Self-adaptive multi-criterion decision model, method and equipment based on monotonic transformation constraint

Abstract

The invention belongs to the technical field of financial analysis, and particularly relates to an adaptive multi-criterion decision model, method and device based on monotonic transformation constraint, and the method comprises the steps: S1, obtaining a group of normalized multi-dimensional financial index vectors; s2, dynamically generating an index weight for each sample in the multi-dimensional financial index vector; s3, monotonically increasing nonlinear transformation is carried out on index dimensions in the multi-dimensional financial index vector, and each index dimension is mapped into a new index dimension; and S4, performing element-by-element multiplication on the index weight obtained in the step S2 and the index dimension obtained in the step S3, performing summation on a plurality of index dimensions corresponding to each sample, and performing normalization operation to obtain a comprehensive score corresponding to the sample. According to the method, the strong nonlinear fitting capability is guaranteed, and meanwhile, absolute monotonicity guarantee is provided through the structural design of the monotonous variation network, so that the decision logic of the model is clear and explainable, and accords with field intuition.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of financial analysis, and particularly relates to an adaptive multi-criteria decision model, method and device based on monotonic transformation constraint. BACKGROUND

[0002] In modern financial services and investment decisions, there are often complex decision-making problems of comprehensive evaluation and ranking of financial products, financial customers or investment targets according to a large number of indicators. For example, in stock investment, the financial indicators such as the price-earnings ratio (PE), the return on equity (ROE), the growth rate, and the debt ratio of a company need to be comprehensively considered to determine its investment value; in bank credit approval, the income, debt, credit history, and asset status of an applicant need to be comprehensively evaluated to determine its credit risk; in asset allocation, the yield, volatility, and liquidity of assets need to be comprehensively considered to build an optimal investment portfolio. Such financial decision-making problems are collectively referred to as financial multi-criteria decision making (Financial MCDM).

[0003] In order to solve such financial decision-making problems, experts and scholars in the financial field have proposed various technical solutions, which can be roughly divided into two categories:

[0004] (1) Traditional financial evaluation methods

[0005] Such methods are mainly based on financial engineering and risk management theory, and rely on rules and weights set by financial experts in advance.

[0006] 1) Analytic Hierarchy Process (AHP): proposed by American operations researcher Thomas L. Saaty in the 1970s. AHP divides complex problems into multiple levels such as target, criteria, and scheme, then constructs a judgment matrix by comparing each indicator with each other by experts, calculates the relative weight of each indicator, and finally obtains the comprehensive score by weighted summation. The disadvantage is that it is highly subjective, it is very difficult to maintain consistency between indicators, and once the weight is set, it cannot be automatically adjusted according to new data and environmental changes.

[0007] 2) Technique for Order Preference by Similarity to Ideal Solution (TOPSIS): This method determines the relative merits of each evaluated object by calculating its distance from both the "positive ideal solution" (a virtual object where all metrics reach their optimal values) and the "negative ideal solution" (a virtual object where all metrics reach their worst values). Objects closer to the positive ideal solution and farther from the negative ideal solution rank higher. Compared to AHP, TOPSIS reduces reliance on subjectivity, but it still requires pre-setting metric weights and is highly sensitive to data distribution and dimensions.

[0008] 3) Simple Additive Weighting (SAW): This is a commonly used method in financial scoring. It directly normalizes each indicator, multiplies them by preset weights, and then sums them to obtain the total score. For example, a traditional credit scoring model might use a simple weighting method like "income × 30% + assets × 25% + credit history × 45%". The core problem lies in the setting of these weights, which usually relies on the experience and judgment of financial experts and lacks scientific basis supported by data.

[0009] (2) Data-driven approach

[0010] With the development of data science, researchers have begun to try using data-driven models to automatically learn indicator weights and evaluation functions.

[0011] 1) Linear Regression: This method fits the relationship between an indicator (independent variable) and the final evaluation result (dependent variable, such as future returns) using a linear model. The coefficients of the model can be seen as the weights of each indicator. The advantages of this method are its simplicity and strong interpretability. However, its disadvantage is that it cannot capture complex non-linear relationships between indicators. For example, a price-to-earnings ratio (P / E ratio) that is too low or too high may both indicate risk; this non-linear relationship cannot be expressed by a linear model.

[0012] 2) Tree models (e.g. GBDT, XGBoost, LightGBM): Models represented by gradient boosting decision trees have achieved great success in various data mining competitions. They can automatically learn complex non-linear relationships and high-order interactions between features, and have very strong prediction performance. However, such models are typical "black box models" with extremely complex internal decision logic that is almost impossible to interpret. This is unacceptable in high-risk fields such as finance. For example, a credit model based on XGBoost may produce counterintuitive conclusions such as "income increase" but credit score decrease for an applicant. The model cannot guarantee the monotonicity of the output for a specific input (such as income, profit rate), i.e. "good indicator input must lead to non-worse score output".

[0013] 3) Neural network and deep learning methods: The rise of deep learning has also driven the application of neural networks in the field of scoring cards. Such models have strong non-linear fitting ability, but like tree models, they are also a "black box". The huge number of internal parameters are combined through complex non-linear activation functions (such as ReLU, Sigmoid), making it impossible to understand the model's decision-making basis intuitively and guarantee its monotonicity for a specific input. To solve this problem, some studies have tried to use lattice regression and other methods to enforce monotonicity, but these methods are usually complex in structure, difficult to train, and sacrifice the model's expressive ability.

[0014] Based on the above analysis, the existing technical solutions have one or more of the following shortcomings:

[0015] (1) Conflict between subjective dependence and explainability: Traditional MCDM methods (such as AHP) rely on subjective expert experience and lack objectivity; while machine learning methods are objective, but their "black box" nature makes their decision logic difficult for experts to understand and trust.

[0016] (2) Conflict between modeling ability and explainability: Linear models are good in explainability but poor in performance; while tree models and neural networks are powerful but lack explainability, which is a rigid requirement in many decision-making scenarios.

[0017] (3) Disconnection between data modeling practice and financial theory prior knowledge: The decision logic of many models (such as ordinary neural networks) may violate basic economic or management principles (such as the Pareto optimality principle), making the model theoretically unsound and difficult to be adopted in practice.

[0018] (4) Conflict between adaptability and modeling cost: Expert rule-based methods are static and cannot adapt to market and data changes; while data-driven methods require a large amount of labeled data for training and modeling, which faces challenges in fields with high labeling costs. SUMMARY

[0019] The present application aims at the above technical problems, and aims to provide a monotonic transformation constraint-based adaptive multi-criteria decision model, method and device.

[0020] A monotonic transformation constraint-based adaptive multi-criteria decision model comprises:

[0021] An input layer acquires a set of normalized multi-dimensional financial indicator vectors, the multi-dimensional financial indicator vectors comprising samples and corresponding indicator dimensions thereof;

[0022] An attention network receives the multi-dimensional financial indicator vectors input by the input layer, and dynamically generates indicator weights for each sample;

[0023] A monotonic transformation network receives the multi-dimensional financial indicator vectors input by the input layer, performs a monotonically increasing nonlinear transformation on the indicator dimensions, and maps each indicator dimension to a new indicator dimension;

[0024] An aggregation output module element-wise multiplies the indicator weights output by the attention network and the indicator dimensions output by the monotonic transformation network, sums the indicator dimensions corresponding to each sample, and obtains a comprehensive score corresponding to the sample after normalization.

[0025] Optionally, the attention network comprises:

[0026] A multilayer perceptron, through which the multi-dimensional financial indicator vectors are processed to obtain a weight score vector corresponding to the indicator dimensions;

[0027] A Softmax function, through which the weight score vector is normalized to obtain a set of non-negative indicator weights with a sum of 1.

[0028] Optionally, the monotonic transformation network is formed by stacking a plurality of sequentially connected monotonic transformation layers, and each monotonic transformation layer is a composite mapping formed by sequentially connecting a plurality of sub-modules that maintain monotonicity in structure, each of the sub-modules having a monotonic non-decreasing property.

