rules, and operation precedence based on the operation characteristics of the operator included in the Sympy format, and generating the feature information based on the operator attribute information.

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[0013] delete Effects of the invention

[0014] According to the present invention, by precisely classifying the main and sub-types of mathematical problems, customized learning materials reflecting the concepts and structures of the problems are provided to learners. This effectively improves the learner's problem-solving ability and mathematical thinking skills, and allows for the design of an optimal learning path tailored to individual levels by accurately diagnosing deficient concepts.

[0015] Furthermore, by systematically analyzing the complex structure of mathematical problems and clearly distinguishing the relationships between main and sub-types, it provides sophisticated learning analysis and feedback in educational settings. Additionally, by automatically categorizing and systematically managing large-scale mathematical problem data, it can be efficiently utilized in various educational environments such as question bank systems, online learning platforms, and CSAT preparation services.

[0016] Meanwhile, the effects of the present invention are not limited to those mentioned above, and various effects may be included within the scope obvious to a person skilled in the art from the contents described below. Brief explanation of the drawing

[0017] FIG. 1 illustrates an artificial intelligence-based mathematical problem assistance type classification system according to an embodiment of the present invention, and FIG. 2 illustrates the connections between the components of a conversion unit of an artificial intelligence-based mathematical problem assistance type classification system according to an embodiment of the present invention, and FIG. 3 illustrates the Sympy format of an artificial intelligence-based mathematical problem assistance type classification system according to an embodiment of the present invention, and Figure 4 illustrates the connections between the components of the classification unit of an artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention. Specific details for implementing the invention

[0018] Hereinafter, some embodiments of the present invention will be described in detail with reference to the exemplary drawings. It should be noted that in assigning reference numerals to the components of each drawing, the same components are given the same reference numeral whenever possible, even if they are shown in different drawings.

[0019] In addition, when describing embodiments of the present invention, if it is determined that a detailed description of related known configurations or functions would hinder understanding of the embodiments of the present invention, such detailed description is omitted.

[0020] In addition, terms such as first, second, A, B, (a), (b), etc., may be used when describing the components of the embodiments of the present invention. These terms are used merely to distinguish the components from other components, and the essence, order, or sequence of the components is not limited by the terms used.

[0021] Additionally, in the specification, the singular form includes the plural form unless specifically stated otherwise in the text. The terms “comprising” and / or “comprising” as used in the specification do not exclude the presence or addition of one or more other components in addition to the mentioned components.

[0022] Additionally, in describing embodiments of the present invention, each "part," "module," or "step" may be implemented through a processor and memory. The term "processor" should be broadly interpreted to include general-purpose processors, central processing units (CPUs), microprocessors, digital signal processors (DSPs), controllers, microcontrollers, state machines, and the like. In some contexts, the term "processor" may refer to an application-specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), and the like. The term "processor" may also refer to a combination of processing devices, such as, for example, a combination of a DSP and a microprocessor, a combination of multiple microprocessors, a combination of one or more microprocessors combined with a DSP core, or any other combination of such configurations.

[0023] Furthermore, memory should be broadly interpreted to include any electronic component capable of storing electronic information. Memory may also refer to various types of processor-readable media such as random access memory (RAM), read-only memory (ROM), non-volatile random access memory (NVRAM), programmable read-only memory (PROM), eraseable-programmable read-only memory (EPROM), electrically eraseable PROM (EEPROM), flash memory, magnetic or optical information storage devices, registers, etc. If a processor can read information from memory or write information to memory, memory is said to be in an electronic communication state with the processor, and each "part," "module," or "stage" may be implemented through a program or application based on the processor and memory in an electronic communication state.

[0024] Furthermore, in the present invention, Artificial Intelligence (AI) refers to a technology that imitates human learning ability, reasoning ability, and perceptual ability, and implements them on a computer, and may include concepts such as machine learning and symbolic logic. Machine Learning (ML) is an algorithmic technology that classifies or learns the characteristics of input information on its own. AI technology can analyze input information as a machine learning algorithm, learn from the results of that analysis, and make judgments or predictions based on the results of that learning. Additionally, technologies that mimic the functions of the human brain, such as cognition and judgment, by utilizing machine learning algorithms can also be understood as falling within the category of AI. For example, technological fields such as linguistic understanding, visual understanding, reasoning / prediction, knowledge representation, and motion control may be included.

