Intelligent accounting optimization method based on meta-heuristic algorithm and CNN

CNN-based multi-modal accounting feature extraction

We propose a CNN-based multi-modal accounting feature extraction method to deepen our understanding of accounting information and enhance method accuracy. Accounting data, comprising raw numbers, letters, and special symbols, is structured as “documents, vouchers, accounts, statements” during accounting events. These records capture objective observations and essential facts, utilizing distinct symbols to differentiate and identify various types of information. These symbols encompass quantitative numerical data and qualitative non-numerical data, forming the foundation of accounting information. Therefore, this study focuses on extracting multi-modal features from accounting information, encompassing commonly used documents, vouchers, and statements in accounting practices, as illustrated in Fig. 2.

In the accounting data processing workflow, accounting data primarily refers to the original data reflecting the increase and decrease in funds during the execution of production and business activities or budget plans. It also covers a series of objective facts that do not directly involve changes in funds but must be recorded and reflected in accounting. These data originate from diverse sources and exhibit various types, characterized by their systematic, periodic, and continuous nature and their high reuse value. Given these unique properties, this article employs an optimized CNN technique to extract features from accounting data. Using CNN, valuable feature information is extracted from vast amounts of accounting data. These feature representations can reflect the complex structure and inherent relationships within accounting data, providing robust support for subsequent accounting analysis and forecasting. This article integrates a location enhancement module to explicitly model each textual element to enhance the even treatment of data sections and contextual backgrounds in current methods.The sequence of attention maps generated by the text detection recognizer is denoted by h_attn ∈ ℝ^T×H×W, where T is the maximum sequence length. Since the text length of different accounting images differs, the original attention map may be misleading due to attention drift. Therefore, this article adopts compression and expansion strategies to solve these problems. Denote the length of a character sequence as L, which ${\mathrm{h}}_{\text{attn}}^{\mathrm{j}}$ represents the attention map corresponding to the j-th text character. Since the text length varies from image to image, ${\left\{{\mathrm{h}}_{\text{attn}}^{\mathrm{j}}\right\}}_{\mathrm{j}=1}^{\mathrm{L}}$ can be obtained by selecting the previous L effective attention map. Then, concatenate them, using a maximum operator to reduce the channel dimension to 1. The result is denoted by h_score: (1)${\displaystyle {\mathrm{h}}_{\text{score}}=\mathrm{Max}\left(\text{Concat}\left({\mathrm{h}}_{\text{attn}}^1,\dots ,{\mathrm{h}}_{\text{attn}}^{\mathrm{L}}\right)\right).}$

Use the C convolution kernel to upsample h_score, and use the Softmax function to obtain the result h_pos: (2)${\displaystyle {\mathrm{h}}_{\mathrm{pos}}=\text{Softmax}\left(\text{Conv}\left({\mathrm{h}}_{\text{score}}\right)\right).}$

The mean and variance contain the information of the image. To facilitate the subsequent registration between the image and the text, we perform instance normalization for X_I, to make the focus of the image more prominent. The normalized features are multiplied with h_pos to obtain position-enhanced features X_pos: (3)${\displaystyle {\mathrm{X}}_{\mathrm{pos}}=\mathrm{IN}\left({\mathrm{X}}_{\mathrm{I}}⨂{\mathrm{h}}_{\mathrm{pos}}\right)}$

The key to the fusion of visual and semantic features is the registration of character regions rather than the attention to background, so feature selection technology is crucial. Instead of manual labelling and individual scoring methods, we can consider using easy-to-obtain attention maps for feature selection. Since pixel-wise character confidence is included in h_score, the one with the highest score in h_score is selected, resulting in the foreground coordinate set F: (4)${\displaystyle \mathrm{F}:=\left(\mathrm{m},\mathrm{n}\right):{\mathrm{h}}_{\text{score}}\left(\mathrm{m},\mathrm{n}\right)\in \text{TopK}\left({\mathrm{h}}_{\text{score}}\right).}$

Next, we use the coordinate set F as an index to collect the foreground character features in X_pos. To avoid loss of neighborhood information, a pixel-to-region strategy is used before collection, where each index pixel is representative of its neighbourhood by weighted summation of local regions: (5)${\displaystyle {\mathrm{X}}_{\mathrm{pos}}^{\prime }=\sum _{\left(△\mathrm{m},△\mathrm{n}\right)\in \mathrm{N}}\omega \left(△\mathrm{m},△\mathrm{n}\right){\mathrm{X}}_{\mathrm{pos}}\left(\mathrm{m}+△\mathrm{m},\mathrm{n}+△\mathrm{n}\right).}$ where N represents the neighborhood displacement and ω(⋅, ⋅) represents the weight of each displacement. Finally, the coordinate pair in F can index ${\mathrm{X}}_{\mathrm{pos}}^{\prime }$ to obtain the selected feature ${\mathrm{X}}_{\mathrm{S}}={\mathrm{X}}_{\mathrm{pos}}^{\prime }\left(\mathrm{i},\mathrm{j}\right)\left(\mathrm{i},\mathrm{j}\right)\in \mathrm{F}$.