[0029] Optionally, the monotonic transformation network comprises sequentially connected:

[0030] A monotonic calibration layer, which maps the input indicator dimensions to a scale-unified and order-preserved representation space through piecewise linear mapping;

[0031] a monotone affine layer having a number of monotone affine experts, each of the monotone affine experts learning a local monotone linear response in a different direction on the output of the monotone calibration layer;

[0032] a monotone aggregation layer having a number of aggregation modules, each of the aggregation modules aggregating the local monotone linear responses output by the monotone affine layer to form a non-linear upper envelope;

[0033] a smooth monotone scaling layer having a number of monotone scaling functions, each of the monotone scaling functions performing amplitude compression and gradient adjustment on the output of its corresponding one of the aggregation modules to obtain a normalized and monotone output.

[0034] Optionally, let the input indicator dimension be denoted as , and the input indicator dimension be denoted as , the monotone calibration layer is represented as:

[0035]

[0036] wherein, is a continuous and monotone non-decreasing piecewise linear function, and the intermediate representation is non-linearly mapping features with different dimensions and distributions to a specified interval; denotes a total of input indicator dimensions;

[0037] In each piecewise linear function, the effective interval of the input indicator dimension is limited, and the endpoint sequence satisfying the increasing sequence is:

[0038]

[0039]

[0040] The effective interval is divided into intervals by the endpoint sequence;

[0041] Let the function value corresponding to each endpoint be , and the value is obtained by non-negative difference:

[0042]

[0043] wherein, , so that is an increasing sequence;

[0044] Parameterize the piecewise linear mapping: ​

[0045]

[0046] wherein, is an activation function, are learnable parameters;

[0047] For any , define linear interpolation:

[0048]

[0049] Within the interval represented by any pair of endpoints, there is:

[0050]

[0051] Restrict the dimension of the indicator of the th input to a fixed range and use normalized difference:

[0052]

[0053] wherein, is a preset constant value.

[0054] Optionally, in each piecewise linear function, the endpoint position is a preset fixed value,

[0055] or, the endpoint position adopts parameterization:

[0056]

[0057] wherein, are learnable parameters.

[0058] Optionally, assuming that the monotonic affine layer has monotonic affine experts, define each monotonic affine expert as a local affine function on the input space:

[0059]

[0060] wherein, is a weight vector, is a bias term, is the output of the monotonic calibration layer;

[0061] In the local affine function, a Softplus transformation is needed for the parameters:

[0062]

[0063] wherein, to ensure that the monotonic dimension is ;

[0064] Therefore, the set of all learnable parameters of the single monotonic affine expert is .

[0065] Optionally, the aggregation module employs a Maxout aggregation function, through which the maximum value in the local monotonic linear responses output by the monotonic affine experts is selected as the output result.

[0066] Alternatively, the aggregation module employs a SmoothMaxout aggregation function, through which the maximum value in the local monotonic linear responses output by the monotonic affine experts is smoothly approximated as the output result.

[0067] Optionally, the output of the aggregation module is ;

[0068] The monotonic scaling function applies a monotonic transformation to the output of the aggregation module in any of the following three ways:

[0069]

[0070] wherein is a learnable or fixed positive scaling factor.

[0071] Optionally, the adaptive multi-criteria decision-making model based on monotonic transformation constraints further comprises:

[0072] a visualization module that visualizes the attention distribution on the sample set;

[0073] The visualization module comprises:

[0074] Gradient-based backtracking analysis is introduced:

[0075]

[0076]

[0077] wherein denotes the input indicator dimension sensitivity to output changes, denotes the input indicator dimension number of denotes the number of monotonic affine experts, denotes the jth input indicator dimension, denotes the indicator weight obtained in step S2, denotes the indicator dimension obtained in step S3;

[0078] If The larger the value of the , the more significant the incremental effect of the input on the output result. The values of the are visualized to show the attention structure and decision basis of the model.

[0079] Optionally, the indicator weight obtained in step S2 is combined with the local gradient information to define a weighted importance indicator:

[0080]

[0081] The value of the represents the comprehensive contribution of the input to the output result. The larger the value of the , the more important the input under the current sample;

[0082] The values of the are visualized to further show the attention structure and decision basis of the model.

[0083] Optionally, the adaptive multi-criteria decision model adopts the following training process to obtain the trained adaptive multi-criteria decision model:

[0084] In the data preparation stage, the data set is obtained and normalized, and all learnable parameters in the adaptive multi-criteria decision model are initialized. Preferably, Xavier or normal distribution initialization is used for initialization;

[0085] In the main loop of training, a batch of sample inputs is randomly selected from the data set and input into the adaptive multi-criteria decision model to obtain the corresponding prediction score of each sample. The adaptive multi-criteria decision model performs forward propagation, calculates the total loss function, and uses the gradient descent algorithm to perform back propagation on the parameters of the adaptive multi-criteria decision model. The gradient of the loss with respect to all learnable parameters is calculated, and the parameters are updated in the negative gradient direction until the adaptive multi-criteria decision model converges on the validation set or meets the preset training number of rounds.

[0086] Optionally, the total loss function is composed of several sub-losses, at least one of which is a ranking loss, and more preferably a Pareto advantage loss.

[0087] Optionally, at least another of the sub-losses is an anchor loss.

[0088] An adaptive multi-criteria decision method based on monotonic transformation constraint, comprising:

[0089] S1, obtaining a set of normalized multi-dimensional financial indicator vectors, the multi-dimensional financial indicator vectors comprising samples and corresponding indicator dimensions;

[0090] S2, dynamically generating indicator weights for each sample in the multi-dimensional financial indicator vectors;

[0091] S3, performing a monotonically increasing nonlinear transformation on the indicator dimensions in the multi-dimensional financial indicator vectors, mapping each indicator dimension to a new indicator dimension;

[0092] S4, element-wise multiplying the indicator weights obtained in step S2 and the indicator dimensions obtained in step S3, summing the corresponding indicator dimensions for each sample, and obtaining a comprehensive score corresponding to the sample after normalization.

[0093] Optionally, the adaptive multi-criteria decision-making method based on monotonic transformation constraint is implemented by using the adaptive multi-criteria decision-making model based on monotonic transformation constraint.

[0094] An adaptive multi-criteria decision-making system based on monotonic transformation constraint, comprising the adaptive multi-criteria decision-making model based on monotonic transformation constraint.

[0095] A computer device comprising a memory and a processor, the memory storing computer readable instructions, the computer readable instructions being executed by the processor to cause the processor to perform the steps of the adaptive multi-criteria decision-making method based on monotonic transformation constraint.

[0096] A storage medium storing computer readable instructions, the computer readable instructions being executed by one or more processors to cause the one or more processors to perform the steps of the adaptive multi-criteria decision-making method based on monotonic transformation constraint.

[0097] Advantages: the present application has at least one or more of the following advantages:

[0098] 1. The present application solves the core contradiction between "performance" and "explainability": compared with traditional statistical machine learning and ordinary neural network black box model, the present application guarantees strong nonlinear fitting ability, provides absolute monotonicity guarantee through the structure design of the monotonic network, and makes the decision logic of the model clear, explainable and consistent with the field intuition.

[0099] 2. Deep integration of "data-driven" and "theory-driven": Compared with classic evaluation methods such as AHP, which rely on subjective expert experience, the present application is completely data-driven and can automatically learn complex evaluation functions. More importantly, by using innovative Pareto advantage loss, the present application endogenously incorporates the Pareto optimality axiom in economics into model training, so that the model decision-making complies with basic economic principles, and the theoretical basis is more solid.