[0025] Artificial intelligence learning models or neural network models can be designed to implement the structure of the human brain on a computer and may include multiple network nodes that simulate neurons of a human neural network and have weights. These multiple network nodes can have interconnected relationships by simulating the synaptic activity of neurons, where neurons exchange signals through synapses. In an artificial intelligence learning model, multiple network nodes can be located in layers of different depths and exchange information according to convolutional connections. An artificial intelligence learning model may be, for example, an Artificial Neural Network (ANN) or a Convolutional Neural Network (CNN). An artificial intelligence learning model can be machine learned according to methods such as supervised learning, unsupervised learning, and reinforcement learning. Machine learning algorithms that can be used to perform machine learning include Decision Trees, Bayesian Networks, Support Vector Machines, Perceptrons, and Clustering.

[0027] Now, with reference to the attached drawings, an artificial intelligence-based math problem assistance type classification system (100) will be described in detail.

[0028] FIG. 1 illustrates an artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention in its entirety, FIG. 2 illustrates the connections between the components of the conversion unit of the artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention, FIG. 3 illustrates the Sympy format of the artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention, and FIG. 4 illustrates the connections between the components of the classification unit of the artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention.

[0029] As illustrated in FIG. 1, the artificial intelligence-based math problem assistance type classification system (100) includes a user terminal (110), an input unit (120), a conversion unit (130), a classification unit (140), and an output unit (150).

[0030] The user terminal (110) transmits a mathematical problem containing a formula to an input unit (120) via a text, image and / or formula input interface, and receives a mathematical problem type classification result from an output unit (150) and displays it to the user.

[0031] The user terminal (110) can be implemented as various electronic devices such as smartphones, desktops, tablet PCs, laptops, or wearable devices, but is not limited to these, and any electronic device in the field of technology capable of performing the function of inputting math problems and receiving results can be used.

[0032] For example, you can upload images of math problems captured by a smartphone camera or write formulas directly using the touch interface of a tablet PC. Additionally, on a desktop, you can input math problems containing formulas as text via keyboard input or use formula editing functions through dedicated software.

[0033] Additionally, the user terminal (110) can be connected to the input unit (120) and output unit (150) via a network connection such as Wi-Fi or a mobile communication network, and supports the user in inputting problems and checking classification results in real time.

[0034] The input unit (120) receives a mathematical problem containing a formula from a user terminal, extracts a formula from the received mathematical problem, and is electrically connected to the conversion unit (130).

[0035] Specifically, the input unit (120) can receive a mathematical problem containing a formula from a user terminal (110), extract the formula, and perform the function of preprocessing it into a form that can be structurally analyzed.

[0036] Here, the format of the inputtable mathematical problem may include text, images, mathematical editor input, mathematical expressions based on LaTeX syntax and KaTeX syntax, and the input unit (120) may perform a mathematical expression extraction and refinement process after receiving data of various formats.

[0037] When a math problem in text format is input, the input unit (120) may apply a regular expression-based symbol search algorithm to detect mathematical expressions in the natural language text of the math problem. The search targets may include operator symbols (+, ?, *, ÷, =, √, etc.), parentheses, variables, and mathematical symbols, and mathematical expression blocks within the sentence may be separated and organized into independent mathematical data.

[0038] When a mathematical problem in image format is input, the input unit (120) can detect areas containing mathematical formulas within the image by applying optical character recognition (OCR) technology for formula recognition and convert the formulas into text based on the recognized symbols, and in this process, image preprocessing steps such as noise removal, binarization, boundary alignment, and distortion correction may be performed beforehand. Additionally, the recognized result may be rearranged into a mathematical formula string for structural analysis.

[0039] Additionally, the input unit (120) can perform syntax error verification on the input math problem.

[0040] The input unit (120) automatically checks whether the pairs of parentheses match, the number of operators and operands, and whether they are arranged in the correct order, and if an error is found, it can automatically correct it or generate an error message for requesting user feedback.

[0041] The input unit (120) performs formula detection, syntax consistency verification, and structured transformation processes in an integrated manner, and serves to provide initial input data for precise problem type analysis based on the operation structure of mathematical problems.

[0042] The conversion unit (130) converts a mathematical formula extracted from a mathematical problem input through the input unit (120) into a Sympy format according to the operation structure of the operator and operand to generate feature information, converts the feature information into natural language text, and is electrically connected to the input unit (120) and the classification unit (140).

[0043] As illustrated in FIG. 2, the conversion unit (130) includes a preprocessing module (131) that converts a formula into a Sympy format according to the operation structure of the operator and operand, a feature extraction module (132) that generates feature information by extracting operator type information, operation order information and tree depth information of the Sympy format, and a natural language processing module (133) that interprets the flow of the formula's solution based on the feature information and converts it into natural language text.

