Swarm intelligence evolution dynamics emergence point positioning and perception identification method

Abstract

The invention relates to the technical field of intelligent cluster control, in particular to a crowd intelligence evolution dynamics emergence point positioning and sensing recognition method. The method comprises the steps that a high-order interaction network generation model and a crowd evolution dynamics model of the enterprise decision network are constructed, the high-order interaction network generation model calculates the probability of interaction between individuals through a homogeneity equation, and hyperedge parameters are introduced to represent a high-order interaction network structure; the crowd evolution dynamic model is used for quantifying individual concept evolution; iteratively updating an interactive network structure and an individual concept value through an evolution simulation algorithm; and averaging the interaction probability between the individuals on a time scale based on a mean field theory to derive an approximate evolution equation of the mean field, and calculating a Jacobian matrix eigenvalue of the equation after linearization at a zero point to obtain a phase change critical curve equation of the crowd-sourcing emergence point so as to realize positioning and sensing identification of the crowd-sourcing emergence point.

Description

Technical Field

[0001] This invention relates to the field of intelligent swarm control technology, and more specifically, to a method for locating and recognizing emerging points in swarm intelligence evolution dynamics. Background Technology

[0002] With the rapid development of society, economy, and information technology, enterprises face increasingly complex external environments and more diverse internal organizational structures and relationships among members during the decision-making process. In complex decision-making scenarios, a single decision-maker often struggles to fully address the challenges of a changing environment and multidimensional information. Therefore, more and more enterprises are beginning to rely on teamwork and collective intelligence to improve the scientific nature and efficiency of their decisions.

[0003] Collective intelligence is a collective wisdom that emerges through interaction and information exchange among group members. This collective wisdom often exhibits a combined effect greater than the sum of its parts, as seen in ant colonies, bee swarms, and whale pods. In a social context, particularly in corporate decision-making, the emergence of collective intelligence usually signifies a certain degree of consensus within the group, thereby promoting internal and external collaboration, optimizing resource allocation, and improving decision-making quality. However, the emergence of collective intelligence is not spontaneous. Factors such as individual differences within an organization, conflicting viewpoints, the spread of biases, and external interference can lead to "ideological polarization" within the decision-making team during its evolution. This polarization indicates a divergence in the positions or viewpoints of different team members, hindering the formation of collaborative consensus and preventing the effective emergence of collective intelligence.

[0004] Against this backdrop, studying the dynamics of collective intelligence evolution in corporate decision-making processes has significant theoretical and practical implications. In recent years, research on collective intelligence evolution has mainly focused on the following areas: 1. Collective intelligence modeling based on complex systems: Using complex systems theory to mathematically model the interactions, idea propagation, and collaborative behaviors among group members, and analyze the dynamic evolution of collective intelligence in the decision-making process.

[0005] 2. Research on Consensus and Polarization: This research explores how group members form consensus through continuous interaction, or how conflict and contradiction lead to polarization. Related studies typically utilize multi-agent models (such as game theory models and opinion propagation models) to analyze the dynamic evolution of divergence and collaboration.

[0006] 3. Identification and Location of Crowd Intelligence Emergence Points: In the dynamic evolution of the decision-making team, attempt to discover key time points or states that mark the emergence of crowd intelligence (i.e., "emergence points"). These emergence points are usually turning points in the system from divergence to consensus, or from disorder to order, and have guiding significance for optimizing corporate decisions.

[0007] 4. Dynamic perception driven by multi-source data: With the development of data acquisition and analysis technologies, data-driven methods (such as time series analysis and network analysis) are used to perceive and identify the collective intelligence state in the decision-making process in real time, helping enterprises to adjust their decision-making strategies in a timely manner.

[0008] Despite the progress made in the aforementioned research, accurately identifying the emergence points of collective intelligence and the state of consensus within the complex social context of corporate decision-making still faces many challenges.

[0009] Currently, although some progress has been made in the research on the dynamics of swarm intelligence evolution and the identification of emerging points, there are still significant shortcomings in the research on the influence of higher-order structures (mesoscale interactions) in enterprise decision-making networks, specifically in the following aspects: 1) Neglect of higher-order interactions, resulting in an oversimplified model: Existing research primarily describes information dissemination and idea evolution among individuals based on first-order relationships or two-entity interactions (such as simple edge connections between individuals) in complex networks. However, in real-world corporate decision-making networks, group collaboration often manifests as higher-order interactions between multiple entities (e.g., teamwork among three or more people, joint discussions between departments, and other complex relationships). These higher-order structures are essentially mesoscale interactions between micro-individuals and the macro-network as a whole, significantly influencing the system's evolutionary dynamics and the emergence of collective intelligence. Existing methods neglect these higher-order relationships, resulting in modeling results that fail to accurately reflect the actual evolutionary patterns of decision-making networks.