[0100] 3. High automation and adaptability: The present application provides an end-to-end solution. The user only needs to provide raw multi-index data, and the system can automatically complete model training and construction of evaluation functions. There is no need for tedious feature engineering or expert rule setting. Due to its universal design, it can easily migrate to solve evaluation and decision-making problems in different fields such as finance, medicine, and management, and has good adaptability.

[0101] 4. The present application converts the decision evaluation task into a data-driven machine learning task that meets the constraints and intuition of financial theory. Specifically, the index weight learned by the attention network is always non-negative, the monotonic transformation network ensures that the value after transformation of each index is monotonous with the original value in structure, and the final comprehensive score is the sum of multiple non-negative terms. Therefore, the comprehensive score is monotonically increasing for any original input index dimension. This key feature is not achieved by "soft constraints" through penalty terms in the loss function, but is guaranteed by the "hard constraints" of the network structure itself, and its reliability is fully supported by theory.

[0102] 5. The present application introduces an attention mechanism (attention mechanism) to construct an attention network, providing a sample adaptive dynamic weighting method. The core idea of this method is to let the model automatically learn "which indicators should each sample pay attention to in the current context", that is, to dynamically generate personalized index weights for each sample according to its own characteristics and context information. This mechanism not only improves the expression ability of the model, but also makes the financial evaluation process more consistent with the diversity and dynamics of economic behavior.

[0103] 6. The monotonic transformation network used in the present application is a strictly monotonic and strongly learning model constructed by innovative nonlinear transformation modules. The core idea is to ensure the monotonicity of the module output with respect to the input dimension through the design of the network structure itself rather than external constraints in the optimization process. The monotonic transformation network can be regarded as a composite mapping composed of a series of monotonic transformation layers. Each layer independently satisfies the monotonicity, so the output of the entire network also maintains monotonicity in the composite sense.

[0104] 7、The attention network of the present application provides dynamic interpretability for decision evaluation (e.g. stock selection). For example, which indicators are more valuable for evaluating the robustness of a stock, and how much do they contribute to the evaluation of robustness.

[0105] Specifically, the indicator weight obtained by the attention network can be regarded as an importance distribution itself, which reflects the "focus mode" of the current sample on different experts. When the weight of a certain expert is larger, it means that the response of the expert contributes more to the overall output, so the indicator weight can be interpreted as the dominant factor of decision in the local area. By visualizing the attention distribution on the sample set, the attention shift of the model under different input modes can be observed, thereby obtaining an intuitive understanding of the input space division and the decision logic of the model.

[0106] 8、The model training process of the present application is an end-to-end optimization process, which aims to maintain monotonicity and rational ordering ability while having good numerical stability by structural constraints and multi-objective loss design.

[0107] During the training process, one of the sub-losses of the total loss function adopts the ranking loss, especially the Pareto advantage loss, which is used to establish a rational ordering relationship between samples, thereby meeting the requirements of financial theory and providing an interpretable decision basis. BRIEF DESCRIPTION OF DRAWINGS

[0108] Figure 1 is a model architecture diagram of the present application;

[0109] Figure 2 is a network architecture diagram of the monotonic transformation network of the present application;

[0110] Figure 3 is a piecewise linear mapping diagram of the piecewise linear function of the present application;

[0111] Figure 4 is an aggregation schematic diagram of the Maxout aggregation function of the present application;

[0112] Figure 5 is a model training process of the present application;

[0113] Figure 6 is a system implementation block diagram of the present application. DETAILED DESCRIPTION

[0114] The preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings, so that the purpose, characteristics and advantages of the present application can be more clearly understood. It should be understood that the embodiments shown in the drawings are not a limitation on the scope of the present application, but only to illustrate the essential spirit of the technical solutions of the present application.

[0115] In the following description, for purposes of explanation, specific details are set forth in order to provide a thorough understanding of the various disclosed embodiments. It will be appreciated, however, that embodiments can be practiced in other ways without one or more of the specific details.

[0116] Reference throughout this specification to "an embodiment" or "the embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrase "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0117] In the following description, for purposes of explanation, specific details are set forth in order to provide a thorough understanding of the various disclosed embodiments. It will be appreciated, however, that embodiments can be practiced in other ways without one or more of the specific details.

[0118] Referring to Figure 1 , the embodiment of the present application provides a kind of adaptive multi-criteria decision model based on monotonic transformation constraint, the adaptive multi-criteria decision model specifically includes input layer, attention network, monotonic transformation network and aggregation output module.

[0119] Input layer obtains a group of normalized multidimensional financial index vector , dimension is , wherein It is the number of samples, It is the number of indexes. That is, in multidimensional financial index vector, single sample has its corresponding several index dimensions.

[0120] For example, in stock evaluation scenario, It can include Robustness index (such as volatility, Beta coefficient, maximum drawdown, S&P ratio, Kama ratio, etc.); in credit evaluation, It can include income, assets, liabilities, credit history and other indexes. Through normalization step, the value of each index is scaled to Interval, wherein Represent the optimal performance of the index in all samples, The worst performance is represented. This normalization method unifies the dimensions of different financial indicators and makes its physical meaning consistent with the monotonicity assumption (i.e. the greater the value, the better the financial situation).

[0121] The attention network receives the multi-dimensional financial indicator vector input by the input layer and dynamically generates an indicator weight for each sample (dimension ), which can also be referred to as an attention weight.

[0122] The core function of the attention network is to learn the relative importance of different indicators. Each value in the attention weight vector represents the degree of attention of the model to the i-th indicator under the current sample. This dynamic, sample-based weight allocation mechanism is much more flexible and powerful than the static global weight of traditional financial scoring methods, and can adaptively adjust according to different financial market environments and sample characteristics.

[0123] The monotonic transformation network receives the multi-dimensional financial indicator vector input by the input layer and performs a monotonically increasing nonlinear transformation on the indicator dimension, mapping each indicator dimension to a new indicator dimension.

[0124] The monotonic transformation network performs a monotonically increasing nonlinear transformation on the indicator. Through the monotonic transformation network, each financial indicator value input is mapped to a new value , and the mapping function is strictly monotonically increasing. That is, if (for example, the ROE of company A is higher than that of company B), then (the score of A after transformation is not lower than that of B). This ensures that the decision logic of the model conforms to the basic financial intuition.

[0125] The aggregation output module element-wise multiplies the indicator weight output by the attention network and the indicator dimension output by the monotonic transformation network, sums the indicator dimensions corresponding to each sample, and after normalization, obtains the comprehensive score Score corresponding to the sample.

[0126] The present application converts the decision evaluation task into a data-driven machine learning task that meets the constraints and intuition of financial theory. Specifically, the indicator weight learned by the attention network is always non-negative, the monotonic transformation network structurally ensures that the value of each indicator after transformation is monotonous with the original value , and the final comprehensive score is the sum of multiple non-negative terms . Therefore, the comprehensive score Score for any original input indicator All are monotonically increasing. This key feature is not achieved by the "soft constraint" of the penalty term of the loss function, but is guaranteed by the "hard constraint" of the network structure itself, and its reliability is fully supported by theory.

[0127] In an embodiment, referring to Figure 1 , the attention network includes a standard multi-layer perceptron (MLP) that outputs a weight score (logit) vector of the same dimension as the indicator vector. This vector is then passed through a Softmax function to generate a set of non-negative and sum-to-one attention weights with dimension . .

[0128] Therefore, the attention network of the present embodiment includes a multi-layer perceptron and a Softmax function. The multi-dimensional financial indicator vector is processed by the multi-layer perceptron to obtain a weight score vector corresponding to the indicator dimension; the weight score vector is normalized by the Softmax function to obtain a set of non-negative and sum-to-one indicator weights.

[0129] Traditional financial multi-indicator decision-making methods usually rely on fixed weight strategies. For example, in the expert experience method. The common problem of such methods is the staticity of the weight. Regardless of the changes in the characteristics of the evaluation object, the industry attributes or the market environment, the indicator weight is always fixed, which is difficult to reflect individual differences and time-varying relationships, thereby limiting the flexibility and adaptability of the model.