[0044] The preprocessing module (131) structures the formula transmitted from the input unit (120) according to the operation structure of the operator and operand, and performs the function of converting the formula into a Sympy format based on this, and is electrically connected to the feature extraction module (132).

[0045] The preprocessing module (131) enables the artificial intelligence model to learn mathematical formulas in a mathematical problem based on structural information rather than simple text or visual mathematical formula representations through the SymPy format.

[0046] For example, the KaTeX format is a markup language primarily used for visually rendering mathematical expressions and does not contain a hierarchical operational structure of expressions, so there are limitations in artificial intelligence models understanding the logical relationships between the components of an expression. On the other hand, the Sympy format generates an internal structure in the form of a tree (Abstract Syntax Tree, AST) in which each operator and operand is composed of nodes, thereby enabling quantitative learning of the order of operations, nesting, and relationships between upper and lower operators.

[0047] Through this transformation process, predictions reflecting the structural characteristics and computational flow of the formula become possible, and the formula interpretation capabilities and classification accuracy of the artificial intelligence model can be significantly improved.

[0048] For example, as illustrated in Fig. 3, a given formula can be expressed in SymPy format according to operator precedence. Here, the root node is the Add operator, which is the final operator, and the Mul operator and Sub operator are placed as child nodes below it, respectively.

[0049] The left substructure follows the operation flow of 5*(2+2)-7, which can be expressed as Sub(Mul(5, Add(2, 2)), 7).

[0050] In the center, 2*7 is structured as Mul(2, 7), which can be connected to a structure that is multiplied by the preceding left operation.

[0051] The right side consists of 10-((6+8)*(-1)), and in SymPy expression form, it is Sub(10, Mul(Add(6, 8), -1)).

[0052] When this structure is integrated into a single expression tree, it is configured such that Mul(Sub(Mul(5, Add(2, 2)), 7), Mul(2, 7)) and Sub(10, Mul(Add(6, 8), -1)) are connected left and right around the top-level operator, Add node, and the entire expression can be expressed as Add(Mul(Sub(Mul(5, Add(2, 2)), 7), Mul(2, 7)), Sub(10, Mul(Add(6, 8), -1))).

[0053] The SymPy format can clearly represent the hierarchical structure of each operator and operand constituting an expression, and can quantitatively reflect operation precedence, associativity, and nesting structures. Specifically, the root node represents the final operator of the entire expression, internal nodes are operators corresponding to intermediate operation stages, and leaf nodes consist of final operands such as numbers, constants, and variables.

[0054] In this Sympy format, the location, depth, and number of branches of each node can be utilized as structural features to classify mathematical problem types in subsequent processing modules, accurately reflect the logical flow of formulas, and contribute to hierarchical structure-based feature analysis.

[0055] The preprocessing module (131) can automatically generate a tree structure for various types of mathematical expressions, such as complex expressions, polynomials, and functional expressions, by utilizing an operator precedence table, operator associativity rules, and parenthesis structure analysis.

[0056] For example, fractional or exponential expressions can each be analyzed as factors that increase the tree depth of the Sympy format, and unary operators such as trigonometric functions or root operations can be converted into operator nodes with a single child node.

[0057] The SymPy format generated in the preprocessing module (131) can be structured to satisfy quantitative analysis criteria including tree depth, number of nodes, operator relationships between nodes, number of child nodes, and distribution of operator types, and can be used to generate feature information necessary for classifying types of mathematical problems in the feature extraction module (132) to be described later.

[0058] The feature extraction module (132) generates feature information by extracting operator type information, operation order information, and tree depth information of the Sympy format generated through the preprocessing module (131), and is electrically connected to the preprocessing module (131) and the natural language processing module (133).

[0059] The feature extraction module (132) can quantitatively analyze the operation structure of a mathematical problem based on the Sympy format generated by the preprocessing module (131) to generate feature information, thereby providing key information necessary for classifying the main type and sub-type of the mathematical problem.

[0060] Here, feature information may refer to a set of quantitative and qualitative attributes generated by analyzing the formula included in a mathematical problem into the operational structure of operators and operands.

[0061] Feature information is generated based on operator type information, operation order information, tree depth information, and operator attribute information, and can quantitatively represent the structural patterns and solution flow of the formula.

[0062] Operator type information refers to information obtained by quantitatively analyzing the types and frequency of occurrence of operators included in the Sympy format.

