Chaotic attractor-based manifold knowledge coding method and system

Abstract

The invention relates to a chaos attractor-based manifold knowledge coding method and system, and the method comprises the step of embedding originally dispersed semantic information into a geometric structure in a more compact manner through the dynamic generation of a chaos trajectory and the high-dimensional expansion of a manifold space. The method has the advantages that potential correlation between semantics can be more accurately captured, space waste caused by linear compression in a traditional method is avoided, more information is contained in limited dimensions, the effect of remarkably improving the coding density is achieved, when high-complexity professional texts are processed, a system can automatically increase the coding dimensions and increase chaos parameters, and the coding efficiency is improved. More semantic details can be accommodated; and for a simple text, the system compresses dimensions and reduces parameters, so that the coding efficiency is improved. The strategy of tailoring according to the body ensures that the coding method can flexibly adapt to different types of knowledge contents.

Description

Technical Field

[0001] This application relates to the technical field of knowledge coding, and in particular to a manifold knowledge coding method and system based on chaotic attractors. Background Technology

[0002] Knowledge coding is a technology and method for expressing and storing human knowledge in a structured, systematic, and computable form. Its core goal is to transform complex concepts, logical relationships, and factual information into computer-recognizable and processable data formats, thereby enabling knowledge sharing, reuse, and intelligent applications. Knowledge coding is typically based on ontology theory, constructing semantic networks or knowledge graphs by defining entities, attributes, relationships, and rules. It is widely used in fields such as artificial intelligence, natural language processing, expert systems, intelligent retrieval, and data integration. Common knowledge coding methods include semantic web technologies (such as RDF and OWL), knowledge graph construction, classification system coding (such as ontology trees), terminologies, and metadata standards. With the development of big data and artificial intelligence technologies, knowledge coding plays an increasingly important role in improving information processing efficiency, enhancing machine understanding capabilities, and supporting intelligent decision-making, and has become one of the key technologies driving the development of the digital economy and innovation in knowledge services.

[0003] However, existing technologies have the following problems: traditional knowledge encoding methods use fixed mathematical transformations, lack dynamism and adaptability, while linear encoding methods suffer from a large amount of information loss when processing complex semantics, existing encoding methods are not robust enough in noisy environments, and lack effective space compression and representation mechanisms. Summary of the Invention

[0004] To avoid the space waste caused by linear compression in traditional methods and to accommodate more information in a limited dimension, this application provides a manifold knowledge encoding method and system based on chaotic attractors.

[0005] This application provides a manifold knowledge encoding method and system based on chaotic attractors, which adopts the following technical solution: A manifold knowledge encoding method based on chaotic attractors, characterized in that: the method includes the following steps: S1: The input knowledge text is segmented, stop words are removed, and semantic standardization is performed. At the same time, the complexity features of the text are extracted. The preprocessing results will be used as the input of dynamic parameters for subsequent chaotic trajectory generation to ensure that the trajectory generation is initially related to the text characteristics.

[0006] S2: Based on the Lorenz chaotic system: σ=10, ρ=28, β=8 / 3, an initial trajectory is generated. The initial state is randomized by a random seed, which is determined by the preprocessed text hash value. The length of the generated trajectory is consistent with the number of preprocessed text tokens, ensuring that each subsequent encoding step corresponds to a unique trajectory point.

[0007] The Lorenz system equations are: dx / dt = σ(yx); dy / dt = x(ρ-z)-y; dz / dt = xy - βz; S3: Calculate the maximum Lyapunov exponent of the initial trajectory, and select trajectory segments with high chaos degree whose exponent is greater than 0.9. The higher the Lyapunov exponent, the stronger the unpredictability of the trajectory and the better the coding diversity. Remove low chaos degree points to avoid coding redundancy. The selected trajectory will serve as the core anchor point of the manifold projection, which directly affects the dynamics of subsequent coding.

[0008] The formula for calculating the Lyapunov index is: λ=lim(t→∞)(1 / t)ln(|δx(t)| / |δx0|); S4: The selected 3D chaotic trajectory points are expanded to a 7-dimensional manifold space using polynomial basis functions {x,y,z,x²,y²,z²,xyz}, forming a manifold point set. The dimension of this manifold space is positively correlated with the text complexity, providing a nonlinear mapping carrier for subsequent semantic coupling.

