CN116595159A - Mathematical question answering model training method and device - Google Patents
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Abstract
The disclosure relates to the technical field of machine learning, and provides a mathematical problem solving model training method and device. The method comprises the following steps: training the pre-training language model by using mathematical problem training data; freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the frozen model based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems; and taking the pre-trained language model of the thinking chain for learning and answering various mathematical questions as a mathematical question answering model, generating the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times by utilizing the mathematical question answering model, and taking the reasoning process and the answer with the largest generation times as the final result corresponding to the target mathematical questions.
Description
Technical Field
The disclosure relates to the technical field of machine learning, in particular to a mathematical problem solution model training method and device.
Background
In recent years, neural network models have achieved great success in the fields of computer vision, pattern matching, natural language processing, reinforcement learning, and the like, and also have been applied to solving mathematical problems. In terms of data, a mathematical problem can be regarded as a sequence, and its solution (a problem solving step or a solving expression) is often presented in the form of a sequence, so that the neural network model solves the mathematical problem as a translation process from a natural language to a mathematical language. The knowledge or the belief omits the reasoning process for solving the mathematical problem to a certain extent, so that the neural network model obtained based on the knowledge or the belief has poor reasoning capability when solving the mathematical problem.
Disclosure of Invention
In view of this, the embodiments of the present disclosure provide a method, an apparatus, an electronic device, and a computer readable storage medium for training a mathematical problem solving model, so as to solve the problem in the prior art that the reasoning capability is poor when the neural network model solves the mathematical problem.
In a first aspect of an embodiment of the present disclosure, a method for training a mathematical problem solution model is provided, including: acquiring mathematic problem training data and mathematic problem reasoning data, wherein the mathematic problem training data comprises a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprises a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers; training the pre-training language model by using mathematical problem training data; freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the frozen model based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems; and taking the pre-trained language model of the thinking chain for learning and answering various mathematical questions as a mathematical question answering model, generating the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times by utilizing the mathematical question answering model, and taking the reasoning process and the answer with the largest generation times as the final result corresponding to the target mathematical questions.
In a second aspect of the embodiments of the present disclosure, there is provided a mathematical problem solution model training apparatus, including: the system comprises an acquisition module, a storage module and a storage module, wherein the acquisition module is configured to acquire mathematical problem training data and mathematical problem reasoning data, the mathematical problem training data comprises a plurality of mathematical problems and answers corresponding to each mathematical problem, and the mathematical problem reasoning data comprises a plurality of mathematical problems, reasoning processes corresponding to each mathematical problem and answers; a training module configured to train the pre-training language model using the mathematical problem training data; the reasoning module is configured to freeze model parameters of the trained pre-training language model, control the pre-training language model after the parameters of the pre-training language model are frozen based on mathematical problem reasoning data, and solve the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to multiple mathematical problems; the problem solving module is configured to take a pre-training language model of a thinking chain for solving various mathematical problems as a mathematical problem solving model, generate the reasoning process and the answer corresponding to the target mathematical problem to be solved for a plurality of times by utilizing the mathematical problem solving model, and take the reasoning process and the answer with the largest generation times as a final result corresponding to the target mathematical problem.
In a third aspect of the disclosed embodiments, an electronic device is provided, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the above method when executing the computer program.
In a fourth aspect of the disclosed embodiments, a computer-readable storage medium is provided, which stores a computer program which, when executed by a processor, implements the steps of the above-described method.
Compared with the prior art, the embodiment of the disclosure has the beneficial effects that: because the embodiment of the disclosure obtains the mathematic problem training data and the mathematic problem reasoning data, wherein the mathematic problem training data comprises a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprises a plurality of mathematic problems, and reasoning processes and answers corresponding to each mathematic problem; training the pre-training language model by using mathematical problem training data; freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the frozen model based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems; the pre-training language model of the thinking chain for learning and answering various mathematical questions is used as a mathematical question answering model, the mathematical question answering model is utilized to generate the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times, and the reasoning process and the answer with the largest generation times are used as the final result corresponding to the target mathematical questions.
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In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings that are required for the embodiments or the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present disclosure, and other drawings may be obtained according to these drawings without inventive effort for a person of ordinary skill in the art.
FIG. 1 is a flow chart of a mathematical problem solution model training method provided by an embodiment of the present disclosure;
FIG. 2 is a flow chart of a method for solving a mathematical problem according to an embodiment of the present application;
FIG. 3 is a schematic structural diagram of a training device for a mathematical problem solution model according to an embodiment of the present disclosure;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the disclosure.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system configurations, techniques, etc. in order to provide a thorough understanding of the disclosed embodiments. However, it will be apparent to one skilled in the art that the present disclosure may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present disclosure with unnecessary detail.