When dealing with documents and vouchers in accounting information, we implement multimodal information extraction by embedding keyword fuzzy matching and the Levenshtein distance algorithm. After extracting information from different modalities, such as text, tables, and images, the system needs to integrate these pieces of information. During the integration process, it is crucial to ensure the accuracy and completeness of the information while also considering the correlations and logical relationships between different modalities. We further embed sequential reconstruction methods for information extraction for complex or specialised accounting documents and vouchers.

Accounting quality assessment methods for accounting

The accounting quality evaluation method for accounting can further evaluate the accounting quality of enterprises by using the obtained features X_S, and provide standards for improving the accounting ability of enterprises.

To solve the problems of local minimization and over-fitting of multi-modal features X_S. We use the Adaboost ensemble learning model to optimize the evaluation results for the accounting objectives of enterprise accounting. The model performs the regression task by weighted combination of multiple weak learners. Firstly, a series of individual learners are generated, and then a suitable combination strategy is used to integrate them into a stronger learner, as shown in Fig. 3.

We employ a sequential structure to link multiple homogeneous weak classifiers, enhancing classifier stability and accuracy. The final learning outcome hinges on effectively combining the classification results from these weak classifiers. Central to our approach is the method for generating diverse weak classifiers. We achieve this by iteratively adjusting the sample weights and increasing focus on previously misclassified samples during subsequent training iterations. After completing all iterations, weights are assigned to each weak classifier based on its classification error rate, ensuring those with lower errors receive greater weights. Ultimately, these weighted weak classifiers are aggregated to form a robust learner with improved predictive accuracy.

If the data quality feature training set sample is X, and its corresponding quality class is w. The weight distribution for high-quality data is initialized, assigning equal weights w_i to each training sample. Perform m iterations, train each weak classifier in turn, select the weights of the weak classifier decision tree B_m(x) to train the quality feature data, and calculate the error rate e_m of the weak classifier at each iteration: (6)${\displaystyle {\mathrm{e}}_{\mathrm{m}}=\frac{\sum _{\mathrm{N}=1}^{\mathrm{Q}}{\mathrm{w}}_{\mathrm{i}}^{\left(\mathrm{m}\right)}\mid \left({\mathrm{c}}_{\mathrm{i}}\ne \mathrm{B}\left({\mathrm{x}}_{\mathrm{i}}\right)\right)}{\sum _{\mathrm{N}=1}^{\mathrm{Q}}{\mathrm{w}}_{\mathrm{i}}^{\left(\mathrm{m}\right)}}.}$

Calculate the weights α_m for the weak classifier B_m(x): (7)${\displaystyle {\alpha }_{\mathrm{m}}=\frac{1}{2}ln\frac{1-{\mathrm{e}}_{\mathrm{m}}}{{\mathrm{e}}_{\mathrm{m}}}.}$

Iterate until m is equal to the set number of iterations M, and the final strong classifier G(x) is obtained by weighting the sum of each weak classifier: (8)${\displaystyle \mathrm{G}\left(\mathrm{x}\right)=sin\left[\sum _{\mathrm{m}=1}^{\mathrm{M}}{\alpha }_{\mathrm{m}}{\mathrm{B}}_{\mathrm{m}}\left(\mathrm{x}\right)\right].}$

Adaboost can not only effectively deal with the local minimization problem caused by multi-modal features but also alleviate the over-fitting phenomenon to a certain extent, to provide more accurate and stable evaluation results for the accounting goal of enterprise accounting X_S.

Meta-heuristics-based accounting optimization method

Accounting optimization through meta-heuristics aims to enhance enterprise efficiency in accounting processes. These algorithms integrate meta-heuristic principles and optimization techniques to tackle the diverse and complex challenges inherent in enterprise accounting. This study optimises accounting methodologies by leveraging multi-modal features and quality assessment outcomes.

The approach employs meta-heuristic algorithms such as Genetic Algorithm (GA) and Simulated Annealing (SA) to solve accounting models and determine optimal enterprise operations. GA, renowned for addressing intricate optimization problems, operates with three key functions—selection, mutation, and crossover—each utilizing parameters to refine solutions. Such constraint is solved by maximizing the accounting quality assessment value, namely: (9)${\displaystyle max\mathrm{E}=\sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{c}\times {\left(\sqrt{{\left({\mathrm{x}}_{\mathrm{j}}+{\mathrm{x}}_{\mathrm{i}}\right)}^2+{\mathrm{B}}^2}\right)}^{\mathrm{n}}\times {\mathrm{D}}_{\mathrm{L}}}$ (10)${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{X}}_{\mathrm{i}}=\mathrm{L}}$ where L refers to the cost of the whole accounting process, each x_i denotes the GA variable and x_j represents the SA variable.