[0009] S5: Perform multi-granularity vectorization on the preprocessed text tokens, aligning the vector dimensions with the manifold space dimensions to ensure that the text vectors and manifold points can be directly coupled in the same space. The result of this step will serve as the key input for calculating the coupling weights.

[0010] S6: Based on the Gaussian kernel function wᵢ=exp(-||pᵢ-c||² / 2σ²) / Σⱼexp(-||pⱼ-c||² / 2σ²), the coupling weight between each text vector and the corresponding manifold point is calculated, where pᵢ is the manifold point and c is the text vector. The weight is dynamically adjusted according to the spatial distance between the text vector and the manifold point. The higher the weight of the manifold point, the greater its contribution to the encoding result, thus achieving fine matching between semantics and geometric structure.

[0011] S7: Combining the Lyapunov index and text complexity, dynamically adjust the coding space dimension: If the Lyapunov index is higher than the threshold and the text complexity is high, increase the coding dimension to accommodate more information; otherwise, compress the dimension to improve efficiency. This adjustment directly affects the information density distribution of the final encoding.

[0012] S8: Multiply and sum the results of each manifold point with its corresponding text vector and coupling weight to generate the final chaotic manifold encoding vector. This vector simultaneously contains textual semantic information, geometric structure information, and dynamic adjustment information, achieving a high-fidelity, noise-resistant, and adaptive encoding representation of knowledge.

[0013] In a preferred embodiment, in step S1, the word segmentation operation can employ a word segmentation tool that combines rules and statistics. The stop word list is a hybrid list containing general stop words and domain-specific stop words to ensure the filtering of redundant words. Semantic standardization processing requires lexical reconstruction of the word segmentation results and replacement of low-frequency words with a thesaurus to improve the consistency of subsequent processing. Complexity feature extraction specifically includes three parts: word frequency distribution is measured by statistically analyzing the frequency of each word and calculating entropy; semantic density is indicated by the number of different semantic units per hundred words; and text length directly affects the number of sampling points for subsequent chaotic trajectories. These three factors together constitute the dynamic parameter input.

[0014] In a preferred embodiment, in step S2, the fourth-order Runge-Kutta method is used to solve the differential equation, with a fixed time span of 0 to 10 seconds, and the number of sampling points is strictly consistent with the number of preprocessed text tokens. The randomization of the initial state is controlled by the text hash value: the preprocessed text is MD5 hashed, and the first 6 digits are used as a random seed to generate a three-dimensional initial value in the range [-5, 5]. This design ensures that the initial state generated by different texts is unique, avoiding encoding duplication, and simultaneously achieving reproducibility through a fixed seed.

[0015] In a preferred embodiment, in step S3, the chaotic trajectory feature enhancement screening requires calculating the maximum Lyapunov exponent of the trajectory using the Wolf algorithm. Specifically, 10 consecutive trajectory points are used as a window to calculate the Euclidean distance divergence rate between adjacent points, and the average value of all windows is taken as the Lyapunov exponent of the trajectory segment. The screening threshold is set to 0.9; if the exponent of a trajectory segment is lower than 0.9, the first 3 points of that segment are removed.

[0016] In a preferred embodiment, in step S4, the high-dimensional cognitive manifold space is constructed based on the selected 3D chaotic trajectory points and expanded to 7 dimensions using polynomial basis functions. Specifically, the expansion rule is as follows: each 3D point (x, y, z) corresponds to a 7-dimensional vector (x, y, z, x², y², z², xyz), where the squared terms are used to capture the nonlinear characteristics of the trajectory; for example, x² reflects the quadratic change in the x-direction, and the cross term xyz enhances the coupling relationship between different dimensions. If the text complexity is high during the preprocessing stage, expansion terms can be dynamically added to increase the dimensions to 10 dimensions to accommodate more complex semantic information.

[0017] In a preferred embodiment, in step S5, word-level vectors are generated using a pre-trained Word2Vec model, phrase-level vectors are extracted using a sliding window and averaged, and sentence-level vectors are generated using the [CLS] vectors from the BERT-base model. To align with the 7-dimensional manifold space, PCA dimensionality reduction is performed on the three types of vectors respectively. Finally, the 7-dimensional vectors at the word, phrase, and sentence levels are weighted and fused with a weight ratio of 0.3:0.4:0.3 to form the final 7-dimensional text vector.