Fig. 1 is a flow chart of a mathematical problem solution model training method according to an embodiment of the present disclosure. The mathematical problem solution model training method of fig. 1 may be performed by a computer or a server, or software on a computer or a server. As shown in fig. 1, the mathematical problem solution model training method includes:
s101, acquiring mathematic problem training data and mathematic problem reasoning data, wherein the mathematic problem training data comprises a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprises a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers;
s102, training a pre-training language model by using mathematical problem training data;
s103, freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the pre-training language model are frozen based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems;
s104, taking the pre-trained language model of the thinking chain for learning and answering various mathematical questions as a mathematical question answering model, generating the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times by utilizing the mathematical question answering model, and taking the reasoning process and the answer with the largest generation times as the final result corresponding to the target mathematical questions.
The Pre-trained language model may be a GPT model, which is known as the generating Pre-traditional transducer, or a BERT model, which is known as Bidirectional EncoderRepresentations from Transformers. The mathematical questions in the mathematical questions training data are regarded as samples, answers corresponding to the mathematical questions are regarded as labels of the samples, the mathematical questions training data are utilized to train the pre-training language model, the model training stage is a common model training method, and the description is omitted. The mathematical questions in the mathematical question reasoning data have corresponding reasoning processes, the pre-training language model which is controlled by the frozen model parameters based on the mathematical question reasoning data solves the mathematical questions according to the reasoning processes corresponding to each mathematical question, and the mathematical question reasoning data belongs to a model reasoning stage, wherein the model reasoning stage is a thinking chain for learning and solving various mathematical questions from the reasoning processes corresponding to a plurality of mathematical questions by the pre-training language model. The thinking chain in machine learning is a discrete prompt learning, and also refers to thinking of a neural network simulation model for solving problems. And generating the target mathematical questions by using the mathematical question solution model for a plurality of times, counting the occurrence times of the generated results, and selecting the result with the largest occurrence times as final output, wherein the generated results comprise the reasoning process and the answer corresponding to the target mathematical questions.
For example, the training data of the math questions are as follows:
| mathematics questions | Answers corresponding to math questions |
| Please give prime numbers Syndrome of infinity Bright: | it is assumed that there are only a limited number of prime numbers. And (3) letting the material flow. Then n+1 is prime or not prime. If N+1 is prime, then N +1 is greater than so it is not in those hypothesized prime number sets. If N+1 is a compound number, because either one of the compound numbers The numbers can be decomposed into products of several prime numbers; and the greatest common divisor of N and N+1 is 1, so N+1 cannot be rounded The prime factors resulting from the composite decomposition are certainly not in the hypothesized prime number set. Thus no matter how much Prime numbers or composite numbers mean that there are other prime numbers in addition to the assumed limited number of prime numbers. To any limit For a prime number set, the prime number set with a prime number which is not assumed can be obtained forever by the method Is a conclusion of (2). The original assumption is not true. That is, there are infinite numbers of prime numbers. |
| The prior art is a cage which is used for a pair of cages, inside is provided with chicken and a plurality of rabbits are used for carrying out the process, one number of numbers, altogether First 14, legs 38 Strip, chicken and rabbit How many of the sub-elements are Only? | Solution: assuming that all chickens are present, there are 14×2=28 legs, 38-28=10 fewer than actually, one chicken becomes one rabbit The number of legs is increased by 2, 10/2=5, so 5 chickens are needed to be changed into rabbits, namely, 5 rabbits, and 14-5=9 chickens. |
According to the technical scheme provided by the embodiment of the disclosure, mathematic problem training data and mathematic problem reasoning data are obtained, wherein the mathematic problem training data comprise a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprise a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers; training the pre-training language model by using mathematical problem training data; freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the frozen model based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems; the pre-training language model of the thinking chain for learning and answering various mathematical questions is used as a mathematical question answering model, the mathematical question answering model is utilized to generate the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times, and the reasoning process and the answer with the largest generation times are used as the final result corresponding to the target mathematical questions.
The pre-training language model after controlling the frozen model parameters based on the mathematical problem reasoning data solves the mathematical problem according to the reasoning process corresponding to each mathematical problem until the answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns the thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems, and the method comprises the following steps: dividing the mathematical questions in the mathematical question reasoning data according to the difficulty level to obtain a plurality of question groups with different difficulty levels, wherein each question group comprises a plurality of mathematical questions and reasoning processes and answers corresponding to each mathematical question; and controlling the pre-training language model after the frozen model parameters are controlled for multiple times according to the order of the plurality of question groups from easy to difficult, and solving the mathematical questions according to the reasoning process corresponding to each mathematical question in each question group until the answers corresponding to the mathematical questions are obtained, so that the pre-training language model learns the thinking chains for solving various mathematical questions from the reasoning process corresponding to the plurality of mathematical questions, wherein the pre-training language model after the frozen model parameters are controlled based on one question group each time.
