A multi-task neural network evaluation and analysis method based on bell inequality test

Abstract

This invention discloses a method for evaluating and analyzing multi-task neural networks based on Bell's inequality test, belonging to the field of artificial intelligence and deep learning technology. This method constructs a non-classical network model, NCnet, mapping task combinations in the multi-task learning process to a Bell-like measurement setting, defining a task prediction consistency index, and constructing a CHSH statistic S based on the correlation of different task combinations. Through the calculation and analysis of the S value, a quantitative evaluation of the model's internal task interaction, parameter sharing conflicts, and generalization ability is achieved. Simultaneously, a low-rank adaptive fine-tuning mechanism is introduced to regulate the model capacity, establishing a correlation between the S value and the model capacity and performance. This invention can reveal non-classical correlation characteristics in multi-task learning from the statistical behavior of model output, providing a basis for model structure design, capacity selection, and optimization.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of artificial intelligence, deep learning and natural language processing, and specifically relates to an innovative analytical framework and quantitative indicators for evaluating the internal task interaction, representation sharing ability, generalization performance and model capacity matching degree of large language models in multi-task learning scenarios. Background Technology

[0002] In recent years, driven by the coordinated growth in parameter scale, data scale, and computing resources, deep neural networks, represented by Transformers, have achieved rapid development, and their general-purpose capabilities have continued to improve. Large-scale language models have shown significant advantages in natural language understanding, generation, reasoning, and cross-task transfer, gradually becoming an important foundation for various downstream applications. However, the rapid enhancement of model capabilities has also made reliable model evaluation an increasingly prominent challenge. On the one hand, traditional evaluation paradigms mainly rely on single-task benchmark tests and performance metrics, and improved scores do not necessarily reflect an enhancement in the model's true capabilities. On the other hand, with the continuous changes in application scenarios, evaluation often relies on performance after fine-tuning or instruction alignment. More importantly, these metrics can usually only describe the statistical structure of each task itself.

[0003] The aforementioned limitations highlight the inadequacy of existing evaluation systems when facing general intelligent systems. In practical applications, models often need to share representations and perform joint optimization across multiple related or heterogeneous tasks. Their performance depends not only on the optimality of individual tasks but also on the significant impact of interactions between tasks, parameter sharing methods, and training dynamics. Therefore, true general capability is not only reflected in high scores on isolated tasks but also in the model's ability to flexibly reorganize learned knowledge and strategies under constantly changing task requirements. This requirement is highly consistent with the core concept of Artificial General Intelligence (AGI), which emphasizes that general intelligent agents should have the ability to dynamically transfer between different tasks and their combinations. In such transfer processes, models typically need to undergo partial retraining (i.e., parameter fine-tuning) to adapt to new tasks or task configurations. Therefore, developing evaluation methods that can reflect the comprehensive behavior of models in multi-task interactions, resource sharing, and dynamic adaptation has become a key link in promoting the evolution of large models towards general intelligence.

[0004] From a fine-tuning perspective, when a model is adapted to different tasks, its parameter space often exhibits systematic differences. This indicates that each fine-tuned model actually represents a different "measurement context" within the same semantic space. However, these contexts do not necessarily share a common "global parameter solution" that can be satisfied simultaneously. On the one hand, the constraints (loss functions) of different tasks on representation and decision boundaries may conflict with each other in the shared parameter dimension, making optimization updates for one task inevitably weaken the adaptability to another task. On the other hand, even if a model performs well on its respective task, it may not induce a set of predictive statistics that can be consistently explained by the same joint distribution for all tasks, making it difficult to provide a unified probability description that is compatible with each other. This leads to multiple probabilistically incompatible predictive distributions. This phenomenon forms a natural analogy with measurement incompatibility in quantum physics: in quantum systems, non-commutative observables cannot be simultaneously determined, leading to violations of certain classically satisfiable constraints, such as Bell's inequality. It is precisely this incompatibility that forms the basis of Bell's inequality theory, revealing structures in systems that transcend the classical framework.