[0130] To overcome this defect, the present embodiment introduces an attention network constructed by an attention mechanism, which provides a sample adaptive dynamic weighting method. The core idea of this method is to let the model automatically learn "which indicators should each sample pay attention to in the current context", that is, to dynamically generate personalized indicator weights for each sample according to its own characteristics and contextual information. This mechanism not only improves the expression ability of the model, but also makes the financial evaluation process more consistent with the diversity and dynamics of economic behavior.

[0131] Let the financial indicator vector of the i-th evaluation object be:

[0132]

[0133] wherein denotes the indicator dimension.

[0134] The attention network of the present embodiment generates a weight vector through the following mathematical mapping process:

[0135] First, the input vector ​Nonlinear feature mapping via multi-layer perceptron:

[0136]

[0137] where, is a composite function consisting of several linear transformations and a nonlinear activation function (e.g., ReLU) for extracting high-order correlation features between indicators.

[0138] Then, the model maps the hidden space vector back to the indicator space through a linear transformation to obtain the unnormalized weight score (logits):

[0139]

[0140] where, and are weight and bias parameters.

[0141] To ensure that the weights have a probability distribution characteristic, the attention mechanism adopts a Softmax function for normalization processing:

[0142]

[0143] After normalization by the Softmax function, all weights satisfy and , so they can be considered as attention distributions in the indicator dimension.

[0144] In another example, the Softmax attention of the present embodiment can be replaced by a Sigmoid gate, multi-head self-attention, etc. After non-negativity and normalization, both can learn feature importance and have interpretability.

[0145] In an embodiment, the monotonic transformation network is formed by stacking several sequentially connected monotonic transformation layers, and a single monotonic transformation layer is a composite mapping formed by sequentially connecting several sub-modules that maintain monotonicity in structure, each of which has a monotonic non-decreasing property.

[0146] Let the input vector be where, denotes the input dimension. For any dimension , it is hoped that the model output satisfies the following partial order preserving property:

[0147]

[0148] Unlike traditional monotonic modeling methods based on constrained optimization, the monotonic transformation network of the embodiment does not need to impose any sign constraints or projection operations during the training process, and the monotonicity is directly determined by the function form and parameterization method within the layer. This structured monotonicity is not only theoretically verifiable, but also more stable in numerical optimization, because the gradient propagation no longer depends on the non-smooth projection or penalty term.

[0149] The monotonic transformation network of the embodiment is composed of multiple monotonic transformation layers stacked together, and each monotonic transformation layer is a composite mapping composed of multiple sub-modules that are sequentially connected and maintain monotonicity in structure. The overall calculation can be represented as:

[0150]

[0151] wherein, represents a function composition operation, and each layer is a monotonic non-decreasing function. As long as the output of each layer is not reduced with respect to the index dimension, the composite function of them is also not reduced, thereby ensuring the monotonicity of the entire model. This way does not rely on any external constraints or projection operations, but naturally realizes the monotonicity inside the model through structural design.

[0152] In an embodiment, referring to Figure 1 and Figure 2 , the monotonic transformation network includes a monotonic calibration layer, a monotonic affine layer, a monotonic aggregation layer, and a smooth monotonic scaling layer connected in sequence.

[0153] Therefore, the flow of the monotonic transformation network of the embodiment is:

[0154] First, the monotonic calibration layer is used to map the input index dimension to a scale-unified and order-maintained representation space through piecewise linear mapping. The role of piecewise linear mapping is to calibrate the input data to achieve scale alignment while maintaining monotonicity, so that the model focuses on feature interaction and logical relationship in subsequent calculations, thereby improving the stability of the model.

[0155] Next, the monotonic affine layer is used to learn local monotonic linear responses in different directions for the output of the monotonic calibration layer by using several monotonic affine experts in the monotonic affine layer;

[0156] Then, the monotonic aggregation layer is used to aggregate the local monotonic linear responses output by the monotonic affine layer to form a nonlinear upper envelope by using several aggregation modules in the monotonic aggregation layer;

[0157] Finally, the smooth monotonic scaling layer is used to compress the amplitude and adjust the gradient of the output of each aggregation module by using several monotonic scaling functions in the smooth monotonic scaling layer, to obtain normalized and monotonic output.

[0158] Thus, the resulting monotonic transformation network is end-to-end differentiable, and its training is no different from that of ordinary neural networks, but it inherently satisfies the monotonic constraint in its structure.

[0159] In this embodiment, the output dimension of the monotonic transform network is independent of the input dimension; the output dimension depends on the number of aggregation modules in the monotonic aggregation layer. Since the output of the monotonic transform network needs to be multiplied element-wise with the output of the attention network, the output dimension of the monotonic transform network is the same as the output dimension of the attention network. In other words, the number of aggregation modules is the same as the output dimension of the attention network.

[0160] In another example, the monotonic transformation network of this implementation can be replaced by a "monotonic lattice network", a positive weighted ReLU piecewise linear network (with non-negative weights constrained in the monotonic dimension), etc., which can achieve end-to-end monotonicity in structure.

[0161] In one embodiment, the goal of the monotonic calibration layer is to learn a continuous, monotonically non-decreasing one-dimensional transformation for each input index dimension before proceeding to subsequent computations, in order to achieve feature scale alignment and monotonicity transitivity.

[0162] In the input metric dimensions, the first The dimension of each input metric is denoted as The monotonic calibration layer is then represented as:

[0163]

[0164] in, It is a continuous and monotonically non-decreasing piecewise linear function, with the middle part representing... Nonlinearly mapping features with different dimensions and distributions to a specified interval; Indicates total Each input metric dimension.

[0165] To balance interpretability, controllability, and efficient training, this embodiment employs a piecewise linear implementation with fixed endpoints and learnable endpoint values. Here, endpoints refer to the upper and lower bounds corresponding to each segment in the piecewise linear function.

[0166] Therefore, in each piecewise linear function, for the th The effective range is limited by the number of input metrics dimensions. And an increasing sequence of endpoints:

[0167]

[0168]

[0169] Valid intervals are determined by endpoint sequences. Divided into interval;

[0170] The piecewise linear mapping of piecewise linear function uses linear interpolation in each interval formed by a pair of adjacent endpoints. Let the function value corresponding to each endpoint be The value is obtained by non-negative difference:

[0171]

[0172] where is an increasing sequence; further, in order to achieve learnable monotonic calibration in a data-driven manner, the piecewise linear mapping needs to be parameterized:

[0173] where

[0174] is an activation function that can map any real number to a non-negative real number, is a learnable parameter. For any

[0175] , define linear interpolation:

[0176] Since

[0177] function is always positive, regardless of the value of the parameter , there is always . So that the model can automatically maintain the monotonic increasing order of . Further, within the interval represented by any pair of endpoints, there is:

[0178] Therefore,

[0179] Although it is a piecewise linear function, it is a nonlinear monotonic increasing function as a whole, and is almost everywhere differentiable and non-negative on derivative, it is easy to solve the parameters using end-to-end gradient descent algorithm. As shown in an example of

[0180] , the piecewise linear function is a nonlinear monotonic increasing function. Figure 3 In order to further avoid the influence of different input dimension value scales and enhance the numerical stability of the training process, the index dimension of the first

[0181] input is constrained to a fixed value range , and the normalized difference is used:

[0182] ​

[0183] wherein, is a very small preset constant value for avoiding denominator taking 0 in numerical calculation.

[0184] The embodiment realizes scale alignment and monotonicity transmission of different dimensional financial indicators by monotone calibration layer which monotonically segments and maps each input feature. The structure can maintain input order information without loss and improve comparability and generalization between features.

[0185] In another example, the monotone calibration layer of the embodiment can be replaced by monotone spline, positive weight RBF / polynomial, etc. The common point is to ensure that the partial derivative of each monotone dimension is non-negative, and to complete scale calibration and order maintenance.