[0063] The feature extraction module (132) iterates through each node of the Sympy format to identify operators and classifies them into arithmetic operators (+, -, *, ÷), relational operators (=, ≠, >, <), exponentiation operators (^), square root operators (√), and function operators (sin, cos, log, etc.). The frequency and ratio of occurrence of each operator type are represented as a multidimensional vector, for example, the formula "a + b * c" can be represented in the form [addition: 1, multiplication: 1, other: 0]. Operator type information indicates how dependent a formula is on a specific type of operation and can be used to identify the conceptual characteristics of the problem.

[0064] Operation order information refers to data that defines the hierarchical relationships of operators and the order of calculation execution within the Sympy format.

[0065] The feature extraction module (132) can analyze the execution order, priority, and associativity of operators by applying a tree traversal method. For example, the formula "a + b * c" can be expressed as [multiplication (b * c), addition (a + result of multiplication)] because multiplication takes precedence over addition. The operation order information models the flow of calculation of the formula and can reflect structural patterns associated with the problem-solving strategy.

[0066] Tree depth information refers to information that indicates the hierarchical complexity of a formula by calculating the longest path length from the root node to the deepest leaf node in Sympy format.

[0067] The feature extraction module (132) calculates the depth of the longest path by searching for a formula converted into Sympy format, for example, the formula "(a + b) * (c + d)" is calculated as a tree depth of 3 (the root node is multiplication, the internal node is addition, and the leaf nodes are a, b, c, and d). The tree depth information can be used to evaluate the level of nested operations, the number of operation steps, and the difficulty of the problem.

[0068] Operator attribute information refers to information generated based on the operational characteristics of an operator, and may include information on the number of terms, associativity rules, and operation precedence.

[0069] The term count information refers to data indicating the number of operands an operator has. For example, addition (+) has two operands, and the square root operator (√) has one operand.

[0070] Associativity rule information refers to information that defines the associativity (left associative, right associative, non-associative) of operators, and addition and multiplication can be classified as left associative, while exponentiation operations can be classified as right associative.

[0071] Operator precedence information refers to information obtained by analyzing the hierarchical position of operators based on their precedence.

[0072] The feature extraction module (132) can generate feature information by integrating operator type information, operation order information, tree depth information and operator attribute information.

[0073] Feature information can be represented as a multidimensional vector or a structured data object and may include an operator distribution vector, an operation order sequence, tree structure metrics (tree depth, number of nodes, number of branches), and a set of operator attributes.

[0074] Feature information quantitatively represents the conceptual characteristics and solution flow of a formula; for example, complex polynomials have high tree depth and diverse operator distributions and are likely to be classified as algebraic problems, while simple arithmetic formulas have low tree depth and limited operator types and can be classified as basic arithmetic problems.

[0075] The feature extraction module (132) can provide basic data that converts the generated feature information into natural language processing module (133) by analyzing the structure of the formula and converting it into natural language text.

[0076] Additionally, the classification unit (140) is used to classify main types and sub-types, and the quantitative characteristics of the feature information can contribute to the artificial intelligence model learning the structural patterns of mathematical problems.

[0077] The feature extraction module (132) goes beyond simple keyword-based classification and reflects the inherent conceptual characteristics and solution strategies of the formula, thereby accurately diagnosing the learner's lacking concepts and enabling systematic management of problem types in a question bank system or online learning platform.

[0078] The natural language processing module (133) analyzes the structure of a formula based on feature information received from the feature extraction module (132) and converts it into natural language text, and is electrically connected to the feature extraction module (132).

[0079] The natural language processing module (133) can contribute to improving the classification accuracy of main types and sub types by converting the operation structure of the formula into a natural language form that can be processed by an artificial intelligence classification model.

[0080] In addition, the natural language processing module (133) can express the structural characteristics and conceptual context of a mathematical problem in natural language to provide semantic information related to the problem-solving strategy, thereby supporting the learner's understanding and problem analysis.

[0081] Here, natural language text refers to data that converts the formula structure and operation flow of a mathematical problem into a linguistic expression that humans can understand, and describes operators, operands, order of operations, and hierarchical relationships in natural language sentences, and may include, for example, the result of converting the formula "2x + 3y = 5" into a sentence such as "the result of adding 2x and 3y is 5."

[0082] Natural language text can be used as input data necessary for artificial intelligence classification models to learn structural patterns of formulas and predict main and subtypes, and can help learners or educators intuitively understand the structure and concepts of mathematical problems.