[0005] It is worth noting that the nonclassical correlations characterized by Bell's inequality are essentially a property of joint statistics regarding observations. In recent years, machine learning techniques have also provided a new analytical paradigm for the study of nonclassical correlations. Tamás Kriváchy et al. verified the non-locality of quantum networks as a nonclassical correlation property by reconstructing classical strategies using neural networks, while Zhang et al. established a nonclassical correlation detection framework using stacked deep neural networks and a three-local network. These studies demonstrate that neural networks have unique advantages in modeling and identifying nonclassical statistical features. However, existing research mainly focuses on the quantum system itself, and its method design and evaluation objectives still rely on specific physical structure assumptions, failing to answer a more general question: Can nonclassical statistics be used in reverse to analyze and evaluate complex systems (neural networks) themselves? Can the statistics in Bell's inequality family be used to detect the emergence of nonclassical features from the external output of the model and use them as an indicator to evaluate the performance of large-scale models? Therefore, a new evaluation method that deeply reveals the internal dynamics of deep networks is urgently needed. Summary of the Invention

[0006] This invention aims to address the problems of existing multi-task neural network evaluation methods, such as the single evaluation dimension, difficulty in characterizing the interaction relationship between tasks, and inability to reveal the internal dynamic mechanism of the model. It provides a multi-task neural network performance evaluation and analysis method based on Bell's inequality test.

[0007] This invention introduces CHSH statistics from quantum physics to establish an evaluation framework that quantifies potential cooperative relationships, competitive relationships, and parameter sharing conflicts among multiple tasks based on external model predictions, thus overcoming the limitations of traditional evaluations based on single-task accuracy metrics. Simultaneously, by constructing a multi-task neural network model with a shared structure and mapping different task combinations to measurement settings similar to Bell's experiments, this invention reveals the non-classical statistical characteristics of the model during multi-task learning caused by resource competition and parameter coupling. Furthermore, this invention incorporates a model capacity control mechanism, introducing a low-rank adaptive fine-tuning method to achieve precise control over the model parameter size and establishes a correlation between CHSH statistics and model capacity and generalization performance, thereby providing theoretical basis and engineering guidance for model structure design, capacity selection, and training strategy optimization.

[0008] To achieve the above objectives, this invention provides a multi-task neural network performance evaluation method based on Bell's inequality test. The overall process includes steps such as multi-task learning model construction, task mapping, result quantification, statistical analysis, and capacity adjustment, as detailed below: 1. A multi-task neural network evaluation method based on Bell's inequality test, the evaluation method being based on a neural network, comprising the following steps: S1. Construct a multi-task learning model, divide multiple tasks into at least two task sets, and map different task combinations to measurement settings in a Bell experiment-like manner, where each task set corresponds to a measurement basis, thereby establishing the correspondence between multi-task learning and Bell experiment; S2. Train the multi-task learning model and obtain the prediction results of each task on the input samples; based on the consistency between the prediction results and the true labels, construct the task measurement results of binary variables; S3. For different task combinations, calculate the mathematical model of the correlation between task measurement results; S4. After obtaining the linear combination of the correlation mathematical models of four different task combinations, construct the CHSH statistic S to comprehensively characterize the overall correlation characteristics of the system; S5. Evaluate and analyze the task interaction relationship, parameter sharing conflict, and generalization ability of the multi-task learning model based on the CHSH statistic S.

[0009] Furthermore, the multi-task learning model includes an input layer, a shared hidden layer, and two output nodes, corresponding to the two task ends in the multi-task learning process. The input layer receives multi-dimensional input variables, which are then transformed into nonlinear features by the shared hidden layer and output to the two task branches respectively. The shared hidden layer contains at least one shared neuron to achieve parameter coupling between different tasks. The two output nodes correspond to the first task end and the second task end respectively, and their output results are used to represent the prediction results of the corresponding tasks, thereby constituting the multi-task learning model structure.

[0010] The binary variable is set to +1 when the model prediction result matches the true label, and -1 otherwise.

[0011] Furthermore, the correlation mathematical model is obtained by statistically averaging the measurement results of all test samples.