[0010] 2) The role of mesoscale structures lacks in-depth analysis: In corporate decision-making networks, typical mesoscale structures include cliques, hypergraphs, and simple complexes. These structures play crucial roles in information dissemination, consensus formation, and polarization. For example, the presence of cliques may strengthen local consensus but simultaneously hinder consensus synergy between different cliques. However, most existing research is limited to global network or micro-individual level analysis, failing to fully consider the impact of mesoscale structures on consensus and decision emergence points. This lack of attention to the role of mesoscale structures often causes existing methods to fail when dealing with complex corporate decision-making networks.

[0011] 3) Insufficient ability to model high-order interactive dynamics: Network modeling methods for high-order interactions are relatively lagging. Existing modeling techniques are mostly based on traditional graph theory or simple dynamic models, which are difficult to effectively describe the complexity of multi-agent interactions. For example, traditional opinion propagation models usually assume that information propagates pairwise along edges between individuals, failing to consider the nonlinear impact of the combined actions of multiple agents on the evolution of ideas in high-order interactions. This lack of modeling capability directly limits the accurate location of emerging points of collective intelligence.

[0012] 4) Emergent point identification lacks adaptability to higher-order interactions: Current methods for identifying emergence points primarily rely on global network metrics (such as degree distribution and clustering coefficients) or local features at the individual level (such as the rate of change in individual opinions). However, these metrics are mostly based on first-order or two-person interactions and cannot effectively capture the dynamic changes brought about by higher-order interactions. For example, in a decision-making network with higher-order interactions, some key emergence points may be closely related to higher-order collaborative relationships within the team, and these points cannot be identified using traditional one-sided or two-sided relationship analysis methods.

[0013] 5) Insufficient practical applicability to enterprise decision-making networks: Higher-order interactions in corporate decision-making scenarios exhibit complex and dynamic characteristics. For example, certain higher-order structures may have a strong influence on the dissemination of ideas within a specific time window, while their effect weakens at other times. Existing methods lack the ability to identify and adapt to these dynamic higher-order interactions, resulting in poor applicability in real-world decision-making scenarios. Furthermore, traditional methods often require simplification or approximation of the network when dealing with higher-order interactions, further weakening their ability to model complex corporate decision-making networks.

[0014] 6) Lack of a unified framework makes it difficult to effectively combine high-order structures and dynamic perception: Currently, few studies combine the modeling of higher-order structures with dynamic perception of systems, resulting in a lack of a unified theoretical framework for the dynamic identification and localization of swarm intelligence emergence points. For example, although higher-order interactions play an important role in the formation of swarm intelligence and the maintenance of consensus, the lack of effective indicators and algorithms to perceive the impact of higher-order structures on the system state in real time further limits the accurate identification of swarm intelligence emergence points.

[0015] In summary, existing technologies still have significant shortcomings in handling high-order interactions and mesoscale structures in enterprise decision-making networks. Specifically, they neglect high-order interactions, lack in-depth analysis of the role of mesoscale structures, have insufficient dynamic modeling capabilities, and have poor adaptability in identifying emerging points.

[0016] Therefore, there is an urgent need for an innovative method that can model high-order structures, reveal the impact of mesoscale interactions on the dynamics of swarm intelligence evolution, and develop emergence point localization and perception recognition algorithms for high-order interactive networks to better meet the actual needs of enterprise decision-making scenarios. Summary of the Invention

[0017] This invention aims to overcome at least one of the defects of the prior art and provide a method for locating and recognizing emerging points of swarm intelligence based on high-order interaction dynamics. By modeling and analyzing enterprise decision-making networks with high-order interaction characteristics, this invention studies the key impact of mesoscale interaction on the evolution of group ideas and proposes an algorithm that can accurately identify emerging points of swarm intelligence.

[0018] This invention overcomes the shortcomings of existing technologies that rely solely on first-order or two-body interaction modeling, which cannot effectively characterize the impact of higher-order interactions on emerging points of collective intelligence, by combining higher-order structures (such as hyperedges and clusters) with swarm intelligence evolution dynamics. It also addresses the problems of insufficient accuracy and poor dynamic adaptability in existing methods for identifying emerging points. This invention can accurately locate the key turning points in the formation of consensus and polarization states within enterprise decision-making networks, providing theoretical support and technical assurance for collaborative optimization in complex enterprise decision-making scenarios.

[0019] The detailed technical solution of this invention is as follows: A method for locating and recognizing emerging points in the dynamics of swarm intelligence evolution, the method comprising: S1. Construct a high-order interactive network generation model and a swarm intelligence evolution dynamics model for the enterprise decision-making network. The high-order interactive network generation model calculates the probability of interaction between individuals using a homogeneity equation and introduces hyperedge parameters. Used to characterize the structure of high-order interactive networks; the swarm intelligence evolution dynamics model is used to quantify the evolution of individual ideas; S2. Given the hyperparameters of the evolutionary simulation algorithm, execute the evolutionary simulation algorithm to iteratively update the interaction network structure generated by the higher-order interaction network generative model and the individual idea values ​​quantified by the swarm intelligence evolutionary dynamics model. ; S3. Based on mean-field theory, the interaction probability between individuals is averaged over a time scale to derive the mean-field approximate evolution equation, and the eigenvalues ​​of the Jacobian matrix after linearization of the equation at the zero point are calculated to obtain the phase transition critical curve equation of the swarm intelligence emergence point, thereby realizing the localization and perception recognition of the swarm intelligence emergence point.