[0186] In an embodiment, in each piecewise linear function, the endpoint position can be a preset fixed value according to the input range.

[0187] In an embodiment, in order to further improve the expression ability, in each piecewise linear function, the endpoint position can be parameterized by using a similar non-negative difference method.

[0188]

[0189] wherein, is a learnable parameter.

[0190] In an embodiment, the monotone affine layer has monotone affine experts, each of which models a local linear pattern in the respective input region by focusing on the interaction relationship between different feature dimensions.

[0191] After the monotone calibration layer, the input is mapped to At this time, each dimension tends to be balanced in numerical scale and monotonicity is guaranteed. Next, it is necessary to capture the linear combination and interaction pattern between multi-dimensional features. The model is required to have two characteristics: one is to express the local monotonic increasing trend in different directions; the other is to maintain global monotonicity and interpretability. Therefore, the embodiment introduces a multi-expert monotone affine layer (MAEL). The layer approximates the local linear response structure in the input space by multiple monotone affine experts with non-negative weights, and combines the outputs of these experts into a whole monotone mapping in the subsequent monotone aggregation layer.

[0192] Consider a monotone affine layer with monotone affine experts, each of which is defined as a local affine function on the input space:

[0193]

[0194] where, is a weight vector, is a bias term, is the output of the monotonic calibration layer.

[0195] To ensure the monotonicity of the model on each input dimension, we need to ensure that the partial derivative on these dimensions is always non-negative. Therefore, we cannot directly parameterize , but need to apply a Softplus transformation to the parameters:

[0196]

[0197] where, to ensure that on the monotonic dimensions; is the th dimension of ; is the th dimension of ;

[0198] Therefore, the set of all learnable parameters of a single monotonic affine expert is .

[0199] By definition, a monotonic affine expert has the partial derivative of :

[0200]

[0201] Since , we have . This shows that is a monotonically non-decreasing function on all input dimensions.

[0202] Each monotonic affine layer consists of monotonic affine experts, each of which corresponds to a hyperplane with a positive slope in the input space, which can be regarded as a family of monotonic affine planes with different directions and limited slopes. The number of experts is directly related to the expression and learning ability of the monotonic affine layer. When , the output is a single linear monotonic function; as increases, the input space is divided into more local linear regions, and the model's expressive power also increases.

[0203] In theory, after After aggregation, each monotonic affine expert is equivalent to a positive piecewise-affine function family, which can be expressed as: Under sufficient conditions, it can approximate any continuous monotonic convex function. Geometrically, the monotonic affine layer divides the input space into several convex regions determined by hyperplanes, and each expert dominates the monotonic trend of a local region, and its weight vector directly reflects the sensitivity of the region to input features.

[0204] This embodiment represents local linear response through a multi-expert monotonic affine layer, and then forms a nonlinear upper envelope through a monotonic aggregation layer, so that the model has nonlinear expression ability while maintaining monotonicity. This design realizes the smooth transition from linear monotonicity to high-order monotonic nonlinear function.

[0205] In an embodiment, the aggregation module uses a Maxout aggregation function, which selects the maximum value of the local monotonic linear response output by several monotonic affine experts as the output result.

[0206] After passing through the monotonic affine layer composed of monotonic affine experts, the model obtains a set of local monotonic linear responses in the input space . If these outputs are directly linearly weighted, the monotonic affine expert layer as a whole is still a linear mapping, lacking the necessary nonlinear expression ability. This is equivalent to the linear layer in ordinary neural networks / deep learning, and without nonlinear activation, stacking more layers will not help improve the model's learning ability.

[0207] The aggregation in this embodiment is to introduce nonlinearity without destroying monotonicity, which plays a role equivalent to the activation function in ordinary neural networks in monotonic transformation.

[0208] Given expert functions , the Maxout aggregation function is defined as:

[0209]

[0210] That is, the maximum value of the outputs of all monotonic affine experts is selected as the overall response. Geometrically, this operation is equivalent to taking the upper envelope surface of several linear hyperplanes:

[0211]

[0212] In one dimension, Maxout aggregation is equivalent to taking the upper envelope of multiple affine lines in the coordinate plane. Each line corresponds to the local response of a monotone affine expert, and the upper envelope forms a piecewise linear function composed of several linear segments. The piecewise linear function is linear in each interval, and the overall function is continuous and monotonically non-decreasing over the entire domain, as shown in Figure 4 . When generalized to multiple dimensions, Maxout operation corresponds to taking the upper envelope of several hyperplanes in the space, resulting in a continuous, convex, and monotonically non-decreasing piecewise affine surface.

[0213] An important property of this geometric structure is that although each monotone affine expert function only represents a linear relationship by itself, their upper envelope forms a piecewise linear nonlinear mapping, introducing variability and curvature in the function shape without violating monotonicity. That is, Maxout aggregation plays a similar role in monotone models as ReLU does in ordinary neural networks. It divides the input space into multiple regions by selectively activating several local linear responses, with each region controlled by a dominant expert, and the boundaries between regions forming the "nonlinear fold surface" of the model. Since the weights of each expert are non-negative, local monotonicity is globally preserved under Maxout aggregation.

[0214] In theory, if the number of experts is large enough, the upper envelope formed by Maxout aggregation can approximate any continuous, monotone, and convex function with arbitrary precision. To approximate general (non-convex) monotone functions, multiple layers can be stacked. As the number of monotone affine experts increases , the model can construct more local linear segments in the input space, refining the shape of the overall surface and achieving a continuous transition from global linearity to high-order monotone nonlinear functions. However, too many experts will increase computational cost and complicate the boundaries of local responses, so the selection of the number of experts often needs to be balanced between model interpretability and expressiveness in practice.

[0215] Maxout aggregation introduces nonlinearity by taking the upper envelope of several monotone affine experts in structure, but its most important theoretical feature is that as long as each monotone affine expert function is monotonically non-decreasing in each dimension of the input, the overall function after Maxout aggregation also remains monotonically non-decreasing.

[0216] To illustrate this property, consider an input vector and any two points in it, if they satisfy the dimension-wise non-decreasing relationship (i.e. For all holds), then since each monotone affine expert is monotone non-decreasing, we have:

[0217]

[0218] Taking the maximum of all the monotone affine experts' outputs gives:

[0219]

[0220] Thus, is monotone non-decreasing in each input dimension. That is, the Maxout operation is closed with respect to monotonicity: the output is still monotone after aggregating the input monotone affine experts via Maxout.

[0221] Geometrically, the output surface of Maxout aggregation is an upper envelope of several positively sloped hyperplanes. The geometric property of the upper envelope is "convex and upwardly open": the projection of the line segment between any two input points onto the output space does not decrease its corresponding output. This geometric structure naturally guarantees that the output does not decrease when the input dimension increases, i.e., it embodies monotonicity. Therefore, the upper envelope function composed of non-negative monotone affine experts strictly preserves monotonicity over the entire domain.

[0222] In summary, Maxout aggregation constructs an upper envelope surface that is pieced together by several monotone planes, which makes it an effective means of introducing nonlinearity in monotone neural networks, providing locally variable function shapes while preserving end-to-end monotonicity.

[0223] This embodiment adopts a monotone transformation network structure based on the Maxout structure, which ensures global or partial monotonicity of the model output in the specified dimension through structural design (non-external constraints), avoiding the numerical instability and gradient discontinuity problems of traditional penalty or projection methods, making the model training more stable and the results more interpretable.

[0224] To obtain better differentiability while maintaining monotonicity and geometric meaning, the hard-max operation of Maxout can also be replaced by its smooth approximation, i.e.:

[0225] The aggregation module uses the SmoothMaxout aggregation function to smooth approximate the maximum value in the local monotone linear response of the outputs of several monotone affine experts as the output result.