[0012] Furthermore, when the CHSH statistic S is greater than a preset threshold, it is determined that there is a non-classical task correlation in the neural network.

[0013] Furthermore, the neural network is a non-classical network NCnet built based on an XOR structure.

[0014] Furthermore, the present invention also includes fine-tuning the model parameters through a low-rank adaptive method to regulate the model capacity.

[0015] Furthermore, the CHSH statistic S is used to guide the selection of multi-task learning model capacity and the optimization of multi-task training strategies.

[0016] Compared with the prior art, the present invention has the following beneficial effects: A multi-task learning model evaluation method based on non-classical statistics is proposed, which breaks through the limitations of traditional single-task indicators and significantly improves the richness of evaluation dimensions. It can reveal the collaborative and competitive relationships between tasks from the model output level, and realize the quantitative analysis of parameter sharing conflicts; By introducing the CHSH statistic, we can indirectly observe and analyze the dynamic mechanism inside the model, thereby improving the interpretability of the model. By combining the model capacity control mechanism, a correlation between evaluation indicators and model performance was established, which can be used to guide model structure optimization and resource allocation; It is suitable for various neural network architectures and multi-task scenarios, and has good versatility and engineering application value. Attached Figure Description

[0017] Figure 1The diagram shows the non-classical network model NCnet constructed based on the XOR structure in this invention; where (a) represents the XORnet network; and (b) represents the NCnet network. Figure 2 This is a schematic diagram of independent information flow under the NCnet framework.

[0018] Figure 3 This is a schematic diagram of information flow coupling under the NCnet framework.

[0019] Figure 4 Evolution and distribution of CHSH statistics under different hidden layer sizes with data_type=1 configuration. Figure 5 The results of 50 independent repeated experiments with data_type=1 under the configuration of hidden layer neurons with H=3.

[0020] Figure 6 Evolution and distribution of CHSH statistics under different hidden layer sizes with data_type = 2 configuration.

[0021] Figure 7 Evolution and distribution of CHSH statistics under different hidden layer sizes with data_type = 3 configuration. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0023] like Figure 1 The diagram shown is a schematic of NCnet, a non-classical network model constructed based on the XOR structure in this invention.

[0024] 1. Multi-task learning model construction and task mapping: A multi-task neural network with a shared parameter structure is constructed, enabling multiple tasks to jointly learn within the same model. Different tasks share some network layers to reuse feature representations. The multi-task is divided into at least two task sets, and different task combinations are mapped to measurement settings similar to Bell experiments, where each task set corresponds to a measurement basis, thus establishing a correspondence between multi-task learning and Bell experiments. In a preferred embodiment, a non-classical network model NCnet based on an XOR structure is constructed. Parameter coupling between different tasks is achieved through shared hidden layer neurons, thereby providing a structural basis for the generation of non-classical statistical behavior.

[0025] The multi-task learning model comprises an input layer, a shared hidden layer, and two output nodes, corresponding to the two task ends in multi-task learning. The input layer receives multi-dimensional input variables, which undergo nonlinear feature transformation by the shared hidden layer before being output to the two task branches. The shared hidden layer contains at least one shared neuron to achieve parameter coupling between different tasks. The two output nodes correspond to the first and second task ends, respectively, and their outputs represent the prediction results for the corresponding tasks, thus forming the basic structure of multi-task learning. Figure 1 This is a schematic diagram of the overall system configuration and signal flow according to an embodiment of the present invention.

[0026] The multi-task learning model of this invention employs a non-classical network based on the XOR structure. To visually demonstrate the non-classical statistical features that may appear in neural networks, this invention constructs a non-classical network (NCnet) based on the XOR network. The multi-task learning model of this invention fuses two XOR networks by sharing neurons in the intermediate hidden layer, forming NCnet. In summary, NCnet is a multilayer perceptron (MLP) containing only one layer of hidden neurons. NCnet has multiple input nodes. to After nonlinear feature transformation in the hidden layer, two decision results are output, corresponding to the observation outputs at Alice and Bob's ends, respectively. Referring to the Bell inequality experiment setup, this invention defines a classification task at Alice's end. Defined on Bob's side The tasks are implemented by top-level neurons a in the Alice end and top-level neurons b in the Bob end, respectively; different task combinations correspond to different measurement basis choices in the Bell inequality Bell experiment. A core feature of NCnet is that its hidden layers contain one or more neurons shared by the Alice and Bob ends. This shared structure is the key region where gradient competition occurs.