The difficulty level of the mathematical problem can be measured by a Bayesian network or the number of mistakes. In order to facilitate the study of the pre-training language model, the pre-training language model is controlled to solve the mathematical problems according to the reasoning process corresponding to each mathematical problem in each problem group according to the order of the problem groups from easy to difficult. For example, the mathematical problem reasoning data is divided into three problem groups, namely a first problem group, a second problem group and a third problem group from easy to difficult, so that the control pre-training language model solves the mathematical problem according to the reasoning process corresponding to each mathematical problem in the first problem group, the second problem group and the third problem group in sequence.
After learning the pre-training language model of the thinking chain for solving various mathematical problems as the mathematical problem solving model, the method further comprises: obtaining a mathematical problem set to be solved, dividing a plurality of mathematical problems in the mathematical problem set according to a preset number N and knowledge points corresponding to each mathematical problem to obtain a plurality of problem groups aiming at different knowledge points, wherein each problem group comprises N pieces of data, the ith piece of data is (i+1)/2 pieces of mathematical problems, the (i+1) th piece of data is an reasoning process and an answer corresponding to the (i+1)/2 pieces of mathematical problems, N is an odd number, the mathematical problems represented by the Nth piece of data have no corresponding reasoning process and answer, i is an odd number in an open interval (0, N), and i+1 is smaller than N; and sequentially inputting a plurality of question groups into a mathematical question answering model, and outputting an reasoning process and an answer corresponding to the mathematical questions represented by the Nth data in each question group, wherein the reasoning process and the answer corresponding to the mathematical questions represented by the Nth data in each question group are obtained by a context learning method through the mathematical question answering model.
Sequentially inputting a plurality of question groups into a mathematical question solution model, and outputting an reasoning process and an answer corresponding to the mathematical questions represented by the Nth data in each question group, wherein the reasoning process comprises the following steps: taking the ith data and the (i+1) th data in each question group as a pair of data, wherein each question group has (N-1)/2 pairs of data; the mathematical problem solving model is based on (N-1)/2 pairs of data in each problem group, and the N-th data in the problem group is inferred by a context learning method, so that an inference process and an answer corresponding to the mathematical problem represented by the N-th data in the problem group are obtained.
For example, 10 mathematical questions of a certain knowledge point in a mathematical question set are divided into two question groups by N being 5, the two question groups have 5 pieces of data, i is 1 and 3, 1 data is 1 st mathematical question, 2 data is an reasoning process and an answer corresponding to 1 st mathematical question, 3 data is 2 nd mathematical question, 4 data is an reasoning process and an answer corresponding to 2 nd mathematical question, 5 data is 3 rd mathematical question, 3 rd mathematical question has no corresponding reasoning process and answer, and i+1 is 4 at most, so i+1 is smaller than N.
And taking each mathematical problem and the corresponding reasoning process and answer thereof as a pair, taking (N-1)/2 pairs of data in one problem group, taking the (N-1)/2 pairs of data in one data group as the above, taking the Nth data in the data group as the below, and reasoning the Nth data in the data group by a context learning method to obtain the reasoning process and the answer corresponding to the mathematical problem represented by the Nth data in the data group.
Or taking all data in one data set as the above, taking the reasoning process and the answer (unknown) corresponding to the mathematical problem represented by the Nth data in the data set as the following, and reasoning the Nth data in the data set by a method of context learning to obtain the reasoning process and the answer corresponding to the mathematical problem represented by the Nth data in the data set.
The embodiment of the application is equivalent to the use of a pre-training language model to infer the (N+1)/2 th reasoning process and answer corresponding to the (N-1)/2 th mathematic problem based on the reasoning process and answer corresponding to the (N-1)/2 th mathematic problem.
After learning the pre-training language model of the thinking chain for solving various mathematical problems as the mathematical problem solving model, the method further comprises: obtaining a question group to be solved, wherein the question group comprises N mathematic questions, the N mathematic questions belong to the same knowledge point or type, the N-1 mathematic questions in front all have corresponding reasoning processes and answers, and the N mathematic questions have no corresponding reasoning processes and answers; inputting N mathematic questions in the question group into a mathematic question solving model, and outputting an reasoning process and an answer corresponding to the N mathematic questions in the question group, wherein the reasoning process and the answer corresponding to the N mathematic questions are obtained by the mathematic question solving model through a context learning method.
Taking high-order mathematical topics as examples, the types include trigonometric functions or arrays, solid geometry, statistics and probabilities, analytical geometry, functions and derivatives, planar geometry evidence, coordinate systems and parametric equations, inequality, and the like. The knowledge point is a point of investigation of a mathematical problem or a knowledge based on which the problem is addressed. The embodiment of the application is equivalent to utilizing the pre-training language model to infer the reasoning process and the answer corresponding to the Nth mathematical problem based on the reasoning process and the answer corresponding to the previous N-1 mathematical problems.
Training the pre-training language model using the mathematical problem training data, comprising: constructing a mathematical problem solving task and a plurality of auxiliary tasks, wherein the plurality of auxiliary tasks comprise: a topic classification task, an intention recognition task, an automatic summary task, and a translation task; the pre-training language model is trained by utilizing the mathematical problem training data based on the mathematical problem solving task, and the pre-training language model is trained based on a plurality of auxiliary tasks in the process of training the pre-training language model based on the mathematical problem solving task.