[0226] At this time, the SmoothMaxout aggregation function is defined as:

[0227]

[0228] where the temperature parameter controls the degree of smoothing. When , ; when is large, the individual expert outputs jointly participate in the aggregation with soft weights, thus providing a continuous and differentiable gradient transition at the boundary. SmoothMax has better stability in numerical optimization and allows end-to-end backpropagation without introducing non-differentiable points.

[0229] This embodiment introduces SmoothMaxout aggregation to replace the hard max operation, controls the differentiability of the upper envelope by smoothing the temperature parameter τ, and enables end-to-end backpropagation of the model without destroying monotonicity, with continuous gradients and stable training.

[0230] In this embodiment, whether Maxout aggregation or SmoothMaxout aggregation is used, their common effect is to introduce necessary nonlinearity while maintaining monotonic structure, so that the model can be constructed by combining multiple monotonic affine experts to form a continuous, interpretable and richly curved monotonic mapping.

[0231] In another example, the Maxout aggregation of the embodiment can be replaced by LogSumExp, Softmax weighted convex combination or weighted average (weights are non-negative and can be normalized); when the input is monotonic, the output is still monotonic, and has a differentiable nonlinear upper envelope effect.

[0232] In an embodiment, the output of the aggregation module is ;

[0233] The monotonic scaling function applies a monotonic transformation to the output of the aggregation module in any of the following three ways:

[0234]

[0235] where is a learnable or fixed positive scaling factor. is a hyperbolic tangent function.

[0236] After the model has monotonic affine layers and monotonic aggregation layers, a multi-layer monotonic neural network with strong nonlinear feature learning capability can be constructed by stacking multiple layers. However, with the increase of the number of layers and the accumulation of the activation amplitude, the numerical range and gradient size of the model output are prone to exponential amplification or contraction. This not only may cause numerical instability in the training process, but also weakens the transmission of monotonicity between different layers. In the traditional deep learning field, methods such as batch normalization (BN) are usually used to normalize the output features to improve stability and accelerate training convergence. However, batch normalization destroys the order preservation between input samples. The relative size of the output may be reversed due to normalization, thereby destroying the monotonicity.

[0237] To solve this problem, the embodiment proposes to use a smooth monotonic scaling operation to compress the amplitude and adjust the gradient of the input through a smooth monotonic scaling function, thereby normalizing the output scale and stabilizing the gradient without relying on batch statistics, while maintaining strict monotonicity.

[0238] The embodiment can be implemented using any one of the three functions described above, all of which are strictly monotonically increasing in the real number domain and differentiable in the entire domain. The first derivatives are respectively:

[0239]

[0240] For any input , there is , and the upper bound satisfies , and satisfies:

[0241]

[0242] This property ensures that the gradient propagation is explicitly constrained in amplitude, thereby preventing gradient explosion or attenuation.

[0243] The smooth monotonic scaling layer operates independently on each sample, and its mapping completely depends on its own input and does not depend on batch statistics. Therefore, for any two points , there is . That is, if the output of the previous layer is monotonic, the monotonicity is still maintained after adding the scaling layer.

[0244] In an embodiment, the aggregation output module uses an attention network to represent the weighted combination of the overall output of the monotonic transformation network as:

[0245]

[0246] where represents the output of the last monotonic transformation layer response of one monotone affine expert or subnetwork at the input , i.e., the output of the monotone transformation network, is the indicator weight generated by the attention network, also called attention weight, satisfying and This structure is equivalent to adaptive weighting between multiple monotone sub-mappings, so that the model can allocate attention between different experts according to the differences of input features, thus realizing flexible and constrained function form.

[0247] From the perspective of interpretation, the attention weight It can be regarded as an importance distribution itself, which reflects the "focus mode" of the current sample on different experts. When the weight of a certain expert is larger, it means that the contribution of the response of the expert to the overall output is higher, so It can be interpreted as the dominant factor of decision-making in the local area.

[0248] By visualizing the attention distribution on the sample set, the attention shift of the model under different input modes can be observed, thus obtaining intuitive understanding of the input space division and the decision-making logic of the model.

[0249] Therefore, the adaptive multi-criteria decision-making model based on monotone transformation constraint also includes a visualization module for visualizing the attention distribution on the sample set. The visualization module includes:

[0250] Introduce gradient-based backtracking analysis:

[0251]

[0252]

[0253] wherein, denotes the number of indicator dimensions of the output change, denotes the number of indicator dimensions of the input, denotes the number of monotone affine experts, denotes the indicator dimension of the jth input, denotes the indicator weight obtained in step S2, denotes the indicator dimension obtained in step S3;

[0254] Since the monotone transformation network guarantees or approximately guarantees the non-negativity of the partial derivative in the structural design, this gradient measure has a clear physical meaning: if is larger, it means that the The more significant the micro-increment of the input dimension is, compared to the general deep network, the more stable the gradient of the monotonic transformation network is in the sign and direction, so that the derivative-based sensitivity analysis has stronger explainability in the model. By visualizing the numerical value of the importance score, the attention structure and decision basis of the model are displayed.

[0255] The embodiment combines the attention weight and the gradient backtracking to calculate the importance score of the input dimension, realizes the explainability analysis of the model decision process, and provides a quantifiable financial indicator influence degree to assist the model audit and regulatory compliance.

[0256] In an embodiment, in order to obtain a more comprehensive explanation, the indicator weight obtained in step S2 is combined with the local gradient information to define a weighted importance indicator:

[0257]

[0258] The indicator integrates two meanings: on the one hand, captures the global allocation of the model at the expert level; on the other hand, captures the local response strength of the expert to the input dimension . After multiplication and summation, the superimposed effect of global attention and local sensitivity can be reflected. Therefore, can be understood as the comprehensive contribution of the input dimension to the output result, and the greater the value is, the more important the input is under the current sample. By visualizing the indicator in the sample space, the attention structure and decision basis of the model can be clearly displayed.

[0259] In another example, in addition to "attention + gradient", the Integrated Gradients, SHAP, LIME, and hierarchical attention aggregation methods can be used when implementing the explainability method. In the monotonic structure, the attributions are consistent in direction and sign.

[0260] In an embodiment, the training process of the adaptive multi-criteria decision model is an end-to-end optimization process, which aims to maintain the monotonicity and rational ordering ability of the model while having good numerical stability through structural constraints and multi-objective loss design. The overall training steps include data preparation, model initialization, forward propagation, loss calculation, back propagation, and parameter update.

[0261] Referring to Figure 5 , the adaptive multi-criteria decision model adopts the following training process to obtain a trained adaptive multi-criteria decision model: ​

[0262] In the data preparation phase, first, the data set is acquired and the data set is normalized, i.e., the data set is linearly mapped to the interval. The normalization process can eliminate dimensional differences, improve the numerical stability of training, and enable the monotonic layer in the model to more accurately capture the true change trend of each feature during the learning process. Subsequently, all learnable parameters in the adaptive multi-criteria decision model are initialized, including the attention network and the monotonic transformation network parameters. When initializing the parameters, it is preferred to use Xavier or normal distribution initialization to ensure that the gradient is balanced between different layers.

[0263] In the main loop of training, a batch of samples is randomly selected from the data set and input into the adaptive multi-criteria decision model to obtain the prediction score corresponding to each sample. The adaptive multi-criteria decision model only performs forward propagation in this stage and does not update the parameters. Then the total loss function is calculated. After calculating the total loss function, the gradient descent algorithm (such as the Adam optimizer) is used to perform backpropagation on the parameters of the adaptive multi-criteria decision model, calculate the gradient of the loss with respect to all learnable parameters, and update the parameters in the negative gradient direction. This process is repeated until the adaptive multi-criteria decision model converges on the validation set or meets the pre-set training number of rounds.

[0264] In an embodiment, the total loss function is composed of several sub-losses, at least one of which is a ranking loss, and more preferably a Pareto advantage loss.

[0265] The ranking loss of this embodiment can also use pairwise ranking loss, ListNet / NDCG ranking loss, etc.; similarly, the model output has "ranking" consistency.