[0083] The natural language processing module (133) can perform the process of interpreting the operation structure of a mathematical expression step by step and converting it into a natural language sentence by comprehensively analyzing operator type information, operation order information, tree depth information and operator attribute information based on feature information received from the feature extraction module (132).

[0084] At this time, the natural language conversion process may include a structural analysis step, a semantic mapping step, and a text generation step.

[0085] In the structural analysis stage, the hierarchical operational relationships of the converted formula can be analyzed through the Sympy format.

[0086] The natural language processing module (133) can identify the calculation flow and nested structure of a formula by utilizing the operation order information and tree depth information included in the feature information during the structure analysis stage. For example, the formula "(a + b) * (c + d)" has a tree depth of 3 and represents a flow in which internal addition operations are connected to multiplication operations.

[0087] In the structural analysis phase, the hierarchical relationship between operator nodes and operand nodes is identified, and the structure can be decomposed into computational steps according to the order of operations.

[0088] In the semantic mapping step, the results of structural analysis can be converted into semantic expressions according to the roles of the operator and operand. The natural language processing module (133) can define the function and context of each operation based on operator attribute information. For example, the addition operator can be mapped to natural language expressions such as "add," the equal sign to "equal," and multiplication to "multiply."

[0089] In addition, operator type information reflects the conceptual characteristics of the expression; for example, function operators sin and cos can be converted into expressions related to trigonometric functions.

[0090] In the semantic mapping stage, the relationship between operators and operands can be restructured to clearly convey the meaning of the operation in natural language while maintaining the structural characteristics of the formula.

[0091] In the text generation stage, the results obtained in the semantic mapping stage can be combined into natural language sentences to finally generate natural language text. The natural language processing module (133) constructs sentences using predefined natural language templates and grammar rules, and can reflect the order of operations and hierarchical structure of formulas. For example, the formula "2x + 3y = 5" can be converted to "the result of adding 2x and 3y is equal to 5," and the formula "(a + b) * (c + d)" can be converted to "multiply the result of adding a and b by the result of adding c and d." In the text generation stage, tree depth information is used to adjust the complexity of the sentence, and in the case of complex formulas, multi-stage operations can be distinguished and described.

[0092] The natural language text generated through the natural language processing module (133) is grammatically accurate and semantically consistent, and can intuitively convey the structure of the formula and the flow of the solution.

[0093] Since natural language text reflects the structural patterns and conceptual characteristics of mathematical formulas, it can play a crucial role in enabling AI models to learn and predict the main and subtypes of mathematical problems. For example, the natural language text of a linear equation exhibits patterns such as "an expression that adds or subtracts terms containing variables to equal a constant," which can be used to classify it as a linear equation type. Furthermore, subtypes can be predicted based on the order of operations and the roles of the operands included in the natural language text.

[0094] In addition, the output of the natural language processing module (133) can provide additional utility for learners and educators as well as for the classification process. The converted natural language text can be used to intuitively explain the process of solving mathematical problems and helps learners understand the concepts and structure of the problems.

[0095] The classification unit (140) classifies the main type of mathematical problem through an artificial intelligence-based classification model based on feature information converted into natural language text, and classifies multiple sub-types that complement the main type, and is electrically connected to the conversion unit (130) and the output unit (150).

[0096] As illustrated in FIG. 5, the classification unit (140) includes a first classification module (141) that classifies the main type of a mathematical problem based on feature information, and a second classification module (142) that sequentially classifies a plurality of sub-types according to a hierarchical classification structure based on the main type.

[0097] The first classification module (141) can predict the main type of math problem by using feature information converted into natural language text as input.

[0098] Here, the main type refers to the representative type central to solving mathematical problems, and it can reflect the core mathematical concepts of the problem.

[0099] The first classification module (141) operates through a multi-class classification method, calculates a probability distribution for each main type, and can derive the optimal main type based on conditional information such as the learner's background information or problem context.

[0100] In addition, the classification result of the main type influences the sub-type classification of the second classification module (142) and functions as the basis for the overall problem type classification.

[0101] Meanwhile, the first classification module (141) can classify the main type based on the learner's grade level information, elective course completion information, and target university entrance exam information.

[0102] Here, the learner's grade information can be entered directly by the learner through the user terminal (110) or obtained through user profile data from an educational platform linked to the user terminal (110) via a network.

[0103] For example, for a first-year high school student, problem types corresponding to the common mathematics of the high school curriculum and the common subjects of the CSAT (Mathematics I, Mathematics II) can be classified, and this classification can be performed based on the trends of CSAT questions.