[0027] like Figure 2 and Figure 3 The diagrams shown illustrate the independent and coupled information flow states within the NCnet framework, respectively. In the independent information flow state, the computational paths between different tasks are independent, with minimal shared parameters and no significant interference between tasks. In the coupled information flow state, different tasks interact through shared hidden neurons, leading to gradient competition or collusion during model training, thus affecting overall performance. This invention introduces a shared structure, enabling the model to exhibit different statistical behaviors under different task combinations, providing a foundation for subsequent non-classical analysis.

[0028] Prediction Result Quantification and Measurement Variable Definition: A test sample is input into the trained multi-task neural network model, and the prediction results for each task are obtained. The model's prediction results are compared with the true labels, and a consistency indicator is defined as the measurement result variable. The value is +1 when the prediction result matches the true label, and -1 otherwise. In this way, continuous or discrete model outputs are uniformly mapped to binary measurement results, thereby constructing an observation variable system suitable for statistical analysis. In this embodiment, the multi-task learning process is mapped to a Bell experiment-like process, with different task combinations corresponding to different measurement settings. For each task combination, after inputting the test sample, the prediction results for both tasks are obtained, and the prediction results are compared with the true labels. When the prediction result matches the true label, the measurement result is defined as +1; otherwise, it is defined as -1, thus converting the model output into a binary measurement variable.

[0029] Correlation function and CHSH statistic construction. Based on the aforementioned measurement outcome variables, correlation functions are calculated for different task combinations. These functions are obtained by averaging the products of the measurement outcomes in the sample set. After obtaining the correlation functions for four different task combinations, a CHSH statistic S is constructed to comprehensively characterize the overall correlation characteristics of the system. When the statistic S exceeds a preset threshold, it indicates the existence of non-classical correlation features in the model, reflecting coupling relationships between tasks that cannot be explained by the classical independent model. Wherein: Correlation function construction: For different task combinations, a correlation function is constructed based on the corresponding measurement result variables to characterize the statistical association between different tasks. The correlation function is obtained by statistically averaging the measurement results across all test samples, thus reflecting the strength of the association between the task combinations in the overall sample space. In a preferred embodiment, when the measurement variables satisfy the conditions of zero mean and unit variance, the correlation function can be equivalent to the Pearson correlation coefficient.

[0030] CHSH Statistic Construction and Non-Classical Determination: Based on the correlation functions of four different task combinations, a CHSH statistic S is constructed to comprehensively characterize the overall correlation structure in a multi-task system. When the CHSH statistic S exceeds a preset threshold, non-classical correlation characteristics are determined to exist in the model, indicating that the statistical relationships between different tasks cannot be explained by a unified classical joint distribution. By analyzing the numerical changes of the CHSH statistic S, the synergistic enhancement effect or resource competition effect between tasks during multi-task learning can be identified, thereby revealing the dynamic mechanism within the model.

[0031] This invention formally defines the prediction results of NCnet and establishes its mapping relationship with the Bell experiment. Considering the prediction behavior of NCnet when performing the above four tasks, the measurement results of the tasks are defined as follows: When Alice performs a task ( When ), if its prediction result With real labels If consistent, then define a consistency indicator. ;otherwise Similarly, when Bob performs a task... At that time, if its prediction result With real labels Consistent, then ;otherwise .

[0032] This invention introduces the CHSH statistic S as a core evaluation indicator. CHSH statistic It is a comprehensive scalar indicator that integrates correlation information from four individuals across different task combinations. Its definition is as follows: In fact, if random variables and If the mean of all values ​​is 0 and the standard deviation of all values ​​is 1, then their correlation is... The calculation formula degenerates into the Pearson correlation coefficient. .