[0018] In a preferred embodiment, in step S6, the dynamic coupling weights are calculated in real time using a Gaussian kernel function, where the σ parameter is dynamically adjusted according to the text complexity: σ = 0.5 when the text complexity is low, and σ = 1.2 when the complexity is high, to balance the influence of local and global factors. Specifically, for each text vector c and its corresponding manifold point pᵢ, the Euclidean distance ||pᵢ-c|| is first calculated, then substituted into the exponential function to obtain the numerator, and finally, softmax normalization is used to ensure that the weight sum is 1.

[0019] In a preferred embodiment, in step S7, the adaptive optimization of the encoding space needs to dynamically adjust the dimensions by combining the Lyapunov index and text complexity. Specifically, the strategy is as follows: if the Lyapunov index > 0.9 and the text complexity is high, the encoding dimension is increased by 2 dimensions; if the index < 0.8 and the complexity is low, the dimension is reduced by 1 dimension; otherwise, the original dimension is maintained.

[0020] In a preferred embodiment, in step S8, the dynamic knowledge encoding vector generation is achieved through weighted accumulation. Specifically, for each manifold point pᵢ, text vector cᵢ, and coupling weight wᵢ, calculate wᵢ*pᵢ+cᵢ, and then accumulate all results to obtain the final encoding vector. To ensure vector stability, the results need to be L2 normalized to ensure that the vector length is uniformly 1.

[0021] In summary, this application includes at least one of the following beneficial technical effects: 1. By dynamically generating chaotic trajectories and expanding the manifold space in a high dimension, the originally scattered semantic information is embedded into the geometric structure in a more compact manner. The unpredictability of chaotic trajectories and the expansion of the manifold space by polynomial basis functions can more accurately capture the potential correlations between semantics, avoiding the space waste caused by linear compression in traditional methods. This allows more information to be contained in a limited dimension, resulting in a significant improvement in encoding density.

[0022] 2. The trajectory of a chaotic attractor exhibits a "butterfly effect" sensitivity; minute differences in initial conditions can lead to significant changes in the trajectory. However, this characteristic actually endows the encoding with stronger robustness—even if some trajectory points are disturbed by noise, the complex structure of the overall trajectory can still remain relatively stable. Furthermore, knowledge encoding does not rely on a single trajectory point, but rather dynamically adjusts the coupling weights between multiple trajectory points and the text vector. Local points affected by noise are "diluted" due to reduced weights, thus maintaining the accuracy of the encoding result even in high-noise environments through the synergistic effect of a large number of effective trajectory points.

[0023] 3. During the encoding process, the system first extracts complexity features through text preprocessing, and then dynamically adjusts the encoding dimension and chaos parameters by combining the Lyapunov exponent of the chaotic trajectory. When processing highly complex professional texts, the system automatically increases the encoding dimension and raises the chaos parameters to accommodate more semantic details; while for simple texts, the system compresses the dimension and lowers the parameters to improve encoding efficiency.

[0024] 4. Through the "chaos-manifold coupling mechanism," word-level, phrase-level, and sentence-level vectors of the text are nonlinearly mapped to chaotic manifold points. Specifically, each text vector is coupled to its corresponding manifold point using a Gaussian kernel function to calculate the coupling weight. The higher the weight of the manifold point, the greater its contribution to the encoding result. This refined matching mechanism can preserve the original semantic features to the maximum extent. At the same time, the high-dimensional expansion of the manifold space can more comprehensively reflect the nonlinear relationships between semantics, thereby strictly controlling the semantic information loss rate to within 2%, achieving high-fidelity representation of knowledge. Attached Figure Description

[0025] Figure 1 This is a schematic diagram illustrating the process principle of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] The following is in conjunction with the appendix Figure 1 This application will be described in further detail.

[0028] See Figure 1 A manifold knowledge encoding method based on chaotic attractors, the method includes the following steps: S1: The input knowledge text is segmented, stop words are removed, and semantic standardization is performed. At the same time, the complexity features of the text are extracted. The preprocessing results will be used as the input of dynamic parameters for subsequent chaotic trajectory generation to ensure that the trajectory generation is initially related to the text characteristics.