[0104] In addition, for high school sophomores and juniors, it is possible to check whether they have completed general elective subjects such as calculus, probability and statistics, and geometry, as well as career elective subjects such as geometry and vectors, and to reflect information on the entrance exams for target universities.

[0105] The target university entrance exam information is collected through web crawling via a user terminal (110) and may include previous year's past exam questions, exam trends, and methods of reflecting elective subjects for the target university designated by the learner.

[0106] The first classification module (141) determines the academic classification of the math problem (e.g., algebra, calculus), then identifies the detailed type (e.g., quadratic equations, applications of definite integrals), and finally determines the main type by applying the exam trends of the target university and the method of reflecting elective subjects.

[0107] For example, if a specific university grants extra points to students who choose calculus and frequently includes high-difficulty integration problems, math problems recommended for second-year high school students aiming for that university can be classified as advanced calculus types. This module integrates data from the CSAT common subjects, elective subjects, and university-specific entrance exams to dynamically adjust classification criteria and provide type classifications optimized for the learner's goals.

[0108] The second classification module (142) can predict sub-types based on the main type determined in the first classification module (141).

[0109] A subtype refers to a detailed type that complements the main type and contributes substantially to solving the problem. For example, if the main type is a linear equation, the subtype may be a type related to solution methods such as separation of variables or substitution.

[0110] Specifically, the second classification module (142) can sequentially classify a plurality of sub-types according to a hierarchical structure separated into Depth 0 to Depth 4 based on the main type classified in the first classification module (141).

[0111] In this case, Depth is a classification level that reflects the conceptual inclusion relationship between subtypes; each level represents a more detailed concept and can be structured so that the types of the lower level logically include the types of the higher level.

[0112] For example, if "Algebra" is selected at Depth0, "Exponential and Logarithmic Functions" should be selected at Depth1, and "Exponent" at Depth2; this corresponds to a correct hierarchical classification structure.

[0113] Conversely, predictions that do not follow a logical inclusion relationship with higher depths—for example, "Common Math 1" at Depth 0, "Trigonometric Functions" at Depth 1, and "Exponent" at Depth 2—are considered incorrect hierarchical structures. These hierarchical structures are evaluated based on reinforcement learning policies, contributing to the maintenance of consistency.

[0114] The second classification module (142) applies a custom loss function to a RoBERTa-base-based classification model to independently predict each subtype from Depth 0 to Depth 4, which can be trained through supervised learning.

[0115] Additionally, a reinforcement learning-based reward policy may be applied to verify the consistency of the predicted subtype hierarchy. In this case, the policy criterion is a logical inclusion relationship in which the type predicted at a higher depth must encompass the type at a lower depth; a penalty may be imposed for following an incorrect hierarchy, while a reward may be given for following the correct structure.

[0116] This reward-based loss is passed to the entire classification model network to ensure that hierarchical consistency is maintained during the training process.

[0117] Additionally, the second classification module (142) can predict the subtype by applying a loss function defined by the following Equation 1, which reflects the structural correlation between the main type and the subtype.

[0118] {Formula 1}

[0119]

[0120] Here, is the total loss value, and is the cross-entropy loss for the subtype, and is the probability distribution of the main type Probability distribution of subtypes It is a non-linear similarity-based loss term between, is a Graph Neural Network (GNN)-based structural correlation correction term, representing the GNN's predicted probability distribution Probability distribution of subtypes It is the Kullback-Leibler (KL) divergence value of the liver, and Is It is a real coefficient that adjusts the weight for the term, and Is It is a real coefficient that adjusts the weight for the term.

[0121] Main type probability distribution and subtype probability distributions Non-linear similarity-based loss term between It suppresses excessive similarity between the main type and the subtype, and is defined by the following formula 2.

[0122] {Equation 2}

[0123]

[0124] Here, k is the sensitivity control coefficient, the cosine distance between the main type and the sub-type. The more similar it is, the more rapidly the loss is adjusted to increase.

[0125] Cosine similarity It can suppress excessive similarity by measuring the distribution similarity between the main type and the sub-type, and is defined by the following Equation 3.

[0126] {Equation 3}

[0127]

[0128] is a connectivity loss term between main types and sub-types based on a Graph Neural Network (GNN) that learns the correlation between main types and sub-types. It optimizes the agreement between the GNN's prediction and sub-types by increasing the loss when the prediction probability of a sub-type frequently connected to a specific main type is low, based on a type graph learned using the GNN, and is defined by the following Equation 4.