[0033] If the experimental results satisfy This indicates the existence of non-classical associations in the system, which cannot be explained by any local latent variable model. Furthermore, to apply this invention to more complex real-world models (such as large language models), this invention employs efficient parameter fine-tuning techniques such as low-rank adaptive (LoRA) to systematically adjust the model capacity.

[0034] This invention allows for fine-tuning of the total number of trainable parameters in a model by changing the rank *r* of the LoRA matrix, thereby studying the impact of model capacity variations on the CHSH statistic *S* and its generalization performance. In this scenario, the CHSH statistic *S* itself serves as a core evaluation metric, revealing the task coupling strength and internal dynamics of the model under different capacity configurations.

[0035] Statistical characteristic analysis (combined with experimental results). For example... Figure 4 As shown, under the first type of data configuration, with the increase of the hidden layer size, the CHSH statistic S shows a gradual changing trend and tends to stabilize within a certain range. Figure 5 As shown, under a fixed hidden layer size, the distribution of the statistic S can be observed through multiple independent experiments, verifying the stability and repeatability of the method. Figure 6 and Figure 7As shown, under different data type configurations, the CHSH statistic S exhibits different evolutionary patterns with the model size, reflecting the impact of different task complexities on the internal dynamics of the model.

[0036] Model Capacity Adjustment and Performance Correlation Analysis: To further analyze the internal dynamics and resource allocation mechanism of the model, a model capacity adjustment method is introduced, using efficient parameter fine-tuning techniques to adjust the model structure. In the preferred embodiment, a low-rank adaptive method is employed, introducing a low-rank matrix into the model parameters and finely controlling the scale of trainable parameters by changing its rank value. Under different capacity configurations, the above training and evaluation process is repeated to obtain the corresponding CHSH statistic S and model performance indicators. By analyzing the trend of CHSH statistic S with model capacity, its correlation with model generalization performance is established, thereby determining the optimal model capacity configuration.

[0037] Model capacity adjustment and optimization process. In this embodiment, a low-rank adaptive method is introduced to adjust the model capacity. This is achieved by introducing a low-rank matrix structure into the model parameters and changing its rank value. Model training and statistical calculation are repeated under different capacity configurations, and the corresponding CHSH statistics S and model performance indicators are recorded. By analyzing the trend of the statistic S with model capacity, the task coupling strength of the model under different resource configurations can be identified. When the statistic S reaches its maximum value or tends to stabilize, the optimal capacity configuration of the model can be determined, thereby avoiding excessive parameter search.

[0038] Application of evaluation results: The analysis results based on the CHSH statistic S can be used to guide the structural design of multi-task learning models, the selection of parameter sharing strategies, and the optimization of the training process.

[0039] Example 1 The evaluation framework of this invention can be applied to more complex and realistic scenarios to guide the fine-tuning and optimization of large models.

[0040] Base Model and Task Selection: The widely used Multilingual BERT (mBERT) is selected as the base model. A multi-task dataset is constructed, containing two typical scenarios: Scenario 1 (Multilingual Task): Using different language variants of the PAWS-X dataset (such as English, French, and German), the task difficulty is relatively balanced.

[0041] Scenario 2 (Hybrid Reasoning Task): Combining tasks such as SST-2 (sentiment analysis), CommonsenseQA (common sense question answering), MRPC (semantic equivalence judgment), and MathQA (mathematical problem solving), these tasks differ significantly in semantic complexity and required reasoning ability.

[0042] Model Architecture and Capacity Tuning: A multi-task learning architecture with hard parameter sharing is adopted, that is, all Transformer encoding layers are shared, and an independent task head is attached to each task. To finely tune the effective capacity of the model, a low-rank adaptive (LoRA) technique is used, injecting trainable low-rank matrices into the Query and Value projection matrices of the self-attention module. The LoRA rank r is systematically set to a series of values ​​(e.g., r∈{1,2,4,8,16,32,64,128,512}).