The topic classification task is a task for classifying mathematical topics according to the text meanings in the mathematical topics; the task of classifying the questions is a task of classifying the digital questions according to knowledge points corresponding to the mathematical questions; an intention recognition task recognizes a task of character meaning in a mathematical question; the automatic summary task is a task for summarizing the meaning of mathematical questions; for example, the object of the mathematical topic solution model service is a student in China, and the translation task is used for translating English version of mathematical topic into Chinese version of mathematical topic.
The training method comprises the steps of simultaneously training the pre-training language model by using a plurality of auxiliary tasks and a plurality of mathematical problem solving tasks, and training the pre-training language model based on the plurality of auxiliary tasks, wherein the pre-training language model can be trained by using mathematical problem training data, and the pre-training language model can also be trained by using training data corresponding to the plurality of auxiliary tasks.
Training the pre-training language model using the mathematical problem training data, comprising: extracting sentence-level representation and question-level representation of each mathematical problem and corresponding answer of each mathematical problem in the mathematical problem training data by using a pre-training language model; through sentence level representation and question level representation of each mathematical problem and corresponding answer of each mathematical problem, understanding of the pre-training language model on each mathematical problem and corresponding answer of each mathematical problem is enhanced, so that training of the pre-training language model is completed.
According to symbols such as commas, periods, question marks and the like, a mathematical question can be divided into a plurality of sentences, a question-level representation of the mathematical question is a feature representation of the whole mathematical question, a sentence-level representation of the mathematical question is a feature representation (detail feature) of each sentence in the mathematical question, and a sentence-level representation is a feature representation more detailed than the question-level representation. Sentence-level and question-level representations of the corresponding answers to the mathematical questions are similar to sentence-level and question-level representations of the mathematical questions. According to the embodiment of the application, the understanding of each mathematical problem and the corresponding answer of each mathematical problem by the pre-training language model is enhanced according to the sentence-level representation and the problem-level representation (namely, when the whole characteristic is concerned, the detail characteristic is also concerned), so that the pre-training language model can perform more accurate reasoning and solving of the problem.
Fig. 2 is a flow chart of a method for solving a mathematical problem according to an embodiment of the present application. As shown in fig. 2, includes:
s201, acquiring a mathematical problem set to be solved;
s202, dividing a plurality of mathematical questions in a mathematical question set according to a preset number N and knowledge points corresponding to each mathematical question to obtain a plurality of question groups aiming at different knowledge points, wherein each question group comprises N pieces of data, the ith piece of data is (i+1)/2 pieces of mathematical questions, the (i+1) th piece of data is an reasoning process and an answer corresponding to the (i+1)/2 pieces of mathematical questions, N is an odd number, the mathematical questions represented by the Nth piece of data have no corresponding reasoning process and answer, i is an odd number in an open interval (0, N), and i+1 is smaller than N;
s203, taking the ith data and the (i+1) th data in each question group as a pair of data, wherein each question group has (N-1)/2 pairs of data, and sequentially inputting a plurality of question groups into a mathematical question solution model:
s204, the mathematical problem solving model is based on (N-1)/2 pairs of data in each problem group, and the N-th data in the problem group is inferred through a context learning method, so that an inference process and an answer corresponding to the mathematical problem represented by the N-th data in the problem group are obtained;
s205, the mathematical problem solving model outputs the reasoning process and the answer corresponding to the mathematical problem represented by the Nth data in each problem group.
Any combination of the above optional solutions may be adopted to form an optional embodiment of the present application, which is not described herein.
The following are device embodiments of the present disclosure that may be used to perform method embodiments of the present disclosure. For details not disclosed in the embodiments of the apparatus of the present disclosure, please refer to the embodiments of the method of the present disclosure.
Fig. 3 is a schematic diagram of a mathematical problem solution model training apparatus according to an embodiment of the present disclosure. As shown in fig. 3, the mathematical problem solution model training apparatus includes:
the acquisition module 301 is configured to acquire mathematic problem training data and mathematic problem reasoning data, wherein the mathematic problem training data comprises a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprises a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers;
a training module 302 configured to train the pre-training language model using the mathematical problem training data;
the reasoning module 303 is configured to freeze model parameters of the trained pre-training language model, control the pre-training language model after the parameters of the pre-training language model are frozen based on the mathematical problem reasoning data, and solve the mathematical problem according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to multiple mathematical problems;
The solving module 304 is configured to take a pre-trained language model of a thinking chain for learning and solving various mathematical questions as a mathematical question solving model, generate the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times by using the mathematical question solving model, and take the reasoning process and the answer with the largest generation times as the final result corresponding to the target mathematical questions.