[0266] Through this end-to-end iterative optimization mechanism for training the model, the model can automatically learn a scoring mapping that meets the Pareto rationality and monotonic structure constraints in the multi-dimensional index space, achieving high-precision, interpretable, and robust model training.

[0267] In specific implementation, the total loss function is composed of several sub-losses:

[0268]

[0269] Among them, the Pareto advantage loss is the core part, which is used to establish a rational ranking relationship between samples; the anchor loss and other auxiliary items are used to enhance the stability of model convergence. As Figure 5 shown, the total loss function is composed of a Pareto advantage loss, an anchor loss, and a regularization loss.

[0270] This embodiment introduces the concept of "Pareto optimality" in economics into the supervision signal, enabling the model to automatically learn the rational decision-making logic, i.e., samples that are not inferior in all indicators should obtain higher scores, significantly improving the logical consistency and interpretability of financial scoring.

[0271] Specifically, the design inspiration of Pareto advantage loss comes from the concept of "Pareto optimality" in economics: if a scheme is not inferior to scheme in all indicators, and strictly superior to in at least one indicator, then is Pareto superior to . For a rational scoring model, it should satisfy . Therefore, the model will construct a Pareto relationship matrix for all sample pairs in each batch: if is Pareto superior to , then ; otherwise ; if neither has an advantage, the corresponding item is zero. Then calculate the score difference of the sample pair, and define the loss according to the Pareto relationship:

[0272]

[0273] where is the set score margin (such as 0.1), indicating that the model needs to reflect clear differences in scores. Taking the average or total of the losses of all sample pairs that satisfy the Pareto relationship in the batch can obtain . To improve efficiency, this embodiment uses matrix implementation to complete the construction of the Pareto relationship and the calculation of the score difference of the entire batch through tensor operation at one time, thereby significantly improving the training speed.

[0274] Anchor loss is used to provide a stable reference direction in the early stage of training. Specifically, by setting a baseline anchor score (the average value of the input indicators), and by minimizing the mean square error between the predicted score and the anchor score, the model quickly converges to a reasonable output interval in the initial stage. As the training progresses, this constraint is gradually weakened, allowing the model to fully utilize the Pareto relationship for adaptive learning.

[0275] In another example, this embodiment can combine the Pareto / sorting loss with regression or classification as a multi-task objective, without changing the core mechanism but improving robustness and accuracy.

[0276] The embodiment of the present application also provides an adaptive multi-criteria decision-making method based on monotonic transformation constraint, which comprises the following steps:

[0277] S1, obtaining a set of normalized multi-dimensional financial indicator vectors, the multi-dimensional financial indicator vectors including samples and corresponding indicator dimensions;

[0278] S2, dynamically generating indicator weights for each sample in the multi-dimensional financial indicator vectors;

[0279] S3, performing a monotonically increasing nonlinear transformation on the indicator dimensions in the multi-dimensional financial indicator vectors, and mapping each indicator dimension to a new indicator dimension;

[0280] S4, element-wise multiplying the indicator weights obtained in step S2 and the indicator dimensions obtained in step S3, summing the indicator dimensions corresponding to each sample, and obtaining a comprehensive score corresponding to the sample after normalization.

[0281] In an embodiment, the adaptive multi-criteria decision-making method based on the monotonous transformation constraint is implemented by using the adaptive multi-criteria decision-making model based on the monotonous transformation constraint provided in the above embodiments.

[0282] Therefore, the adaptive multi-criteria decision-making method specifically includes the following steps:

[0283] S1, obtaining a set of normalized multi-dimensional financial indicator vectors, the multi-dimensional financial indicator vectors including samples and corresponding indicator dimensions;

[0284] S2, learning the multi-dimensional financial indicator vectors through an attention network to dynamically generate indicator weights for each sample;

[0285] S3, performing a monotonically increasing nonlinear transformation on the indicator dimensions in the multi-dimensional financial indicator vectors through a monotonous transformation network, and mapping each indicator dimension to a new indicator dimension;

[0286] S4, element-wise multiplying the indicator weights obtained in step S2 and the indicator dimensions obtained in step S3 through an aggregation output module, summing the indicator dimensions corresponding to each sample, and obtaining a comprehensive score corresponding to the sample after normalization.

[0287] The adaptive multi-criteria decision-making method can further include: S5, visualizing the attention distribution on the sample set. Step S5 is preferably implemented through a visualization module in the adaptive multi-criteria decision-making model based on the monotonous transformation constraint.

[0288] The embodiments of the present application also provide an adaptive multi-criteria decision-making system based on the monotonous transformation constraint, which includes the adaptive multi-criteria decision-making model based on the monotonous transformation constraint provided in the above embodiments.

[0289] In a specific implementation, the adaptive multi-criteria decision system comprises the following main functional modules:

[0290] Data receiving and preprocessing module: that is, the input layer of the model, is responsible for receiving multi-dimensional financial indicator data and performing normalization and standardization operations to uniformly map the input variables to the [0, 1] interval for subsequent model processing.

[0291] Attention weight calculation module: that is, the attention network of the model, is used to automatically learn the importance distribution of each financial indicator through the attention mechanism.

[0292] Monotonic transformation module: that is, the monotonic transformation network of the model, is used to apply monotonic nonlinear mapping to the input features, thereby maintaining the partial order consistency of the model output.

[0293] Comprehensive score calculation module: that is, the aggregation output module of the model, is used to weight and aggregate the aforementioned results to generate the final financial comprehensive score.

[0294] Model training module: that is, the training process of the model, is used to implement the end-to-end optimization process of loss function calculation, back propagation and parameter update, etc., to ensure that the model converges to the optimal solution in continuous iteration.

[0295] The embodiment of the present application also provides a computer device comprising a memory and a processor, the memory storing computer readable instructions, and the computer readable instructions being executed by the processor to make the processor execute the steps of the adaptive multi-criteria decision method based on monotonic transformation constraint provided by each embodiment of the present application.

[0296] The embodiment of the present application also provides a storage medium storing computer readable instructions, and the computer readable instructions being executed by one or more processors to make the one or more processors execute the steps of the adaptive multi-criteria decision method based on monotonic transformation constraint provided by each embodiment of the present application.

[0297] Reference Figure 6The present application can be implemented on a single or distributed computer device. The device generally includes one or more processors, such as a central processing unit (CPU), and can also be equipped with high-performance computing devices for accelerating deep learning calculations, such as a graphics processing unit (GPU) or a dedicated artificial intelligence chip (TPU, NPU, etc.). The device also includes memory for temporarily storing program instructions and runtime data, such as random access memory (RAM) and read-only memory (ROM); in addition, it is also configured with storage devices for long-term data and model parameter storage, such as hard disks or solid state disks, for storing training data sets, model weights, and intermediate calculation results. The system is also equipped with input / output interfaces to interact with external devices, user interfaces, or network systems. Under this hardware architecture, a set of computer-readable instructions is pre-stored in the memory. When the processor reads and executes these instructions, the complete process of the adaptive multi-criteria decision-making method based on monotonic transformation constraints provided by the above-mentioned embodiments of the present application can be implemented. All method steps of the present application can be completed by the computer device, and each functional module can be deployed on a single device for centralized implementation, or can be run in parallel in a cloud or distributed environment to adapt to different scales of financial evaluation application scenarios.

[0298] The preferred embodiments of the present application have been described in detail above, but it should be understood that, after reading the above teachings of the present application, those skilled in the art can make various modifications or improvements to the present application. These equivalent forms also fall within the scope defined by the claims attached hereto.