Mutation function is an important part of GA, and it includes Gaussian variograms, uniform variograms, and adaptive variograms. We chose to use a Gaussian variator with a shrinkage scale factor to successfully tune the minimum energy. When the shrinkage parameter is 1, the variance linearly decreases to 0 over the generations. This design makes the mutation process more flexible and controllable, which is helpful in boosting the performance of GA.

The SA model is locally based on the solution of a constrained optimization model. This constrained optimization model has the following steps:

(1) The corresponding objective g_j+1 is randomly generated by providing the starting temperature and selecting the variable x_j. The temperature then decreases as the number of cycles increases.

(2) Each time through the loop, a novel objective g_j+1 is created and compared with the current objective.

(3) If g_j+1<g_j, replace g _j with g_j+1 and enter the next cycle until the temperature value is really reduced.

The key of the SA model is to escape from the local optimal solution, which is determined by the Metropolis criterion. At high temperatures, the probability of which is wrong solution is high. As the temperature decreases, the probability of accepting the suboptimal solution is gradually reduced so the algorithm tends to search near the optimal solution.

The accounting optimization method based on Yuanqifa considers the diversity and complexity of enterprise accounting problems more comprehensively and is committed to providing more effective accounting solutions. This method can be popularized and applied in different industries and enterprise types to promote the improvement of enterprise accounting efficiency.

Dataset and implement details

We tested intelligent accounting using a method combining CNN and meta-heuristics optimization, utilizing the Synthetic Financial Dataset available at Zenodo (DOI: 10.5281/zenodo.7543591).

Our training setup utilized hardware comprising an i5-14400F processor and 2 Nvidia RTX 4060Ti GPUs. Throughout the training phase, TensorFlow was our deep learning framework, configured with specific settings detailed in Table 1.

During model training, we incorporated a weight decay term with a value of 0.00009. These choices in test environments and configurations were made to ensure our method demonstrates superior efficiency and accuracy in addressing intelligent accounting challenges.

In this article, Accuracy (Acc) and Mean Average Precision (mAP) are employed as the criteria of intelligent accounting optimization method based on meta-heuristics and CNN, and the calculation formula is as follows: (11)${\displaystyle Acc=\frac{Y\left(pr\right)}{Y\left(gt\right)}}$ (12)${\displaystyle mAP=\frac{\sum A{P}_i}{n}}$ where pr and gt refer to the predicted and true values, n denotes the entire classes, and AP_i is the average precision for the i th class. AP is the area under the precision and recall curves and reflects the model’s performance in each class. Therefore, the mAP means the average of the AP over all classes and is used to measure the average performance of the model over all classes. In addition, when calculating AP, we first need to get the precision and recall values.

Ablation experiments

Table 2 presents detailed ablation experiments on intelligent accounting optimization methods using meta-heuristic algorithms and CNNs based on the Synthetic Financial Dataset. We systematically evaluate the impact of three modules: MAFE, AQAA, and MAO, both individually and in various combinations, on model performance.

Firstly, individually introducing MAFE enhances [email protected]:0.95 to 0.739, AQAA contributes a score of 0.731 for [email protected]:0.95, and MAO achieves 0.748 for [email protected]:0.95. These results highlight the positive influence of each module in optimizing accounting processes.

Next, through detailed analysis in Figs. 4 and 5, we observe that combining these modules consistently improves model performance. Specific combinations demonstrate significant achievements, with some configurations reaching as high as 0.798 on [email protected], underscoring the synergy between modules.

Finally, integrating all three modules—MAFE, AQAA, and MAO—yields compelling results: [email protected] scores 0.852, [email protected] scores 0.834, and [email protected] scores 0.812. The overall [email protected]:0.95 reaches 0.838, affirming the effectiveness of our method and demonstrating the potential of multi-module combinations to enhance model performance in intelligent accounting optimization.

Our ablation experiments comprehensively explore the roles of MAFE, AQAA, and MAO modules in enhancing intelligent accounting optimization. These findings validate the efficacy of our approach and offer promising avenues for future research in this field.

Compare our method and other methods

In our experiment on the Synthetic Financial Dataset, we evaluated the performance of the MAFE method by comparing it with DAMUN (Feng et al., 2023), FDGNet (Zhang et al., 2023), AdaMoW (Zhang, Wu & Huang, 2023), and Megcf (Liu et al., 2023a). The results, detailed in Fig. 6 and Table 3, demonstrate that MAFE outperforms all other methods across all evaluation metrics.