[0129] {Equation 4}

[0130]

[0131] Here Rho, the prediction probability distribution of GNN Probability distribution of subtypes It is calculated as the Kullback-Leibler (KL) divergence between the two, and is defined by the following Equation 5.

[0132] {Equation 5}

[0133]

[0134] This loss function structure is directly applied to the logit of the classification model and can be reflected in the entire parameter update process.

[0135] The main structure of the classification model utilizes a pre-trained language model (RoBERTa-base) based on the Transformer architecture, to which a loss function is added to refine and normalize semantic relationships between main and subtypes; this loss function uses correlation information obtained through GNNs as a complementary signal, thereby simultaneously improving the precision and validity of predictions.

[0136] For example, if the main type is predicted as a "linear equation," the loss function can reduce the phenomenon of irrelevant subtypes being selected by inducing the selection of subtypes such as "variable separation," which frequently appear alongside it.

[0137] Accordingly, the classification unit (140) can precisely analyze mathematical problems by type using natural language-based feature information and ensure consistency and significance of the prediction results through a structured loss function.

[0138] The output unit (150) transmits the main type and sub-type classified through the classification unit (140) to the user terminal and is electrically connected to the classification unit (140).

[0139] The output unit (150) transmits the classification results to the user through the user terminal (110) so that they can be utilized in a learning and education environment.

[0140] The output unit (150) can support various output formats based on the main type and sub-type information received from the classification unit (140).

[0141] The output format may consist of text, JSON objects, and visual graphics, and can be dynamically adjusted according to the characteristics of the user terminal (110). For example, a simple text format may be provided on a smartphone, and detailed visual graphics on a desktop. The output unit (150) optimizes the amount of data transmitted by considering the network conditions, and can transmit lightweight data in a limited network environment.

[0142] The output unit (150) can provide personalized feedback based on the classification results to individual learners and generate a class-based learning analysis report for educators so that the classification results can be utilized in a learning environment.

[0143] Additionally, the output unit (150) can be used in a question bank system or an online learning platform to categorize large-scale problem data and recommend problems suitable for the learner's level.

[0144] Meanwhile, the output unit (150) may further include a learning path module that recommends a customized learning path for college admission to the user based on the problem type classification result received from the classification unit (140).

[0145] The learning path module can construct a learning path for problem types suitable for admission to the university the learner aims to enter by comprehensively analyzing the learner's grade level information, elective course completion information, target university information, and main type and sub-type classification results.

[0146] The learning path is determined based on the classification results of math problems by type, the subjects reflected in the entrance exams of target universities, and past exam trends, and can be dynamically adjusted based on the learner's real-time problem-solving records and achievement data by type.

[0147] For example, if a learner is in their second year of high school and the target university designates calculus as a major subject and includes many problems of differential application type, the learning path module can generate a learning path consisting of a review stage based on Mathematics II concepts, learning core concepts of the calculus unit, intensive training on high-difficulty calculus application type, a learning stage based on past exam types of the target university, and a practice problem-solving stage based on predicted problems.

[0148] The learning path can automatically link and provide math problems based on the difficulty, conceptual scope, and type distribution of the math problems, and the entry conditions for the next stage can be determined based on the problem-solving results.

[0149] The learning path module collects the correct answer rate by type, solution time, repetition of incorrect answers, and accuracy by operation structure from the learner's problem-solving history, and can evaluate the learning necessity for each type based on this.

[0150] In addition, learning priorities can be set for each problem type based on the user's quantitative achievement data, and the set priorities can be updated in real time.

[0151] In addition, the learning path module can adjust the appearance ratio of question types and the weight of learning based on elective course completion information and the target university's method of reflecting elective courses.

[0152] For example, if a specific university designates Probability and Statistics as a major subject, it may place learning levels for types belonging to that subject (e.g., probability distribution, expected value, statistical estimation, etc.) at the top and prioritize providing problems of that type from the question bank system.

[0153] The learning path module can provide the learner with the current learning stage, conditions for entering the next stage, accumulated learning history, and achievement analysis results through the user terminal (110), and the learner can check their learning path in real time and receive feedback.

[0154] In addition, the learning path module can automatically generate analysis reports on a class-by-class basis, including learners' achievement by type, progress rate, problem-solving status by type, and level of preparation for target universities.

[0155] Analysis reports can be generated to enable educators to provide customized feedback to individual learners and to utilize them for lesson planning and problem selection.

[0156] The learning path module collects entrance exam information for target universities through web crawling or database linkage, and can update recommended questions and learning paths in real time based on indicators related to past exam question types, the reflection ratio of elective subjects, and the difficulty level of questions, according to the collected admission information.