[0029] S2: Based on the Lorenz chaotic system: σ=10, ρ=28, β=8 / 3, an initial trajectory is generated. The initial state is randomized by a random seed, which is determined by the preprocessed text hash value. The length of the generated trajectory is consistent with the number of preprocessed text tokens, ensuring that each subsequent encoding step corresponds to a unique trajectory point.

[0030] S3: Calculate the maximum Lyapunov exponent of the initial trajectory, and select trajectory segments with high chaos degree whose exponent is greater than 0.9. The higher the Lyapunov exponent, the stronger the unpredictability of the trajectory and the better the coding diversity. Remove low chaos degree points to avoid coding redundancy. The selected trajectory will serve as the core anchor point of the manifold projection, which directly affects the dynamics of subsequent coding.

[0031] The formula for calculating the manifold embedding function is: f:R³→M 7 ,f(x,y,z)=(x,y,z,x²,y²,z²,xyz); S4: The selected 3D chaotic trajectory points are expanded to a 7-dimensional manifold space using polynomial basis functions {x,y,z,x²,y²,z²,xyz}, forming a manifold point set. The dimension of this manifold space is positively correlated with the text complexity (the higher the complexity, the more the number of extended basis functions can be dynamically increased), providing a nonlinear mapping carrier for subsequent semantic coupling.

[0032] S5: Perform multi-granularity vectorization (including word-level, phrase-level, and sentence-level vectors) on the preprocessed text tokens. Align the vector dimensions with the manifold space dimensions to ensure that the text vectors and manifold points can be directly coupled in the same space. The result of this step will serve as the key input for calculating the coupling weights.

[0033] S6: Based on the Gaussian kernel function wᵢ=exp(-||pᵢ-c||² / 2σ²) / Σⱼexp(-||pⱼ-c||² / 2σ²), the coupling weight between each text vector and the corresponding manifold point is calculated, where pᵢ is the manifold point and c is the text vector. The weight is dynamically adjusted according to the spatial distance between the text vector and the manifold point. The higher the weight of the manifold point, the greater its contribution to the encoding result, thus achieving fine matching between semantics and geometric structure.

[0034] S7: Combining the Lyapunov index and text complexity, dynamically adjust the coding space dimension: If the Lyapunov index is higher than the threshold and the text complexity is high, increase the coding dimension to accommodate more information; otherwise, compress the dimension to improve efficiency. This adjustment directly affects the information density distribution of the final encoding.

[0035] S8: Multiply and sum the results of each manifold point with its corresponding text vector and coupling weight to generate the final chaotic manifold encoding vector. This vector simultaneously contains textual semantic information, geometric structure information, and dynamic adjustment information, achieving a high-fidelity, noise-resistant, and adaptive encoding representation of knowledge.

[0036] The formula for calculating the knowledge coupling weight is: w_i=exp(-||p_i-c||² / 2σ²) / Σjexp(-||p_j-c||² / 2σ²); In step S1, word segmentation can be performed using a rule-based and statistically-based tool. A hybrid stop word list containing both general and domain-specific stop words is used to ensure the filtering of redundant words. Semantic standardization requires lexical reconstruction of the segmentation results and replacement of low-frequency words (e.g., replacing "chaos" with "disordered dynamics") using a thesaurus to improve consistency in subsequent processing. Complexity feature extraction comprises three parts: word frequency distribution is measured by statistically analyzing the frequency of each word and calculating its entropy; semantic density is indicated by the number of different semantic units (e.g., entities, relations) per hundred words; and text length directly affects the number of sampling points for subsequent chaotic trajectories. These three factors together constitute the dynamic parameter input. When the word frequency entropy value is greater than 0.7, the time span for subsequent trajectory generation needs to be extended by 10% to accommodate more dynamic changes.

[0037] In step S2, the fourth-order Runge-Kutta method is used to solve the differential equation, with a fixed time span of 0 to 10 seconds. The number of sampling points is strictly consistent with the number of preprocessed text tokens. The randomization of the initial state is controlled by the text hash value: the preprocessed text is hashed using MD5, and the first 6 digits are used as a random seed to generate a three-dimensional initial value in the range [-5, 5]. This design ensures that the initial state generated by different texts is unique, avoiding encoding duplication. Simultaneously, the fixed seed achieves reproducibility; for example, with the same text input, the generated trajectory is completely identical each time.