[0020] According to a preferred embodiment of the present invention, in step S1, the homogeneity equation is:

[0021] In the formula: Represents an individual With individuals The probability of interaction occurring; , Each represents an individual and individuals Individual perception value; parameter It is a homogeneity index; the higher the index, the greater the tendency of individuals to engage in homogeneous interactions.

[0022] According to a preferred embodiment of the present invention, in step S1, the individual concept value is quantified through the differential equation of the swarm intelligence evolution dynamics model. Evolution:

[0023] In the formula: Represents an individual Rate of change of conceptual value; Represents an individual Individual perception value; Represents an individual Individual perception value; Represents an individual Individual perception value; Indicates the intensity of low-order dynamic interactions; Indicates the intensity of higher-order dynamic interactions; Indicates the number of individuals in the network; Indicates the activation function; Indicate the importance of the decision-making issue; express At any given moment, the adjacency matrix of the low-order interactive network is in The element at position 0 is equal to 1. express At any given moment, the adjacency matrix of the higher-order interactive network is in The element at the specified position; The quantization of high-order interactive network structures is achieved by a three-dimensional tensor matrix. express:

[0024] In the formula: Represents any individual in the firm's decision-making network. ; They represent The elements in the adjacency matrix of the low-order interaction network at each time point are the elements at the corresponding positions.

[0025] According to a preferred embodiment of the present invention, in step S2, the interaction network structure generated by the higher-order interaction network generation model and the individual concept value quantified by the swarm intelligence evolution dynamics model are... Iterative updates are based on the following steps: S21, Each individual With its activity level Activated into an active individual; S22, Group Structure Iteration: Individual Once activated, it proceeds with a probability choose indivual Interacting with singletons, i.e., selecting There are 10 neighboring individuals, and all selected neighboring individuals are arranged in the order of selection. Individuals and individuals Generate a simplex, and generate a total of A single form; or, an individual With probability choose Connect each neighboring individual with a point-to-point edge; If the edge If it is generated, then = =1; if the three-body structure If it is generated, then = = = =1; In this process, all edges that make up a simplex are also considered as low-order point-to-point edges in the algorithm evolution process. ; S23. Collective Intelligence Evolution and Iteration: Individual Concept Value Evolution proceeds according to the differential equations of the swarm intelligence evolution dynamics model; S24, at each time step At the end, the network adjacency matrix and It will be reset to all zeros, waiting for the next loop to regenerate a new interactive network.

[0026] According to a preferred embodiment of the present invention, in step S3, the interaction probabilities between individuals are averaged over a time scale based on mean-field theory to derive the mean-field approximate evolution equation, specifically including: For network adjacency matrix and By averaging over the time scale, the evolutionary differential equation is transformed into:

[0027] In the formula: Represents an individual With individuals The average probability of interaction; Represents an individual ,individual ,individual The average probability of belonging to the same higher-order structure; Using mean-field theory as the core analysis: Individual With individuals Average probability of interaction and individuals ,individual ,individual Average probability of belonging to the same higher-order structure ; For individuals With individuals Average probability of interaction With probability Generate edges right The contributions are as follows:

[0028] With probability Generate higher-order structures containing edges right The contributions are as follows:

[0029] For individuals ,individual ,individual Average probability of belonging to the same higher-order structure With probability Generate edges right The contribution is 0; with probability Generate a three-body structure right The contributions are as follows:

[0030] In the formula: This represents the average number of low-order interactions per individual. This indicates the average activity level of individuals; Each represents an individual Activity level; All are intermediate quantities; In conclusion:

[0031] In the formula: All are intermediate quantities; Substituting it into the mean-field approximation, the evolution equation is: .

[0032] According to a preferred embodiment of the present invention, in step S3, the eigenvalues ​​of the Jacobian matrix after linearization of the evolution equation at the zero point are calculated, i.e. The Jacobian matrix at point is:

[0033] All off-diagonal elements of the matrix are equal to The largest eigenvalue of the matrix is ​​obtained through algebraic simplification. for:

[0034] when hour, The satisfied relation corresponds to the phase transition critical value curve of collective intelligence emergence:

[0035] In the formula: This represents the critical value of the emergence phase transition of collective intelligence.

[0036] According to a preferred embodiment of the present invention, when the group size At that time, there was:

[0037] The expression for the phase transition critical curve parameters of collective intelligence emergence is as follows: .

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention provides a method for locating and recognizing emerging points in the dynamics of swarm intelligence evolution, which can accurately capture emerging points with small positioning errors and has good adaptability to dynamic high-order interactive networks.