The Pre-trained language model may be a GPT model, which is known as the generating Pre-traditional transducer, or a BERT model, which is known as Bidirectional EncoderRepresentations from Transformers. The mathematical questions in the mathematical questions training data are regarded as samples, answers corresponding to the mathematical questions are regarded as labels of the samples, the mathematical questions training data are utilized to train the pre-training language model, the model training stage is a common model training method, and the description is omitted. The mathematical questions in the mathematical question reasoning data have corresponding reasoning processes, the pre-training language model which is controlled by the frozen model parameters based on the mathematical question reasoning data solves the mathematical questions according to the reasoning processes corresponding to each mathematical question, and the mathematical question reasoning data belongs to a model reasoning stage, wherein the model reasoning stage is a thinking chain for learning and solving various mathematical questions from the reasoning processes corresponding to a plurality of mathematical questions by the pre-training language model. The thinking chain in machine learning is a discrete prompt learning, and also refers to thinking of a neural network simulation model for solving problems. And generating the target mathematical questions by using the mathematical question solution model for a plurality of times, counting the occurrence times of the generated results, and selecting the result with the largest occurrence times as final output, wherein the generated results comprise the reasoning process and the answer corresponding to the target mathematical questions.
According to the technical scheme provided by the embodiment of the disclosure, mathematic problem training data and mathematic problem reasoning data are obtained, wherein the mathematic problem training data comprise a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprise a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers; training the pre-training language model by using mathematical problem training data; freezing model parameters of the trained pre-training language model, controlling the pre-training language model after the parameters of the frozen model based on mathematical problem reasoning data, and solving the mathematical problems according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problems is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems; the pre-training language model of the thinking chain for learning and answering various mathematical questions is used as a mathematical question answering model, the mathematical question answering model is utilized to generate the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times, and the reasoning process and the answer with the largest generation times are used as the final result corresponding to the target mathematical questions.
Optionally, the reasoning module 303 is further configured to divide the math questions in the math question reasoning data according to the difficulty level to obtain a plurality of question groups with different difficulty levels, where each question group includes a plurality of math questions and reasoning processes and answers corresponding to each math question; and controlling the pre-training language model after the frozen model parameters are controlled for multiple times according to the order of the plurality of question groups from easy to difficult, and solving the mathematical questions according to the reasoning process corresponding to each mathematical question in each question group until the answers corresponding to the mathematical questions are obtained, so that the pre-training language model learns the thinking chains for solving various mathematical questions from the reasoning process corresponding to the plurality of mathematical questions, wherein the pre-training language model after the frozen model parameters are controlled based on one question group each time.
The difficulty level of the mathematical problem can be measured by a Bayesian network or the number of mistakes. In order to facilitate the study of the pre-training language model, the pre-training language model is controlled to solve the mathematical problems according to the reasoning process corresponding to each mathematical problem in each problem group according to the order of the problem groups from easy to difficult. For example, the mathematical problem reasoning data is divided into three problem groups, namely a first problem group, a second problem group and a third problem group from easy to difficult, so that the control pre-training language model solves the mathematical problem according to the reasoning process corresponding to each mathematical problem in the first problem group, the second problem group and the third problem group in sequence.
Optionally, the reasoning module 303 is further configured to obtain a math question set to be solved, divide a plurality of math questions in the math question set according to a preset number N and knowledge points corresponding to each math question to obtain a plurality of question groups for different knowledge points, where each question group includes N pieces of data, the i piece of data is (i+1)/2 pieces of math questions, the i+1 piece of data is a reasoning process and an answer corresponding to the (i+1)/2 pieces of math questions, N is an odd number, the math questions represented by the N piece of data have no corresponding reasoning process and answer, i is an odd number in an open interval (0, N), and i+1 is smaller than N; and sequentially inputting a plurality of question groups into a mathematical question answering model, and outputting an reasoning process and an answer corresponding to the mathematical questions represented by the Nth data in each question group, wherein the reasoning process and the answer corresponding to the mathematical questions represented by the Nth data in each question group are obtained by a context learning method through the mathematical question answering model.
Optionally, the reasoning module 303 is further configured to take the ith data and the (i+1) th data in each question group as a pair of data, each question group having (N-1)/2 pairs of data; the mathematical problem solving model is based on (N-1)/2 pairs of data in each problem group, and the N-th data in the problem group is inferred by a context learning method, so that an inference process and an answer corresponding to the mathematical problem represented by the N-th data in the problem group are obtained.
For example, 10 mathematical questions of a certain knowledge point in a mathematical question set are divided into two question groups by N being 5, the two question groups have 5 pieces of data, i is 1 and 3, 1 data is 1 st mathematical question, 2 data is an reasoning process and an answer corresponding to 1 st mathematical question, 3 data is 2 nd mathematical question, 4 data is an reasoning process and an answer corresponding to 2 nd mathematical question, 5 data is 3 rd mathematical question, 3 rd mathematical question has no corresponding reasoning process and answer, and i+1 is 4 at most, so i+1 is smaller than N.