[0038] In step S3, the enhanced screening of chaotic trajectory features requires calculating the maximum Lyapunov exponent of the trajectory using the Wolf algorithm. Specifically, 10 consecutive trajectory points are used as windows to calculate the Euclidean distance divergence rate between adjacent points, and the average of all windows is taken as the Lyapunov exponent of that trajectory segment. The screening threshold is set to 0.9; if the exponent of a trajectory segment is lower than 0.9, the first 3 points of that segment are removed.

[0039] In step S4, the high-dimensional cognitive manifold space is constructed based on the selected 3D chaotic trajectory points and expanded to 7 dimensions using polynomial basis functions. Specifically, each 3D point (x, y, z) corresponds to a 7-dimensional vector (x, y, z, x², y², z², xyz), where the squared terms capture the nonlinear characteristics of the trajectory; for example, x² reflects the quadratic change in the x-direction, and the cross term xyz enhances the coupling relationship between different dimensions. If the text complexity is high during preprocessing, expansion terms can be dynamically added to increase the dimensions to 10 dimensions to accommodate more complex semantic information.

[0040] In step S5, word-level vectors are generated using a pre-trained Word2Vec model, phrase-level vectors are extracted using a sliding window (window size 2-3 words) and averaged, and sentence-level vectors use the [CLS] vectors from the BERT-base model. To align with the 7-dimensional manifold space, PCA dimensionality reduction is performed on the three types of vectors respectively. Finally, the 7-dimensional vectors at the word, phrase, and sentence levels are weighted and fused with a weight ratio of 0.3:0.4:0.3 to form the final 7-dimensional text vector. When processing the sentence "chaotic systems have dynamic characteristics," the word-level vectors emphasize "chaos" and "system," the phrase-level vectors emphasize "chaotic system," and the sentence-level vectors emphasize the overall semantics. The fused vectors can comprehensively reflect the multi-granular features of the text.

[0041] In step S6, the dynamic coupling weights are calculated in real time using a Gaussian kernel function, where the σ parameter is dynamically adjusted according to the text complexity: σ = 0.5 when the text complexity is low (semantic density < 10 words / 100 words), and σ = 1.2 when the complexity is high (semantic density > 20 words / 100 words), to balance the influence of local and global factors. Specifically, for each text vector c and its corresponding manifold point pᵢ, the Euclidean distance ||pᵢ-c|| is first calculated, then substituted into the exponential function to obtain the numerator, and finally, softmax normalization is used to ensure that the weight sum is 1.

[0042] In step S7, the adaptive optimization of the encoding space requires dynamic adjustment of the dimensions based on the Lyapunov exponent and text complexity. The specific strategy is as follows: if the Lyapunov exponent > 0.9 and the text complexity is high (semantic density > 20 words / 100 words), the encoding dimension is increased by 2 dimensions (e.g., from 7 to 9 dimensions); if the exponent < 0.8 and the complexity is low (semantic density < 10 words / 100 words), the dimension is reduced by 1 dimension (e.g., from 7 to 6 dimensions); otherwise, the original dimension is maintained. The adjusted dimensions are then remapped to the trajectory points and text vectors through linear interpolation. For example, when the dimension increases from 7 to 9 dimensions, a new dimension is added to fill the higher-order terms of the trajectory points (e.g., x). 4 y 4 This ensures optimal information density.

[0043] In step S8, the dynamic knowledge encoding vector is generated through weighted accumulation. Specifically, for each manifold point pᵢ, text vector cᵢ, and coupling weight wᵢ, wᵢ*pᵢ+cᵢ (the weight term and semantic term are added together) are calculated, and then all results are accumulated to obtain the final encoding vector. To ensure vector stability, the results need to be L2 normalized (i.e., each dimension value is divided by the vector magnitude) to ensure the vector length is uniformly 1. When processing a text containing 100 tokens, the final encoding vector is formed by accumulating 100 weighted terms, which preserves the dynamic characteristics of the chaotic trajectory (from pᵢ) and integrates text semantics (from cᵢ), while normalization avoids the problem of excessively large or small values.

[0044] A manifold knowledge encoding system based on chaotic attractors is proposed, wherein the system uses the aforementioned manifold knowledge encoding method based on chaotic attractors during runtime.