[0039] (2) The present invention effectively identifies the key turning point in the formation of conceptual consistency and polarization state, and meets the needs of collective intelligence state perception in enterprise decision-making scenarios.

[0040] (3) The present invention is simple to implement, has strong high-level interaction modeling capabilities and accurate recognition, thus it can assist enterprises in making decisions more efficiently, help enterprises improve collaborative efficiency, optimize resource allocation, and thus gain a more competitive advantage in complex decision-making environments. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for locating and recognizing emerging points in the swarm intelligence evolution dynamics described in this invention.

[0042] Figure 2 This is a schematic diagram illustrating the construction of an activity-driven probabilistic high-order interaction network generation model in an embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram illustrating the construction of the swarm intelligence evolution dynamics model in an embodiment of the present invention.

[0044] Figure 4 These are the higher-order dynamic interaction parameters in the embodiments of the present invention. A schematic diagram illustrating the consensus reached through the simulation of collective intelligence evolution dynamics model.

[0045] Figure 5 These are the higher-order dynamic interaction parameters in the embodiments of the present invention. A schematic diagram illustrating the polarization achieved by the swarm intelligence evolution dynamics model.

[0046] Figure 6 This is a higher-order interaction tendency parameter in the embodiments of the present invention. A schematic diagram illustrating the consensus reached through the simulation of collective intelligence evolution dynamics model.

[0047] Figure 7 These are the higher-order dynamic interaction parameters in the embodiments of the present invention. A schematic diagram illustrating the polarization achieved by the swarm intelligence evolution dynamics model.

[0048] Figure 8 The low-order dynamic interaction intensity in the embodiments of the present invention Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0049] Figure 9 The low-order dynamic interaction intensity in the embodiments of the present invention Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0050] Figure 10 The low-order dynamic interaction intensity in the embodiments of the present invention Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0051] Figure 11 The low-order dynamic interaction intensity in the embodiments of the present invention Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0052] Figure 12 The low-order dynamic interaction intensity in the embodiments of the present invention Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0053] Figure 13 The low-order dynamic interaction intensity in the embodiments of the present invention The point of swarm intelligence emergence at The positioning and recognition effect diagram of the curve.

[0054] Figure 14 is the low-order dynamic interaction intensity in the embodiment of the present invention The point of swarm intelligence emergence at The positioning and recognition effect diagram of the curve. Specific implementation manners

[0055] The following further describes the present disclosure in conjunction with the drawings and embodiments.

[0056] It should be noted that the following detailed description is exemplary and intended to provide further illustration of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present disclosure belongs.

[0057] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0058] In the case of no conflict, the embodiments in the present disclosure and the features in the embodiments can be combined with each other.

[0059] Aiming at the deficiencies of the prior art, the present invention proposes a method for positioning and sensing and recognizing the emergence point of swarm intelligence evolution dynamics, considering the high-order structure and high-order dynamic interaction in enterprise decision-making, proposes a high-order dynamic model framework for swarm intelligence evolution, and explores the influence of non-linear features such as high-order structure and high-order dynamics on swarm intelligence dynamics, especially the effect on the phase transition point between group decision-making consistent behavior and opinion polarization behavior; at the same time, based on the mean-field approximation and dynamic system theory, a method for positioning and sensing and recognizing the phase transition point for high-order dynamics of swarm intelligence evolution is proposed, realizing the accurate positioning of intelligent emergence.

[0060] The following further describes the method of the present invention in conjunction with specific embodiments.

[0061] Embodiment 1, Refer Figure 1 , this embodiment provides a method for positioning and sensing and recognizing the emergence point of swarm intelligence evolution dynamics, and the method includes: S1. Construct a high-order interaction network generation model and a swarm intelligence evolution dynamics model for the enterprise decision-making network. Among them, the high-order interaction network generation model calculates the probability of interaction between individuals through a homophily equation and introduces a hyperedge parameter Used to characterize the structure of high-order interactive networks; the swarm intelligence evolution dynamics model is used to quantify the evolution of individual ideas.

[0062] In this embodiment, the high-order interactive network generation model for constructing the enterprise decision-making network is specifically a high-order probabilistic network generation model driven by the activity of homogeneous interactive choices.

[0063] In enterprise interaction scenarios, interactions are often diverse and instantaneous, resulting in a constantly changing network. Furthermore, different individuals exhibit varying levels of interaction activity; some prefer sharing information, while others prefer solitude. To characterize this property, this method employs a time-series activity-driven model, where the time interval of the time series diagram is determined by parameters... This indicates that, when facing decision-making, people tend to seek validation and choose to interact with like-minded individuals, while ignoring or filtering out ideas that differ significantly from their own understanding. In the context of the internet, this method uses a probabilistic approach to make it easier for individuals to choose interaction partners whose views are similar to their own, i.e., individuals... With individuals The probability of interaction occurring is:

[0064] The above equation is a homogeneity equation, where: Represents an individual With individuals The probability of interaction occurring; , Each represents an individual and individuals Individual perception value; parameter It is a homogeneity index; the higher the index, the greater the tendency of individuals to engage in homogeneous interactions.