Specifically, MAFE achieved remarkable results across various accuracy metrics, with scores of 0.887 for Acc@1, 0.902 for Acc@5, 0.936 for Acc@10, and 0.966 for Acc@20. Compared to DAMUN, our method significantly improved 3.2% in Acc@1. Furthermore, MAFE surpassed FDGNet and AdaMoW in all indicators, outperforming them by 2.3% in Acc@5 and 1.4% in Acc@10, respectively. Lastly, MAFE achieved a 3.0% lead over Megcf in Acc@20. These comparisons underscore MAFE’s superior performance in intelligent accounting. MAFE excels in accuracy, ranking first in Acc@1, and demonstrates significant advancements in broader recommendation accuracy and scope. MAFE’s superiority equips enterprises with more reliable and efficient intelligent solutions to address increasingly complex financial data and accounting challenges.

In our detailed analysis of AQAA’s performance on the Synthetic Financial Dataset, we compared it against well-known methods CRFIQA (Boutros et al., 2023), PCQA (Liu et al., 2023b), and FAQA (Idland et al., 2023) to thoroughly assess its strengths and capabilities. As shown in Fig. 7 and Table 4, the results highlight AQAA’s significant advantages across several key evaluation metrics.

Compared to CRFIQA, AQAA excels in overall performance and leads by a significant 2.8% in the Acc@5 metric, exemplifying its prowess in precisely categorizing questions. Furthermore, when benchmarked against PCQA and FAQA, AQAA maintains its competitive edge. Specifically, AQAA outperforms PCQA with a remarkable 6.3% improvement in [email protected], demonstrating its robustness in accurately identifying problematic areas. Additionally, AQAA surpasses FAQA with a 1.8% enhancement in Acc@5, further reinforcing its effectiveness in enhancing the accuracy of question identification. These findings collectively validate AQAA’s prowess in improving the precision and effectiveness of question identification within the context of intelligent accounting optimization.

Through our detailed examination of MAO’s performance on the Synthetic Financial Dataset, we have successfully enhanced AQAA’s capabilities through parameter optimization. Comparing MAO with established benchmarks CRFIQA, PCQA, and FAQA, we observe that MAO achieves superior performance in Acc@1 and [email protected] values, reaching 0.943 and 0.812, respectively. These detailed results are illustrated in Fig. 8.

MAO’s optimization approach stands out among other advanced methods, exhibiting remarkable performance in accounting optimization. These superior metrics offer enterprises more efficient and dependable solutions for refining their accounting processes. The significant improvements in Acc@1 and [email protected] values demonstrate MAO’s robust adaptability in handling intricate financial data and accounting challenges. As a result, enterprises can confidently rely on MAO to provide flexible and effective accounting solutions, which are crucial for navigating dynamic economic environments and regulatory landscapes. MAO’s method not only achieves substantial enhancements over existing benchmarks but also showcases its versatility in diverse domains and complex scenarios. This comprehensive performance validates MAO’s excellence in intelligent accounting, offering enterprises a reliable basis for decision-making and investors credible financial information.

Finally, to simulate the performance of our method in real-world scenarios, as shown in Fig. 9, we restructured the data to form tourism sample sets with varying numbers of real-world samples, including 20, 50, 100, 200, and 500 samples. By comparing the running time under different sample sets, we better understood our method’s performance with different data scales. As shown in Fig. 7, we have recorded the computation time of MAFE, AQAA, and MAO under different sample sizes. Comparative analysis shows that regardless of the actual scenario, the system’s computation time remains below 210 ms. This result indicates that our model can handle concurrent requests that may arise in real-world scenarios, thus providing users with stable and efficient services.

Discussion

The experiments conducted on CNN-based multi-modal accounting feature extraction, accounting quality assessment, and meta-heuristics-based accounting optimization have yielded satisfactory results, validating the effectiveness of intelligent accounting optimization using meta-heuristics and CNN. This approach demonstrates exceptional performance across various environmental and data challenges, offering a comprehensive and practical solution for accounting tasks.

The CNN-based multi-modal accounting feature extraction technique successfully extracts crucial information from complex accounting data. By integrating data from diverse modalities, our method comprehensively reflects enterprise financial statuses and business outcomes, providing a robust foundation for subsequent accounting quality assessment and optimization. Secondly, our adopted method for accounting quality assessment incorporates deep data mining and machine learning algorithms, enhancing the objectivity and accuracy of evaluation results beyond traditional financial indicators. This capability aids enterprises in the timely identification of risks and issues, facilitating informed decision-making. Lastly, the meta-heuristics-based accounting optimization method optimizes accounting processes by intelligently adjusting model parameters and structures. This not only boosts accounting accuracy and efficiency but also reduces manual intervention, thereby easing the workload on financial personnel.

In summary, our intelligent accounting optimization method leveraging meta-heuristics and CNN proves to be an efficient, reliable solution with broad application potential. We aim to explore additional optimization strategies and technological advancements to enhance accounting accuracy further and support enterprise development.