[0043] Multi-task training process: For each rank r, a multi-task learning strategy is used to train the model. In each training batch, a combination of tasks (corresponding to a measurement basis pair in the CHSH experiment) is randomly sampled for joint optimization. The training process follows standard deep learning practices, including learning rate scheduling and early stopping.

[0044] Performance and S-score evaluation: On the validation set, the following evaluation is performed for each trained model: For each task combination (e.g.) ), traverse the validation set samples, and determine the correctness of the prediction based on whether it is correct or not. The value is (+1 / -1).

[0045] Calculate four correlation functions And the final CHSH statistic S.

[0046] Results Analysis and Engineering Decisions: Mechanism Analysis: Comparing the results of the two scenarios. In Scenario 1, where task difficulty is balanced, the S-value smoothly approaches 2 as r increases; however, in Scenario 2, where task difficulty varies significantly, the S-value peaks at a low rank (e.g., r=2) and exceeds 2, then decreases. This verifies the "resource contention hypothesis," which states that optimization conflicts between tasks are the key driver of nonclassicality.

[0047] Engineering Guidance: Plot the curves of S-value and average accuracy as a function of rank r. A strong positive correlation is observed between the two. In actual production, engineers can use the method of this invention: starting with a low rank (e.g., r=1), gradually increase the rank and calculate the corresponding S-value. When the S-value reaches its highest point or stabilizes near 2 for the first time, stop increasing the rank, considering that the optimal capacity configuration for the current task set has been found. This method avoids expensive grid search and achieves efficient and intelligent model tuning.

[0048] Through the implementation of the above two stages, this invention not only theoretically reveals the non-classical dynamics inside deep neural networks, but also transforms them into a set of practical tools, providing a brand-new solution for evaluation, analysis and optimization in the era of large models.

[0049] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural modifications made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A multi-task neural network evaluation method based on Bell's inequality test, wherein the evaluation method is based on a neural network, characterized in that, Includes the following steps: S1. Construct a multi-task learning model, divide multiple tasks into at least two task sets, and map different task combinations to measurement settings in a Bell experiment-like manner, where each task set corresponds to a measurement basis, thereby establishing the correspondence between multi-task learning and Bell experiment; S2. Train the multi-task learning model and obtain the prediction results of each task on the input samples; based on the consistency between the prediction results and the true labels, construct the task measurement results of binary variables; S3. For different task combinations, calculate the mathematical model of the correlation between task measurement results; S4. After obtaining the linear combination of the correlation mathematical models of four different task combinations, construct the CHSH statistic S to comprehensively characterize the overall correlation characteristics of the system; S5. Evaluate and analyze the task interaction relationship, parameter sharing conflict, and generalization ability of the multi-task learning model based on the CHSH statistic S.

2. The method according to claim 1, characterized in that, The multi-task learning model includes an input layer, a shared hidden layer, and two output nodes, which correspond to the two task ends in the multi-task learning process, respectively. The input layer receives multi-dimensional input variables, which are then transformed by the shared hidden layer using nonlinear features and output to the two task branches, respectively. The shared hidden layer contains at least one shared neuron to achieve parameter coupling between different tasks; the two output nodes correspond to the first task end and the second task end respectively, and their output results are used to represent the prediction results of the corresponding tasks, thereby forming a multi-task learning model structure.

3. The method according to claim 1, characterized in that, The binary variable is set to +1 when the model prediction result matches the true label, and -1 otherwise.

4. The method according to claim 1, characterized in that, The correlation mathematical model is obtained by statistically averaging the measurement results of all test samples.

5. The method according to claim 1, characterized in that, When the CHSH statistic S is greater than a preset threshold, it is determined that there is a non-classical task correlation in the neural network.

6. The method according to claim 1, characterized in that, The neural network is a non-classical network NCnet built based on an XOR structure.

7. The method according to claim 1, characterized in that, It also includes fine-tuning the model parameters through low-rank adaptive methods to adjust the model capacity.

8. The method according to claim 1, characterized in that, The CHSH statistic S is used to guide the selection of multi-task learning model capacity and the optimization of multi-task training strategies.

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