And taking each mathematical problem and the corresponding reasoning process and answer thereof as a pair, taking (N-1)/2 pairs of data in one problem group, taking the (N-1)/2 pairs of data in one data group as the above, taking the Nth data in the data group as the below, and reasoning the Nth data in the data group by a context learning method to obtain the reasoning process and the answer corresponding to the mathematical problem represented by the Nth data in the data group.
Or taking all data in one data set as the above, taking the reasoning process and the answer (unknown) corresponding to the mathematical problem represented by the Nth data in the data set as the following, and reasoning the Nth data in the data set by a method of context learning to obtain the reasoning process and the answer corresponding to the mathematical problem represented by the Nth data in the data set.
The embodiment of the application is equivalent to the use of a pre-training language model to infer the (N+1)/2 th reasoning process and answer corresponding to the (N-1)/2 th mathematic problem based on the reasoning process and answer corresponding to the (N-1)/2 th mathematic problem.
Optionally, the reasoning module 303 is further configured to obtain a question set to be solved, where the question set includes N mathematic questions, where the N mathematic questions all belong to the same knowledge point or type, the first N-1 mathematic questions have corresponding reasoning processes and answers, and the nth mathematic questions have no corresponding reasoning processes and answers; inputting N mathematic questions in the question group into a mathematic question solving model, and outputting an reasoning process and an answer corresponding to the N mathematic questions in the question group, wherein the reasoning process and the answer corresponding to the N mathematic questions are obtained by the mathematic question solving model through a context learning method.
Taking high-order mathematical topics as examples, the types include trigonometric functions or arrays, solid geometry, statistics and probabilities, analytical geometry, functions and derivatives, planar geometry evidence, coordinate systems and parametric equations, inequality, and the like. The knowledge point is a point of investigation of a mathematical problem or a knowledge based on which the problem is addressed. The embodiment of the application is equivalent to utilizing the pre-training language model to infer the reasoning process and the answer corresponding to the Nth mathematical problem based on the reasoning process and the answer corresponding to the previous N-1 mathematical problems.
Optionally, training module 302 is further configured to construct a mathematical problem solving task and a plurality of auxiliary tasks, wherein the plurality of auxiliary tasks includes: a topic classification task, an intention recognition task, an automatic summary task, and a translation task; the pre-training language model is trained by utilizing the mathematical problem training data based on the mathematical problem solving task, and the pre-training language model is trained based on a plurality of auxiliary tasks in the process of training the pre-training language model based on the mathematical problem solving task.
The topic classification task is a task for classifying mathematical topics according to the text meanings in the mathematical topics; the task of classifying the questions is a task of classifying the digital questions according to knowledge points corresponding to the mathematical questions; an intention recognition task recognizes a task of character meaning in a mathematical question; the automatic summary task is a task for summarizing the meaning of mathematical questions; for example, the object of the mathematical topic solution model service is a student in China, and the translation task is used for translating English version of mathematical topic into Chinese version of mathematical topic.
The training method comprises the steps of simultaneously training the pre-training language model by using a plurality of auxiliary tasks and a plurality of mathematical problem solving tasks, and training the pre-training language model based on the plurality of auxiliary tasks, wherein the pre-training language model can be trained by using mathematical problem training data, and the pre-training language model can also be trained by using training data corresponding to the plurality of auxiliary tasks.
Optionally, the training module 302 is further configured to extract each mathematical question in the mathematical question training data and a sentence-level representation and a question-level representation of the answer corresponding to each mathematical question using the pre-training language model; through sentence level representation and question level representation of each mathematical problem and corresponding answer of each mathematical problem, understanding of the pre-training language model on each mathematical problem and corresponding answer of each mathematical problem is enhanced, so that training of the pre-training language model is completed.
According to symbols such as commas, periods, question marks and the like, a mathematical question can be divided into a plurality of sentences, a question-level representation of the mathematical question is a feature representation of the whole mathematical question, a sentence-level representation of the mathematical question is a feature representation (detail feature) of each sentence in the mathematical question, and a sentence-level representation is a feature representation more detailed than the question-level representation. Sentence-level and question-level representations of the corresponding answers to the mathematical questions are similar to sentence-level and question-level representations of the mathematical questions. According to the embodiment of the application, the understanding of each mathematical problem and the corresponding answer of each mathematical problem by the pre-training language model is enhanced according to the sentence-level representation and the problem-level representation (namely, when the whole characteristic is concerned, the detail characteristic is also concerned), so that the pre-training language model can perform more accurate reasoning and solving of the problem.