[0157] The learning path module can provide a step-by-step learning path optimized for the student's admission to their target university by configuring problem recommendations and learning stages based on classified math problem type results, individual learner characteristics, and the question trends of the target university.

[0158] As described above, according to the artificial intelligence-based math problem assistance type classification system (100) of one embodiment of the present invention, by precisely classifying the main type and sub-type of math problems, customized learning materials reflecting the concept and structure of the problem are provided to the learner, thereby effectively improving the learner's problem-solving ability and mathematical thinking skills, and accurately diagnosing deficient concepts to design an optimal learning path tailored to the individual level.

[0159] Furthermore, by systematically analyzing the complex structure of mathematical problems and clearly distinguishing the relationships between main and sub-types, it provides sophisticated learning analysis and feedback in educational settings. Additionally, by automatically categorizing and systematically managing large-scale mathematical problem data, it can be efficiently utilized in various educational environments such as question bank systems, online learning platforms, and CSAT preparation services.

[0161] Although all components constituting the embodiments of the present invention have been described above as being combined or operating together, the present invention is not necessarily limited to such embodiments. That is, within the scope of the purpose of the present invention, all components may be selectively combined and operated in one or more ways.

[0162] Furthermore, terms such as "include," "compose," or "have" described above, unless specifically stated otherwise, mean that the relevant component may be inherent; therefore, they should be interpreted as allowing for the inclusion of additional components rather than excluding them. All terms, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains, unless otherwise defined. Commonly used terms, such as those defined in advance, should be interpreted in accordance with their meaning in the context of the relevant technology and should not be interpreted in an ideal or overly formal sense unless explicitly defined in the present invention.

[0163] Furthermore, the above description is merely an illustrative explanation of the technical concept of the present invention, and those skilled in the art to which the present invention pertains will be able to make various modifications and variations within the scope of the essential characteristics of the present invention.

[0164] Accordingly, the embodiments disclosed in this invention are intended to illustrate, not limit, the technical concept of the invention, and the scope of the technical concept of the invention is not limited by these embodiments. The scope of protection of this invention shall be interpreted by the claims below, and all technical concepts within an equivalent scope shall be interpreted as being included within the scope of rights of this invention. Explanation of the symbols

[0165] 100: Artificial intelligence-based math problem assistance type classification system according to an embodiment of the present invention 110: User terminal 120: Input section 130: Conversion unit 131: Preprocessing Module 132: Feature Extraction Module 133: Natural Language Processing Module 140: Classification section 141: Classification Module 1 142: Classification Module 2 150: Output section

Claims

Claim 1 An AI-based mathematical problem auxiliary type classification system comprising: a user terminal; an input unit that receives a mathematical problem containing a formula from the user terminal and extracts the formula from the mathematical problem; a conversion unit that converts the extracted formula into a Sympy format according to the operation structure of an operator and an operand to generate feature information and converts the feature information into natural language text; a classification unit that classifies the main type of the mathematical problem through an AI-based classification model based on the feature information converted into natural language text and classifies a plurality of sub-types that complement the main type; and an output unit that transmits the main type and the sub-types to the user terminal, wherein the classification unit comprises a first classification module that classifies the main type through an AI-based classification model based on the feature information and a second classification module that sequentially classifies a plurality of sub-types according to a hierarchical classification structure based on the main type. Claim 2 The artificial intelligence-based mathematical problem assistance type classification system according to claim 1, wherein the conversion unit comprises: a preprocessing module that converts the mathematical formula into a Sympy format according to the operation structure of the operator and operand; a feature extraction module that generates feature information by extracting operator type information, operation order information, and tree depth information of the Sympy format; and a natural language processing module that analyzes the structure of the mathematical formula based on the feature information and converts it into natural language text. Claim 3 delete Claim 4 The artificial intelligence-based mathematical problem assistance type classification system according to claim 1, wherein the second classification module predicts the subtype by applying a loss function that reflects the structural correlation between the main type and the subtype, and the loss function includes a non-linear similarity-based loss term for the prediction probability distribution between the main type and the subtype and a Graph Neural Network (GNN)-based correlation correction term. Claim 5 An artificial intelligence-based mathematical problem assistance type classification system according to claim 2, wherein the feature extraction module generates operator attribute information including the number of terms of the operator, associative rule information, and operation priority information based on the operation characteristics of the operator included in the Sympy format, and generates the feature information based on the operator attribute information.

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