[0045] Example 1: Chaotic Trajectory Generator This embodiment achieves the function of generating dynamic trajectories by encapsulating the solution process of the differential equations of the Lorenz chaotic system. In specific implementation, a ChaoticTrajectoryGenerator class is first defined, and during initialization, the classic parameters of the Lorenz system (σ=10.0, ρ=28.0, β=8.0 / 3) are set. These parameters ensure that the system is in a chaotic state.

[0046] The class contains two core methods: the first is `lorenz_system`, which calculates the instantaneous rate of change of the Lorenz differential equation—taking the current time `t` and the three-dimensional state (x, y, z) as input, and outputting the derivatives (dx / dt, dy / dt, dz / dt) in three dimensions, corresponding to the calculation results of σ(yx), x(ρ-z)-y, and xy-βz, respectively; the second is `generate_trajectory`, which generates specific chaotic trajectories. This method receives the initial state (e.g., (x0, y0, z0)), the time span, and the number of sampling points, calls the `solve_ivp` differential equation solver from the scipy library, integrates within the specified time range, and finally returns a trajectory array of shape (number of time points, 3).

[0047] Example 2: Knowledge Encoder This embodiment implements the encoding function of mapping knowledge text to a chaotic manifold space, relying on the trajectory generator of the previous embodiment. First, the ChaoticKnowledgeEncoder class is defined, which requires a trajectory generator instance and manifold dimension to be passed in during initialization. The core method encode_knowledge includes the following steps: if the user specifies a random seed, it is set through np.random.seed to ensure reproducibility; a three-dimensional random initial state in the range [-5, 5] is generated; The process involves calling a trajectory generator to generate chaotic trajectories with the same number of text segments; vectorizing the text; and coupling chaos with the manifold using the `_couple_chaos_manifold` method: traversing each text vector, sequentially extracting corresponding points from the trajectory (if the trajectory length is insufficient, looping to extract points), expanding the 3D trajectory points into 7-dimensional manifold points, calculating the coupling weight between the text vector and the manifold point, and finally multiplying the weight by the manifold point to obtain the encoding at that position. The encodings of all positions are combined to form the final chaotic manifold encoding vector.

[0048] Example 3: Adaptive Coding Optimizer This embodiment achieves adaptive coding strategy to text complexity by dynamically adjusting chaos parameters. An `AdaptiveChaoticEncoder` class is defined, and a Lyapunov exponent threshold (default 0.9) is set during initialization to determine the degree of chaos in the trajectory.

[0049] The class contains two key methods: `compute_lyapunov_exponent` calculates the maximum Lyapunov exponent of the trajectory. It iterates through the trajectory points, calculates the Euclidean distance between adjacent points, takes the logarithm, and finally averages the results to obtain the exponent value. The `adaptive_encode` method adjusts the encoding strategy based on text complexity: first, it assesses the text complexity, then adjusts the Lorenz system parameters based on the complexity factor to generate the adjusted parameter combination; it creates a `ChaoticTrajectoryGenerator` instance using the new parameters and passes it to `ChaoticKnowledgeEncoder`, finally calling the `encode_knowledge` method to complete the adaptive encoding of the text. When processing highly complex text, the system increases the value of ρ to enhance the chaos of the trajectory, thereby increasing the information capacity of the encoding; when processing simple text, it decreases the parameters to reduce computational complexity.

[0050] From the above, we can conclude that: In this application, by dynamically generating chaotic trajectories and expanding the manifold space in a high dimension, the originally scattered semantic information is embedded into the geometric structure in a more compact manner. The unpredictability of chaotic trajectories and the expansion of the manifold space by polynomial basis functions can more accurately capture the potential correlations between semantics, avoiding the space waste caused by linear compression in traditional methods. This allows more information to be contained in a limited dimension, resulting in a significant improvement in encoding density.

[0051] In this application, the trajectory of the chaotic attractor exhibits a "butterfly effect" sensitivity, where minute differences in initial conditions can lead to significant trajectory changes. However, this characteristic actually endows the encoding with stronger robustness—even if some trajectory points are disturbed by noise, the complex structure of the overall trajectory can still remain relatively stable. Furthermore, knowledge encoding does not rely on a single trajectory point, but rather dynamically adjusts the coupling weights between multiple trajectory points and the text vector. Local points affected by noise are "diluted" due to reduced weights, thus maintaining the accuracy of the encoding result even in high-noise environments through the synergistic effect of a large number of effective trajectory points.