[0065] To model higher-order interactions, this method introduces hyperedges into the network. In an enterprise, both lower-order and higher-order interactions exist simultaneously. Lower-order interactions characterize point-to-point interactions between colleagues or superiors and subordinates, while higher-order structures characterize group interactions between teams or departments. This method introduces hyperedge parameters. This is used to control an individual's tendency to choose higher-order interactions.

[0066] The constructed high-order interactive network generative model, such as Figure 2 As shown.

[0067] Within a corporate group, the interactions between individuals are diverse, occurring at different times. The interactive objects within the system are constantly changing, and individuals exhibit varying levels of activity. For example, staff in product departments have more opportunities to interact, while those in technical departments interact less. Therefore, this method models individuals. The activity level is During the time period The probability that it will be activated and actively interact with others is Once activated, the individual... A higher-order structure is generated with a probability of [ ]. The probability of generating the same number of interactions (in this model is) =3) is a low-order structure. When each individual generates the interaction structure using the same procedure, the group network modeling is successful at that moment, and the collective intelligence evolves on a high-order temporal network.

[0068] In this embodiment, the collective intelligence evolution dynamics model for constructing the enterprise decision-making network is specifically a nonlinear evolution dynamics model that considers colleague pressure and the importance of issues.

[0069] The foundation for accurately identifying and locating emerging points of swarm intelligence lies in the expressive power of the swarm evolution interaction model, ensuring the practical significance of the model's parameters and their sufficient sensitivity to swarm intelligence phase transitions. The model needs to consider the formation and evolution mechanisms of swarm intelligence at different scales. Comparing existing research, the role of the mesoscale in swarm intelligence interaction cannot be ignored, and this is characterized using higher-order structures in the network model. Therefore, the evolutionary differential equation of this model is written, utilizing… Quantifying individual perception values:

[0070] In the formula: Represents an individual Rate of change of conceptual value; Represents an individual Individual perception value; Represents an individual Individual perception value; Represents an individual Individual perception value; Indicates the intensity of low-order dynamic interactions; Indicates the intensity of higher-order dynamic interactions; Indicates the number of individuals in the network; Indicates the activation function; Indicate the importance of the decision-making issue; express At any given moment, the adjacency matrix of the low-order interactive network is in The element at position 0 is equal to 1. express At any given moment, the adjacency matrix of the higher-order interactive network is in The element at the specified position.

[0071] parameter Used to characterize the strength of point-to-point interactions between individuals, i.e., the degree to which an individual is influenced by other individuals; by analogy, the strength of an individual's influence by a group (social media scale) needs to be determined by... Encoding is incorporated into the model; the quantization of high-order network structures is achieved through a three-dimensional tensor matrix. express:

[0072] In the formula: Represents any individual in the firm's decision-making network. ; They represent The elements in the adjacency matrix of the low-order interaction network at each time point are the elements at the corresponding positions.

[0073] parameter This parameter can characterize the importance of the decision-making problems faced by enterprises, or it can be understood as the influence of the problem itself. The more important the problem, the greater the attention it will attract from employees, which in turn makes more extreme ideas more stimulating to the group. This parameter enables the model to characterize the emergence process of collective intelligence on problems of different degrees and scales.

[0074] A schematic diagram of the constructed swarm intelligence evolution dynamics model is shown below. Figure 3 As shown.

[0075] Within a group of firms, individuals' judgments (perceptions) on decision-making issues are influenced by interactions at different scales. In this model, mesoscale interactions are represented by higher-order structures, which have a role that transcends the simple linear sum of lower-order interactions and are a key tool for analyzing the emergence of collective intelligence. Parameters Indicates the intensity of low-order interactions, Indicates the intensity of higher-order interactions, It indicates the complexity or importance of the decision-making issue.

[0076] During the interaction at each time step, the affected individuals (as individuals) For example, a person's perception is influenced by the perception values ​​of other individuals in the same structure after activation. (Activation function) This introduces nonlinearity into the model, resulting in a function that is nearly linear near the zeros, but its range is limited. Therefore, the degree of interaction and influence is limited. In enterprises, people tend to be more cautious in accepting extreme ideas. Such behavior promotes the formation of social systems or demonstrates collective intelligence.

[0077] S2. Given the hyperparameters of the evolutionary simulation algorithm, execute the evolutionary simulation algorithm to iteratively update the interaction network structure generated by the higher-order interaction network generative model and the individual idea values ​​quantified by the swarm intelligence evolutionary dynamics model. .

[0078] An evolution simulation algorithm is designed based on the high-order interactive network generation model and the swarm intelligence evolution dynamics model constructed in S1.