Optionally, the solving module 304 is further configured to obtain a set of mathematical questions to be solved; dividing a plurality of mathematical questions in a mathematical question set according to a preset number N and knowledge points corresponding to each mathematical question to obtain a plurality of question groups aiming at different knowledge points, wherein each question group comprises N pieces of data, the ith piece of data is (i+1)/2 mathematical questions, the (i+1) th piece of data is an reasoning process and an answer corresponding to the (i+1)/2 mathematical questions, N is an odd number, the mathematical questions represented by the Nth piece of data have no corresponding reasoning process and answer, i is an odd number in an open interval (0, N), and i+1 is smaller than N; taking the ith data and the (i+1) th data in each question group as a pair of data, wherein each question group has (N-1)/2 pairs of data, and sequentially inputting a plurality of question groups into a mathematical question solution model: the mathematical problem solving model is based on (N-1)/2 pairs of data in each problem group, and the N-th data in the problem group is inferred by a context learning method to obtain an inference process and an answer corresponding to the mathematical problem represented by the N-th data in the problem group; and outputting an reasoning process and an answer corresponding to the mathematical questions represented by the Nth data in each question group by the mathematical question solving model.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic of each process, and should not constitute any limitation on the implementation process of the embodiments of the disclosure.
Fig. 4 is a schematic diagram of an electronic device 4 provided by an embodiment of the present disclosure. As shown in fig. 4, the electronic apparatus 4 of this embodiment includes: a processor 401, a memory 402 and a computer program 403 stored in the memory 402 and executable on the processor 401. The steps of the various method embodiments described above are implemented by processor 401 when executing computer program 403. Alternatively, the processor 401, when executing the computer program 403, performs the functions of the modules/units in the above-described apparatus embodiments.
The electronic device 4 may be a desktop computer, a notebook computer, a palm computer, a cloud server, or the like. The electronic device 4 may include, but is not limited to, a processor 401 and a memory 402. It will be appreciated by those skilled in the art that fig. 4 is merely an example of the electronic device 4 and is not limiting of the electronic device 4 and may include more or fewer components than shown, or different components.
The processor 401 may be a central processing unit (Central Processing Unit, CPU) or other general purpose processor, digital signal processor (Digital Signal Processor, DSP), application specific integrated circuit (Application SpecificIntegrated Circuit, ASIC), field programmable gate array (Field-Programmable Gate Array, FPGA) or other programmable logic device, discrete gate or transistor logic device, discrete hardware components, or the like.
The memory 402 may be an internal storage unit of the electronic device 4, for example, a hard disk or a memory of the electronic device 4. The memory 402 may also be an external storage device of the electronic device 4, for example, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash Card (Flash Card) or the like, which are provided on the electronic device 4. Memory 402 may also include both internal storage units and external storage devices of electronic device 4. The memory 402 is used to store computer programs and other programs and data required by the electronic device.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit.
The integrated modules/units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present disclosure may implement all or part of the flow of the method of the above-described embodiments, or may be implemented by a computer program to instruct related hardware, and the computer program may be stored in a computer readable storage medium, where the computer program, when executed by a processor, may implement the steps of the method embodiments described above. The computer program may comprise computer program code, which may be in source code form, object code form, executable file or in some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth. It should be noted that the content of the computer readable medium can be appropriately increased or decreased according to the requirements of the jurisdiction's jurisdiction and the patent practice, for example, in some jurisdictions, the computer readable medium does not include electrical carrier signals and telecommunication signals according to the jurisdiction and the patent practice.
The above embodiments are merely for illustrating the technical solution of the present disclosure, and are not limiting thereof; although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the disclosure, and are intended to be included in the scope of the present disclosure.
Claims (10)
1. A method for training a mathematical solution model, comprising:
acquiring mathematic problem training data and mathematic problem reasoning data, wherein the mathematic problem training data comprises a plurality of mathematic problems and answers corresponding to each mathematic problem, and the mathematic problem reasoning data comprises a plurality of mathematic problems, reasoning processes corresponding to each mathematic problem and answers;
training a pre-training language model by utilizing the mathematical problem training data;
freezing model parameters of the trained pre-training language model, controlling the pre-training language model frozen with the model parameters based on the mathematical problem reasoning data to solve the mathematical problem according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to multiple mathematical problems;
And taking the pre-trained language model of the thinking chain for learning and answering various mathematical questions as a mathematical question answering model, generating the reasoning process and the answer corresponding to the target mathematical questions to be solved for a plurality of times by utilizing the mathematical question answering model, and taking the reasoning process and the answer with the largest generation times as the final result corresponding to the target mathematical questions.
2. The method according to claim 1, wherein the pre-training language model after the model parameters are frozen is controlled based on the mathematical problem reasoning data to solve each mathematical problem according to the reasoning process corresponding to the mathematical problem until the answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to a plurality of mathematical problems, and the method comprises:
dividing the mathematical questions in the mathematical question reasoning data according to the difficulty level to obtain a plurality of question groups with different difficulty levels, wherein each question group comprises a plurality of mathematical questions and reasoning processes and answers corresponding to each mathematical question;
and controlling the pre-training language model frozen with the model parameters for multiple times according to the order of the multiple question groups from easy to difficult, and solving the mathematical questions according to the reasoning process corresponding to each mathematical question in each question group until the answers corresponding to the mathematical questions are obtained, so that the pre-training language model learns the thinking chain for solving various mathematical questions from the reasoning process corresponding to the multiple mathematical questions, wherein the pre-training language model frozen with the model parameters is controlled based on one question group each time.