[0052] In this application, during the encoding process, the system first extracts complexity features (such as word frequency distribution and semantic density) through text preprocessing, and then dynamically adjusts the encoding dimension and chaos parameters by combining the Lyapunov exponent of the chaotic trajectory (reflecting the degree of chaos of the trajectory). When processing highly complex professional texts (such as technical documents containing a large number of terms and logical relationships), the system automatically increases the encoding dimension and raises the chaos parameters to accommodate more semantic details; while for simple texts, the system compresses the dimension and lowers the parameters to improve encoding efficiency, ensuring that the encoding method can flexibly adapt to different types of knowledge content.

[0053] In this application, a "chaotic-manifold coupling mechanism" is used to nonlinearly map word-level, phrase-level, and sentence-level vectors of text to chaotic manifold points. Specifically, each text vector is coupled to its corresponding manifold point using a Gaussian kernel function to calculate the coupling weight. The higher the weight of the manifold point, the greater its contribution to the encoding result. This refined matching mechanism can preserve the original semantic features to the greatest extent. At the same time, the high-dimensional extension of the manifold space (such as including square terms and intersection terms) can more comprehensively reflect the nonlinear relationships between semantics, thereby achieving a high-fidelity representation of knowledge.

[0054] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A manifold knowledge encoding method based on chaotic attractors, characterized in that: The method includes the following steps: S1: The input knowledge text is segmented, stop words are removed, and semantic standardization is performed. At the same time, the complexity features of the text are extracted. The preprocessing results will be used as the input of dynamic parameters for subsequent chaotic trajectory generation to ensure that the trajectory generation is initially related to the text characteristics. S2: Based on the Lorenz chaotic system: σ=10, ρ=28, β=8 / 3, an initial trajectory is generated. The initial state is randomized by a random seed, which is determined by the preprocessed text hash value. The length of the generated trajectory is consistent with the number of preprocessed text tokens, ensuring that each subsequent encoding step corresponds to a unique trajectory point. The Lorenz system equations are: dx / dt = σ(yx); dy / dt = x(ρ-z)-y; dz / dt = xy - βz; S3: Calculate the maximum Lyapunov exponent of the initial trajectory, and select trajectory segments with high chaos degree whose exponent is greater than 0.

9. The higher the Lyapunov exponent, the stronger the unpredictability of the trajectory and the better the coding diversity. Remove low chaos degree points to avoid coding redundancy. The selected trajectory will be used as the core anchor point of the manifold projection, which directly affects the dynamics of subsequent coding. The formula for calculating the Lyapunov index is: λ=lim(t→∞)(1 / t)ln(|δx(t)| / |δx0|); S4: The selected 3D chaotic trajectory points are expanded to a 7-dimensional manifold space through the polynomial basis function {x,y,z,x²,y²,z²,xyz} to form a set of manifold points; the dimension of this manifold space is positively correlated with the text complexity, providing a nonlinear mapping carrier for subsequent semantic coupling; S5: Perform multi-granularity vectorization on the preprocessed text tokens, aligning the vector dimension with the manifold space dimension to ensure that the text vectors and manifold points can be directly coupled in the same space. The result of this step will serve as the key input for calculating the coupling weight. S6: Based on the Gaussian kernel function wᵢ=exp(-||pᵢ-c||² / 2σ²) / Σⱼexp(-||pⱼ-c||² / 2σ²), the coupling weight between each text vector and the corresponding manifold point is calculated, where pᵢ is the manifold point and c is the text vector. The weight is dynamically adjusted according to the spatial distance between the text vector and the manifold point. The higher the weight of the manifold point, the greater its contribution to the encoding result, thus achieving fine matching between semantics and geometric structure. S7: Combining the Lyapunov index and text complexity, dynamically adjust the coding space dimension: If the Lyapunov index is higher than the threshold and the text complexity is high, increase the coding dimension to accommodate more information; otherwise, compress the dimension to improve efficiency. This adjustment directly affects the information density distribution of the final encoding. S8: Multiply and sum each manifold point with its corresponding text vector and coupling weight to generate the final chaotic manifold encoding vector; this vector simultaneously contains textual semantic information, geometric structure information and dynamic adjustment information, realizing a high-fidelity, noise-resistant and adaptive encoding representation of knowledge.

2. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S1, the word segmentation operation can be performed using a word segmentation tool that combines rules and statistics. The stop word list is a hybrid list that includes general stop words and domain-specific stop words to ensure that redundant words are filtered out. Semantic standardization processing requires word form restoration of the word segmentation results and replacement of low-frequency words with a thesaurus to improve the consistency of subsequent processing. Complexity feature extraction specifically includes three parts: word frequency distribution is measured by statistically analyzing the frequency of each word and calculating the entropy value; semantic density is measured by the number of different semantic units per hundred words; and text length directly affects the number of sampling points for subsequent chaotic trajectories. The three together constitute the dynamic parameter input.

3. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S2, the fourth-order Runge-Kutta method is used to solve the differential equation. The time span is fixed at 0 to 10 seconds, and the number of sampling points is strictly consistent with the number of preprocessed text tokens. The randomization of the initial state is controlled by the text hash value: the preprocessed text is hashed using MD5, and the first 6 digits are taken as a random seed to generate a three-dimensional initial value in the range of [-5, 5]. This design ensures that the initial state generated by different texts is unique, avoids encoding duplication, and achieves reproducibility through a fixed seed.

4. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S3, the enhanced screening of chaotic trajectory features requires calculating the maximum Lyapunov exponent of the trajectory using the Wolf algorithm. Specifically, 10 consecutive trajectory points are used as windows to calculate the Euclidean distance divergence rate between adjacent points, and the average value of all windows is taken as the Lyapunov exponent of the trajectory segment. The screening threshold is set to 0.

9. If the exponent of a certain trajectory segment is lower than 0.9, the first 3 points of that segment are removed.

5. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S4, the high-dimensional cognitive manifold space is constructed based on the selected 3D chaotic trajectory points and extended to 7 dimensions through polynomial basis functions. The specific extension rule is as follows: each 3D point (x,y,z) corresponds to a 7-dimensional vector (x,y,z,x²,y²,z²,xyz), where the squared terms are used to capture the nonlinear characteristics of the trajectory, such as x² reflecting the quadratic change in the x direction, and the cross terms xyz enhancing the coupling relationship between different dimensions. If the text complexity is high during the preprocessing stage, extension terms can be dynamically added to increase the dimension to 10 dimensions to accommodate more complex semantic information.

6. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S5, word-level vectors are generated using a pre-trained Word2Vec model, phrase-level vectors are extracted using a sliding window and averaged, and sentence-level vectors are generated using the [CLS] vectors from the BERT-base model. To align with the 7-dimensional manifold space, PCA dimensionality reduction is performed on the three types of vectors respectively. Finally, the 7-dimensional vectors of word-level, phrase-level, and sentence-level vectors are weighted and fused with a weight of 0.3:0.4:0.3 to form the final 7-dimensional text vector.

7. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S6, the dynamic coupling weights are calculated in real time using a Gaussian kernel function, where the σ parameter is dynamically adjusted according to the text complexity: σ = 0.5 when the text complexity is low and σ = 1.2 when the complexity is high, in order to balance the influence of local and global factors. In the specific calculation, for each text vector c and the corresponding manifold point pᵢ, the Euclidean distance ||pᵢ-c|| is first calculated, then substituted into the exponential function to obtain the numerator, and finally the softmax normalization is used to ensure that the weight sum is 1.

8. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S7, the adaptive optimization of the encoding space needs to dynamically adjust the dimension by combining the Lyapunov index and the text complexity. The specific strategy is as follows: if the Lyapunov index is >0.9 and the text complexity is high, the encoding dimension is increased by 2 dimensions; if the index is <0.8 and the complexity is low, the dimension is reduced by 1 dimension; otherwise, the original dimension is maintained.

9. The manifold knowledge encoding method based on chaotic attractors according to claim 1, characterized in that: In step S8, the dynamic knowledge encoding vector is generated through weighted accumulation. Specifically, for each manifold point pᵢ, text vector cᵢ, and coupling weight wᵢ, wᵢ*pᵢ+cᵢ is calculated, and all results are accumulated to obtain the final encoding vector. To ensure vector stability, the results need to be L2 normalized to make the vector length uniform to 1.

10. A manifold knowledge encoding system based on chaotic attractors, characterized in that: The system uses the manifold knowledge encoding method based on chaotic attractors as described in any one of claims 1 to 9 during operation.

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