[0079] Before each evolutionary simulation experiment begins, the hyperparameters for that simulation, including the number of network individuals, are fixed. =1000, Time Steps =2000, duration per step =0.01, and set the higher-order structure scale. =3, assign initial state values ​​to each individual in a uniform distribution. And assign each individual the same degree of higher-order interaction tendency. and activity level .

[0080] Each time step of the algorithm Network structure , and all individual concept values Iterative updates should be performed using the following steps: S21, Each individual With its activity level They are activated and become active individuals.

[0081] S22, Group Structure Iteration: If individuals Activated, individual With probability choose indivual Interacting with a singlet requires choosing according to the homogeneity equation. There are 10 neighboring individuals, and all selected neighboring individuals are arranged in the order of selection. Individuals and individuals Generate a simplex, and generate a total of A single form; or, an individual With probability choose Connect each neighboring individual with a point-to-point edge. If the edge If it is generated, then = =1; if the three-body structure If it is generated, then = = = =1.

[0082] It should be noted that all edges that make up a simplex (higher-order structure) should also be considered as lower-order point-to-point edges in the algorithm evolution process, i.e. .

[0083] S23. Collective Intelligence Evolution and Iteration: Individual Concept Value Evolution occurs according to the dynamic differential equation.

[0084] S24, at each time step At the end, the network adjacency matrix and It will be reset to all zeros, waiting for the next loop to regenerate a new interactive network.

[0085] The algorithm pseudocode is as follows:

[0086] S3. Based on mean-field theory, the interaction probability between individuals is averaged over a time scale to derive the mean-field approximate evolution equation, and the eigenvalues ​​of the Jacobian matrix after linearization of the equation at the zero point are calculated to obtain the phase transition critical curve equation of the swarm intelligence emergence point, thereby realizing the localization and perception recognition of the swarm intelligence emergence point.

[0087] Specifically, the identification of emerging points of collective intelligence is based on whether individual ideas can reach consensus (generate cooperation) through group interaction and evolution. From a mathematical perspective, this involves analyzing the stability of the system's zeros as attractors. Since the model equations are defined at the microscopic level and cannot be solved analytically, the mean-field approximation method is used to simplify the system to solve for the critical phase transition curve of the emerging point. The first challenge is to address the coefficients... and After averaging over the time scale, the system evolution differential equation is transformed into:

[0088] Using mean-field theory as the core analysis: Individual With individuals Average probability of interaction ;individual ,individual ,individual Average probability of belonging to the same higher-order structure .

[0089] For individuals With individuals Average probability of having a connected edge With probability Generate edges right The contributions are as follows:

[0090] In the formula: This represents the average number of low-level interactions per individual. This indicates the average activity level of individuals; The second equation in the formula averages the activity of individuals at the system level; With probability Generate higher-order structures containing edges right The contributions are as follows:

[0091] For individuals ,individual ,individual Average probability of belonging to the same higher-order structure With probability Generate edges right The contribution is 0; with probability Generate a three-body structure right The contributions are as follows:

[0092] In conclusion:

[0093] The evolution equation after substituting into the mean-field approximation is: .

[0094] To obtain the phase transition critical curve representing the emergence point of folk intelligence, we need the eigenvalues ​​of the Jacobian matrix of this nonlinear system after linearization at the zero point. The Jacobian matrix at point A is as follows:

[0095] All off-diagonal elements of the matrix are equal to After algebraic simplification, the largest eigenvalue of the matrix is:

[0096] The sign of the largest eigenvalue determines the stability of the zero as the equilibrium point of the system. hour, The satisfied relation corresponds to the phase transition critical value curve of collective intelligence emergence:

[0097] In the formula: This represents the critical value of the emergence phase transition of collective intelligence.

[0098] When the group size At that time, it can be calculated that:

[0099] After processing, the expression for the phase transition critical curve parameters of collective intelligence emergence is obtained as follows:

[0100] The above parameter expressions enable the identification, perception, prediction, and regulation of collective intelligence.

[0101] Figure 4 and Figure 5 The following diagrams show the evolution of the model simulating the collective intelligence evolution to reach consensus and polarization under different parameters. Figure 4 For higher-order dynamic interaction parameters A schematic diagram illustrating the consensus reached in the evolution of collective intelligence using a dynamic model of collective intelligence evolution. Figure 5 For higher-order dynamic interaction parameters A schematic diagram illustrating the polarization achieved by the swarm intelligence evolution dynamics model.

[0102] Should Figure 4 and Figure 5 For individual concept value Over time Evolutionary diagram Each line in the diagram is composed of =0 starting from = The curve represents the evolution of an individual's ideas during the interaction process; the orange curve (upper curve) indicates... Individual opinion value at time 0 A value greater than 0 indicates support for a decision problem; the blue curve (lower curve) indicates... =0 time <0, indicating opposition to the issue pending a decision.