3. The method according to claim 1, wherein after learning a pre-trained language model of a thought chain for solving various mathematical problems as a mathematical problem solving model, the method further comprises:
obtaining a mathematical problem set to be solved, dividing a plurality of mathematical problems in the mathematical problem set according to a preset number N and knowledge points corresponding to each mathematical problem to obtain a plurality of problem groups aiming at different knowledge points, wherein each problem group comprises N pieces of data, the ith piece of data is (i+1)/2 mathematical problems, the (i+1) th piece of data is an reasoning process and an answer corresponding to the (i+1)/2 mathematical problems, N is an odd number, the mathematical problems represented by the (N) th piece of data are not corresponding to the reasoning process and the answer, i is an odd number in an open interval (0, N), and i+1 is smaller than N;
and sequentially inputting a plurality of question groups into the mathematical question answering model, and outputting an reasoning process and an answer corresponding to the mathematical questions represented by the Nth data in each question group, wherein the reasoning process and the answer corresponding to the mathematical questions represented by the Nth data in each question group are obtained by a context learning method through the mathematical question answering model.
4. A method according to claim 3, wherein sequentially inputting a plurality of question groups into the mathematical question answering model, outputting an inference process and an answer corresponding to the mathematical question represented by the nth data in each question group, comprises:
Taking the ith data and the (i+1) th data in each question group as a pair of data, wherein each question group has (N-1)/2 pairs of data;
the mathematical problem solving model is based on (N-1)/2 pairs of data in each problem group, and the N data in the problem group is inferred through the context learning method, so that an inference process and an answer corresponding to the mathematical problem represented by the N data in the problem group are obtained.
5. The method according to claim 1, wherein after learning a pre-trained language model of a thought chain for solving various mathematical problems as a mathematical problem solving model, the method further comprises:
obtaining a question group to be solved, wherein the question group comprises N mathematic questions, the N mathematic questions belong to the same knowledge point or type, the N-1 mathematic questions in front all have corresponding reasoning processes and answers, and the N mathematic questions have no corresponding reasoning processes and answers;
inputting N mathematical questions in the question group into the mathematical question solving model, and outputting an reasoning process and an answer corresponding to the N mathematical questions in the question group, wherein the reasoning process and the answer corresponding to the N mathematical questions are obtained by a context learning method through the mathematical question solving model.
6. The method of claim 1, wherein training a pre-training language model using the mathematical topic training data comprises:
constructing a mathematical problem solving task and a plurality of auxiliary tasks, wherein the plurality of auxiliary tasks comprise: a topic classification task, an intention recognition task, an automatic summary task, and a translation task;
training the pre-training language model by utilizing the mathematical problem training data based on the mathematical problem solving task, and training the pre-training language model based on a plurality of auxiliary tasks in the process of training the pre-training language model based on the mathematical problem solving task.
7. The method of claim 1, wherein training a pre-training language model using the mathematical topic training data comprises:
extracting each mathematical problem in the mathematical problem training data and sentence-level representation and problem-level representation of answers corresponding to each mathematical problem by using the pre-training language model;
and enhancing the understanding of the pre-training language model to each mathematical problem and the corresponding answer of each mathematical problem through sentence level representation and question level representation of each mathematical problem and the corresponding answer of each mathematical problem so as to complete the training of the pre-training language model.
8. A mathematical problem solution model training apparatus, comprising:
the system comprises an acquisition module, a storage module and a storage module, wherein the acquisition module is configured to acquire mathematical problem training data and mathematical problem reasoning data, the mathematical problem training data comprises a plurality of mathematical problems and answers corresponding to each mathematical problem, and the mathematical problem reasoning data comprises the plurality of mathematical problems, and reasoning processes and answers corresponding to each mathematical problem;
a training module configured to train a pre-training language model using the mathematical problem training data;
the reasoning module is configured to freeze model parameters of the trained pre-training language model, control the pre-training language model frozen with the model parameters based on the mathematical problem reasoning data to solve the mathematical problem according to the reasoning process corresponding to each mathematical problem until an answer corresponding to the mathematical problem is obtained, so that the pre-training language model learns a thinking chain for solving various mathematical problems from the reasoning process corresponding to multiple mathematical problems;
the problem solving module is configured to take a pre-trained language model of a thinking chain for solving various mathematical problems as a mathematical problem solving model, generate reasoning processes and answers corresponding to target mathematical problems to be solved for a plurality of times by utilizing the mathematical problem solving model, and take the reasoning processes and the answers with the largest generation times as final results corresponding to the target mathematical problems.
9. An electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1 to 7 when the computer program is executed.
10. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of the method according to any one of claims 1 to 7.
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