Claims

1. An adaptive multi-criteria decision-making model based on monotonic transformation constraints, characterized in that, The adaptive multi-criteria decision-making model based on monotonic transformation constraints includes: The input layer obtains a set of normalized multidimensional financial indicator vectors, which include samples and their corresponding indicator dimensions. An attention network receives the multidimensional financial indicator vector input from the input layer and dynamically generates indicator weights for each sample. A monotonic transformation network receives the multidimensional financial indicator vector input from the input layer, performs a monotonically increasing nonlinear transformation on the indicator dimensions, and maps each indicator dimension to a new indicator dimension. The aggregation output module multiplies the index weights output by the attention network with the index dimensions output by the monotonic transformation network element-wise, sums the index dimensions corresponding to each sample, and obtains the comprehensive score corresponding to the sample after normalization.

2. The adaptive multi-criteria decision-making model based on monotonic transformation constraints as described in claim 1, characterized in that, The attention network includes: A multilayer perceptron is used to process the multidimensional financial indicator vector to obtain a weight score vector corresponding to the indicator dimension. The Softmax function normalizes the weight score vector to obtain a set of non-negative index weights that sum to 1. And / or, The monotonic transform network is formed by superimposing several monotonic transform layers connected in sequence. Each monotonic transform layer is a composite mapping formed by sequentially connecting several sub-modules that maintain monotonicity in structure. Each sub-module has monotonic non-decreasing characteristics.

3. The adaptive multi-criteria decision-making model based on monotonic transformation constraints as described in claim 2, characterized in that, The monotonic transform network comprises sequentially connected: The monotonic calibration layer maps the input index dimensions to a scale-uniform, order-preserving representation space through piecewise linear mapping. A monotonic affine layer, wherein the monotonic affine layer has a plurality of monotonic affine experts, and the plurality of monotonic affine experts respectively learn local monotonic linear responses in different directions based on the output of the monotonic calibration layer; A monotonic aggregation layer, wherein the monotonic aggregation layer has several aggregation modules, and the several aggregation modules respectively aggregate the local monotonic linear response output by the monotonic affine layer to form a nonlinear upper envelope; A smooth monotonic scaling layer has several monotonic scaling functions. The several monotonic scaling functions respectively perform amplitude compression and gradient adjustment on the output of one of the corresponding aggregation modules to obtain a normalized output with monotonicity. Preferably, among the input metric dimensions, the first... The dimension of each input metric is denoted as Then the monotonic calibration layer is represented as: ； in, It is a continuous and monotonically non-decreasing piecewise linear function, with the middle part representing... Nonlinearly mapping features with different dimensions and distributions to a specified interval; Indicates total Each input metric dimension; In each piecewise linear function, for the th The effective range is limited by the number of input metrics dimensions. And an increasing sequence of endpoints: ； ； Valid intervals are determined by endpoint sequences. Divided into A range; Let the function value corresponding to each endpoint be... The value is obtained through nonnegative difference: ； in, , making It is an increasing sequence; Parameterizing the piecewise linear mapping: ； in, It is an activation function. These are learnable parameters; For any Define linear interpolation: ； Within any interval represented by a pair of endpoints, we have: ； The first Each input metric dimension is constrained to a fixed value range. And using normalized difference: ； in, It is a preset constant value; More preferably, in each piecewise linear function, the endpoint positions To preset a fixed value, Or, endpoint location Using parameterization: ； in, These are learnable parameters; Preferably, the monotonic affine layer has There are three monotone affine experts, each defined as a local affine function in the input space: ； in, For the weight vector, For bias terms, It is the output of the monotonic calibration layer; In the local affine function, the parameters need to be transformed using a Softplus transformation: ； in, To ensure that in the monotonic dimension ; Therefore, the set of all learnable parameters for a single monotone affine expert is: ; Preferably, the aggregation module uses the Maxout aggregation function to select the maximum value among the local monotonically linear responses output by several monotonically affine experts as the output result. Alternatively, the aggregation module may employ the SmoothMaxout aggregation function, which smoothly approximates the maximum value among the local monotonically linear responses output by several monotonically affine experts as the output result. Preferably, the output of the aggregation module is: ; The monotonic scaling function applies a monotonic transformation to the output of the aggregation module using any one of the following three methods: ； in, It is a learnable or fixed positive scaling factor.

4. The adaptive multi-criteria decision-making model based on monotonic transformation constraints as described in any one of claims 1 to 3, characterized in that, The adaptive multi-criteria decision-making model based on monotonic transformation constraints also includes: A visualization module that visualizes the attention distribution on a sample set; The visualization module includes: Introducing gradient-based backtracking analysis: ； in, Indicates the dimension of the input metrics Sensitivity to changes in output Indicates the dimension of the input metrics Quantity, This indicates the number of monotonic affine experts. This represents the dimension of the j-th input metric. This represents the index weights obtained in step S2. This indicates the dimension of the indicator obtained in step S3; like The larger the value, the higher the input value. The more significant the increase in the value, the better the improvement in the output. The numerical values ​​are visualized to show the model's focus structure and decision-making basis; Preferably, the index weights obtained in step S2 are combined with local gradient information to define a weighted importance index: ； pass Indicates input The overall contribution to the output results, if The larger the value, the higher the input value. The more important it is in the current sample; Through the The numerical values ​​are visualized to further demonstrate the model's focus structure and decision-making basis.

5. The adaptive multi-criteria decision-making model based on monotonic transformation constraints as described in any one of claims 1 to 3, characterized in that, The adaptive multi-criteria decision model is trained using the following process: In the data preparation stage, the dataset will be acquired and normalized, and all learnable parameters in the adaptive multi-criteria decision model will be initialized. Xavier or normal distribution initialization is preferred during initialization. In the main training loop, a batch of samples is randomly selected from the dataset and input into the adaptive multi-criteria decision model to obtain the prediction score corresponding to each sample. The adaptive multi-criteria decision model performs forward propagation, calculates the total loss function, uses the gradient descent algorithm to backpropagate the parameters of the adaptive multi-criteria decision model, calculates the gradient of the loss with respect to all learnable parameters, and updates the parameters along the negative gradient direction until the adaptive multi-criteria decision model converges on the validation set or meets the preset number of training rounds. Preferably, the total loss function is composed of a weighted sum of several sub-losses, wherein at least one of the sub-losses is a ranking loss, more preferably a Pareto advantage loss; More preferably, at least one of the sub-losses is an anchor point loss.

6. An adaptive multi-criteria decision-making method based on monotonic transformation constraints, characterized in that, The adaptive multi-criteria decision-making method based on monotonic transformation constraints includes: S1, obtain a set of normalized multidimensional financial indicator vectors, the multidimensional financial indicator vectors including samples and their corresponding indicator dimensions; S2, dynamically generate indicator weights for each sample in the multidimensional financial indicator vector; S3, perform a monotonically increasing nonlinear transformation on the indicator dimensions in the multidimensional financial indicator vector, mapping each indicator dimension to a new indicator dimension; S4. Multiply the index weights obtained in step S2 with the index dimensions obtained in step S3 element by element, sum the index dimensions corresponding to each sample, and after normalization, obtain the comprehensive score corresponding to the sample.

7. The adaptive multi-criteria decision-making method based on monotonic transformation constraints as described in claim 6, characterized in that, The adaptive multi-criteria decision-making model based on monotonic transformation constraints, as described in any one of claims 1 to 5, is used for implementation.

8. An adaptive multi-criteria decision-making system based on monotonic transformation constraints, characterized in that, The adaptive multi-criteria decision system based on monotonic transformation constraints includes the adaptive multi-criteria decision model based on monotonic transformation constraints as described in any one of claims 1 to 5.

9. A computer device, characterized in that, The system includes a memory and a processor, wherein the memory stores computer-readable instructions that, when executed by the processor, cause the processor to perform the steps of the adaptive multi-criteria decision-making method based on monotonic transformation constraints as described in any one of claims 6 to 7.

10. A storage medium storing computer-readable instructions, characterized in that, When the computer-readable instructions are executed by one or more processors, the one or more processors perform the steps of the adaptive multi-criteria decision-making method based on monotonic transformation constraints as described in any one of claims 6 to 7.

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