[0103] get Figure 4 and Figure 5 The method involves simulating the group interaction process for 2000 time steps using the evolutionary algorithm designed in this paper and recording the experimental data. The results show different collective intelligence evolution effects. The basic parameters of the model in the figure are... =1.0, =0.5, =2.0, =2.0, =0.05, =2000.

[0104] contrast Figure 4 and Figure 5 The two figures illustrate how increasing the intensity of higher-order dynamic interactions... As time progresses (the reinforcing effect of the group on the spread of ideas increases), the collective wisdom shifts from consensus to polarization, crossing the system's threshold point, leading to... An increase in [the value of something] has an inhibitory effect on the emergence of collective intelligence. (The vertical axis in the figure...) Represents conceptual values; horizontal axis This represents the number of evolution time steps in the simulation algorithm.

[0105] Figure 6 and Figure 7 The following diagrams illustrate the evolution of consensus and polarization in the model's perception of group decision-making behavior under different parameters. Figure 6 It is a higher-order interaction tendency parameter A schematic diagram illustrating the consensus reached in the evolution of collective intelligence using a dynamic model of collective intelligence evolution. Figure 7 These are higher-order dynamic interaction parameters A schematic diagram illustrating the polarization achieved by the swarm intelligence evolution dynamics model.

[0106] and Figure 4 and Figure 5 Similarly, the basic parameters of the model are =4.0, =0.5, =2.0, =2.0, =0.05, =2000, the activity parameter is the same for each individual.

[0107] contrast Figure 6 and Figure 7 The two figures illustrate how increasing the proportion of higher-order structures can improve the overall design. When individuals engage in higher-order interactions with greater probability, the concept of collective intelligence shifts from consensus to polarization, crossing the system's threshold point, leading to... The increase of has an inhibitory effect on the emergence of collective intelligence.

[0108] Figures 8 to 10 The heatmap illustrates the location and identification of the emergence point curve of collective intelligence. Figure 8 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition; Figure 9 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition; Figure 10 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0109] Figures 8 to 10 Each coordinate point in the diagram represents a simulation result completed according to the evolutionary algorithm designed in this method, and the black area represents the last time step of the simulation. Achieving consensus in group opinion (using indicators) To measure (the index on the right side of the heat map color temperature meter). Indicates when hour The average of absolute values, i.e. The black area represents =0), consensus is reached, group cooperation is formed, and intelligence emerges; bright areas represent polarization of ideas ( >0), hindering collaborative decision-making and failing to achieve intelligence; the white curve (dashed line) is the critical value location, i.e., the emergence point, calculated using the derivation method in this approach, and its expression is: (Legend in the upper right corner of the image).

[0110] Figure 8 , Figure 9 and Figure 10 The three figures correspond to the low-order dynamic interaction intensities, respectively. For cases where the values ​​are 0.5, 1.0, and 2.0, the horizontal axis represents the complexity of the problem. The vertical axis represents the intensity of higher-order dynamic interactions. The graph shows that the white curve accurately matches the simulated location of the emerging collective intelligence points, confirming the accuracy of the positioning and identification methods.

[0111] Figures 11 to 14 The heatmap also demonstrates the location and identification of the emergence point curve of collective intelligence. Figure 11 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition; Figure 12 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition; Figure 13 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition; Figure 14 It is the intensity of low-order dynamic interaction. Emergence of collective intelligence The effect diagram of curve positioning and recognition.

[0112] Its and Figures 8 to 10 The difference is Figures 11 to 14 The vertical axis of the four graphs represents the probability of an individual choosing a higher-order structural interaction. The four figures correspond to the low-order dynamic interaction intensity. =1.0, 1.2, 1.5, 2.0.

[0113] In summary, the emergence point localization and perception recognition method of the swarm intelligence evolution dynamics of this invention was experimentally verified on an enterprise decision-making network with high-order interaction characteristics. In a simulated enterprise decision-making network containing high-order interactions (such as three-body or higher collaborative relationships), the emergence points of the concept consistency state were located and identified by adjusting the interaction intensity and problem complexity.

[0114] Experimental results show that this invention can accurately capture emergence points with small positioning errors and exhibits good adaptability to dynamically changing high-order interactive networks. The results also demonstrate that this method effectively identifies key inflection points in the formation of consensus and polarization states, meeting the needs of collective intelligence state perception in enterprise decision-making scenarios.

[0115] This invention is simple to implement, has strong high-level interaction modeling capabilities, and is accurate in its identification. Therefore, it can assist enterprises in making decisions more efficiently, help them improve collaborative efficiency, optimize resource allocation, and thus gain a more competitive advantage in complex decision-making environments.

[0116] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the specific implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for locating and recognizing emerging points in the dynamics of swarm intelligence evolution, characterized in that, The method includes: S1. Construct a high-order interactive network generation model and a swarm intelligence evolution dynamics model for the enterprise decision-making network. The high-order interactive network generation model calculates the probability of interaction between individuals using a homogeneity equation and introduces hyperedge parameters. Used to characterize the structure of high-order interactive networks; the swarm intelligence evolution dynamics model is used to quantify the evolution of individual ideas; S2. Given the hyperparameters of the evolutionary simulation algorithm, execute the evolutionary simulation algorithm to iteratively update the interaction network structure generated by the higher-order interaction network generative model and the individual idea values ​​quantified by the swarm intelligence evolutionary dynamics model. ; S3. Based on mean-field theory, the interaction probability between individuals is averaged over a time scale to derive the mean-field approximate evolution equation, and the eigenvalues ​​of the Jacobian matrix after linearization of the equation at the zero point are calculated to obtain the phase transition critical curve equation of the swarm intelligence emergence point, thereby realizing the localization and perception recognition of the swarm intelligence emergence point.

2. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 1, characterized in that, In S1, the homogeneity equation is: In the formula: Represents an individual With individuals The probability of interaction occurring; , Each represents an individual and individuals Individual perception value; parameter It is a homogeneity index; the higher the index, the greater the tendency of individuals to engage in homogeneous interactions.

3. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 1, characterized in that, In S1, the individual concept value is quantified through the differential equation of the collective intelligence evolution dynamics model. Evolution: In the formula: Represents an individual Rate of change of conceptual value; Represents an individual Individual perception value; Represents an individual Individual perception value; Represents an individual Individual perception value; Indicates the intensity of low-order dynamic interactions; Indicates the intensity of higher-order dynamic interactions; Indicates the number of individuals in the network; Indicates the activation function; Indicate the importance of the decision-making issue; express At any given moment, the adjacency matrix of the low-order interactive network is in The element at position 0 is equal to 1. express At any given moment, the adjacency matrix of the higher-order interactive network is in The element at the specified position; The quantization of high-order interactive network structures is achieved by a three-dimensional tensor matrix. express: In the formula: Represents any individual in the firm's decision-making network. ; They represent The elements in the adjacency matrix of the low-order interaction network at each time point are the elements at the corresponding positions.

4. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 3, characterized in that, In S2, the interaction network structure generated by the higher-order interaction network generation model and the individual concept values ​​quantified by the swarm intelligence evolution dynamics model are also included. Iterative updates are based on the following steps: S21, Each individual With its activity level Activated into an active individual; S22, Group Structure Iteration: Individual Once activated, it proceeds with a probability choose indivual Interacting with singletons, i.e., selecting There are 10 neighboring individuals, and all selected neighboring individuals are arranged in the order of selection. Individuals and individuals Generate a simplex, and generate a total of A single form; or, an individual With probability choose Connect each neighboring individual with a point-to-point edge; If the edge If it is generated, then = =1; if the three-body structure If it is generated, then = = = =1; In this process, all edges that make up a simplex are also considered as low-order point-to-point edges in the algorithm evolution process. ; S23. Collective Intelligence Evolution and Iteration: Individual Concept Value Evolution proceeds according to the differential equations of the swarm intelligence evolution dynamics model; S24, at each time step At the end, the network adjacency matrix and It will be reset to all zeros, waiting for the next loop to regenerate a new interactive network.

5. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 4, characterized in that, In S3, the interaction probabilities between individuals are averaged over a time scale based on mean-field theory to derive the mean-field approximate evolution equation, specifically including: For network adjacency matrix and By averaging over the time scale, the evolutionary differential equation is transformed into: In the formula: Represents an individual With individuals The average probability of interaction; Represents an individual ,individual ,individual The average probability of belonging to the same higher-order structure; Using mean-field theory as the core analysis: Individual With individuals Average probability of interaction and individuals ,individual ,individual Average probability of belonging to the same higher-order structure ; For individuals With individuals Average probability of interaction With probability Generate edges right The contributions are as follows: With probability Generate higher-order structures containing edges right The contributions are as follows: For individuals ,individual ,individual Average probability of belonging to the same higher-order structure With probability Generate edges right The contribution is 0; with probability Generate a three-body structure right The contributions are as follows: In the formula: This represents the average number of low-order interactions per individual. This indicates the average activity level of individuals; Each represents an individual Activity level; All are intermediate quantities; In conclusion: In the formula: All are intermediate quantities; Substituting it into the mean-field approximation, the evolution equation is: 。 6. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 5, characterized in that, In step S3, the eigenvalues ​​of the Jacobian matrix after linearization of the evolution equation at the zero point are calculated, i.e. The Jacobian matrix at point is: All off-diagonal elements of the matrix are equal to The largest eigenvalue of the matrix is ​​obtained through algebraic simplification. for: when hour, The satisfied relation corresponds to the phase transition critical value curve of collective intelligence emergence: In the formula: This represents the critical value of the emergence phase transition of collective intelligence.

7. The method for locating and recognizing emerging points in swarm intelligence evolution dynamics according to claim 6, characterized in that, When the group size At that time, there was: The expression for the phase transition critical curve parameters of collective intelligence emergence is as follows: 。

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