Design of an intelligent optimization framework for corporate financial management based on GA-FL-transformer

Multi-source financial data perception and feature extraction based on transformer

In the context of corporate financial management, data sources are extremely diverse and varied in format, encompassing structured financial statements, semi-structured management reports, unstructured market news, policy texts, and social media information. Effectively processing and comprehending massive volumes of heterogeneous financial data is crucial. To address this challenge, this study first introduces the Transformer model as the perception module for economic data, as illustrated in Fig. 1. This module leverages its attention mechanism to achieve deep understanding and key feature extraction from multi-source financial data. The following formula can express it:

(1) $$Attention\left(Q,K,V\right)=softmax\left(Q{K}^T/d_k\right)V.$$

Here, Q, K, and V represent the query, key, and value matrices respectively, $d_k$ is the dimension of the key vectors, and $softmax(\cdot )$ is the probability distribution function that ensures the sum of all weights equals 1. This enables automatic capture of associations across different data sources and identification of information patterns that significantly impact a company’s financial condition. In this study, a unified encoding strategy for multimodal financial data is designed. The specific encoding process is as follows:

(2) $$F_{\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{d}}=Transformer\left(\left[E_{financial}\oplus E_{\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{t}}\oplus E_{text}\oplus E_{temporal}\right]\right).$$

Here, $E_{financial}$ denotes the embedding of financial indicators, $E_{\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{t}}$ represents the embedding of market information, $E_{text}$ stands for the text embedding, $E_{temporal}$ is the time-series embedding, $\oplus$ which indicates the feature concatenation operation. Subsequently, through the multi-head attention mechanism, the model comprehends financial data from multiple perspectives. The formula for the multi-head attention mechanism is expressed as:

(3) $$\mathrm{M}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{i}\mathrm{H}\mathrm{e}\mathrm{a}\mathrm{d}\left(Q,K,V\right)=\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{t}\left(\mathrm{h}\mathrm{e}\mathrm{a}{\mathrm{d}}_1,...,\mathrm{h}\mathrm{e}\mathrm{a}{\mathrm{d}}_h\right)W^o.$$

Here, each attention head $hea{d}_i$ Focuses on different financial dimensions. For instance, $hea{d}_1$ pays attention to cash—liquidity indicators, $hea{d}_2$ focuses on stock earnings, and $hea{d}_3$ centers on the market environment, and so on. This design enables the model to assess an enterprise’s financial health comprehensively. The theoretical justification for the unified encoding strategy lies in its superior capacity for cross-modal alignment and feature disentanglement. Unlike simple concatenation that often creates entangled representations, the cross-modal attention mechanism explicitly models interactions between all pairs of tokens across different data types. This allows the model to dynamically contextualize information, for instance, by refining a financial ratio based on relevant news sentiment. Consequently, it suppresses irrelevant features and enhances discriminative power, fostering a more coherent and disentangled feature space optimized for financial inference tasks compared to isolated modality processing.

The multi-source financial data perception and feature extraction based on the Transformer can process multi-source heterogeneous financial data in parallel, effectively capturing long-range dependencies and cross-modal associations. The unified encoding strategy not only preserves the temporal characteristics and semantic information of various data types but also enables in-depth fusion of different modal data in the feature space.

Attention-guided genetic-fuzzy financial decision optimization mechanism

This study constructs a novel financial decision optimization mechanism that deeply integrates GA with the interpretability of FL and leverages Transformer attention weights as guidance to form an adaptive decision optimization mechanism. The core of this mechanism lies in leveraging the Transformer’s in-depth perception of financial environmental features to dynamically guide the entire evolutionary process of the algorithm, ensuring that the generated fuzzy decision rules exhibit high accuracy. The fuzzy logic system employs Gaussian membership functions to fuzzify inputs such as Liquidity and leverage into three linguistic sets: Low, Medium, and High. The output, Decision_Output, is defined by five Gaussian sets ranging from Conservative to Aggressive. An initial rule base is constructed from all possible combinations of input sets. Subsequently, the Genetic Algorithm dynamically optimizes the parameters of these membership functions and the fuzzy rule weights, guided by the Transformer’s attention mechanism. Based on the features $F_{\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{d}}$ extracted by the Transformer model in the previous section, the chromosome encoding structure for environmental perception is formulated as follows:

(4) $$C=\left\{R_i^{\mathrm{f}\mathrm{i}\mathrm{n}}\left(F_{encoded}\right),M_j^{\mathrm{i}\mathrm{n}\mathrm{d}}\left(W_{\mathrm{a}\mathrm{t}\mathrm{t}}\right),P_k^{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{k}}\left(\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}\right)\right\}.$$

Here, $R_i^{\mathrm{f}\mathrm{i}\mathrm{n}}\left(F_{encoded}\right)$ represents the financial decision rules generated based on the features. The membership function parameters $M_j^{\mathrm{i}\mathrm{n}\mathrm{d}}\left(W_{\mathrm{a}\mathrm{t}\mathrm{t}}\right)$ are dynamically refined using the attention weights $W_{\mathrm{a}\mathrm{t}\mathrm{t}}$ from the Transformer. This process adjusts the shape and position of the fuzzy membership functions to prioritize features that the model deems most critical. Consequently, the chromosome-encoding process evolves to reflect the current financial context better, ensuring that the genetic search is guided by semantically salient information. $P_k^{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{k}}\left(\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{x}\mathrm{t}\right)$ denotes the context-dependent risk weights. This encoding approach establishes an intrinsic connection between the genetic algorithm’s evolutionary space and the environment perceived by the Transformer, providing a structural foundation for subsequent multi-objective optimization.

The design of the fitness function fully integrates traditional financial metrics with environmental context information, leveraging Transformer outputs to achieve multi-objective financial optimization. The mathematical expression for the fitness function is as follows:

(5) $$f\left(C\right)=\alpha \cdot \mathrm{R}\mathrm{O}\mathrm{I}\left(C\right)+\beta \cdot \mathrm{R}\mathrm{i}\mathrm{s}\mathrm{k}\left(C\right)+\gamma \cdot \mathrm{L}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{y}\left(C\right)+\delta \cdot \mathrm{A}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(C,{\mathrm{W}}_{\mathrm{a}\mathrm{t}\mathrm{t}}\right).$$

Here, ROI(C), Risk(C), Liquidity(C) represent the investment return, risk level, and liquidity status after applying the decision rules. The $\mathrm{A}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(C,{\mathrm{W}}_{\mathrm{a}\mathrm{t}\mathrm{t}}\right)$ term in the fitness function quantitatively measures the alignment between a chromosome’s decision rules and the feature importance profile. Chromosomes whose rules resonate with highly weighted features receive a fitness boost, steering the population toward contextually relevant solutions. This integration ensures that optimization objectives are dynamically adapted to the perceived financial environment. This fitness function design ensures that the evolutionary process simultaneously optimizes both traditional financial metrics and contextual relevance, resulting in a rule set highly pertinent to the financial environment.

To provide a more rigorous mathematical foundation, we now derive the complete formulation of the fitness function with all hyperparameters explicitly defined. The attention alignment term in Eq. (5) is mathematically defined as:

(6) $$\mathrm{A}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(C,W_{\mathrm{a}\mathrm{t}\mathrm{t}}\right)={\displaystyle \frac{1}{N_r}\sum _{i=1}^{N_r}{w}_i^{\mathrm{a}\mathrm{t}\mathrm{t}}.}$$

In Eq. (6), $N_r$ denotes the total number of rules in chromosome $C$, and $w_i^{\mathrm{a}\mathrm{t}\mathrm{t}}$ represents the average attention weight associated with the rule $r_i$, which reflects the importance of features involved in that rule. This formulation quantifies how well the chromosome’s rule set aligns with the features deemed important by the Transformer’s attention mechanism.

The attention-guided genetic operation mechanism guarantees the algorithm’s exploratory capability, avoiding local optima. When exchanging rule segments between two chromosomes, features with high attention weights are more likely to be exchanged. The following formula gives the attention-guided crossover probability:

(7) $$P_{\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}\left(r_i\right)=P_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}\cdot \left(1+\eta \cdot {\overline{w}}_{\mathrm{a}\mathrm{t}\mathrm{t},i}\right).$$

Here, $P_{\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}}\left(r_i\right)$ denotes the final crossover probability, representing the actual probability that rule segment $r_i$ is selected for crossover operation. $P_{base}$ is the base crossover probability, a preset benchmark probability value. $\eta$ is an adjustment coefficient used to control the extent to which attention weights influence the final crossover probability. ${\overline{w}}_{\mathrm{a}\mathrm{t}\mathrm{t},i}$ represents the average attention weight, the mean of the attention weights for all features related to the rule segment, reflecting the segment’s importance.

The attention-guided crossover mechanism requires a precise mathematical derivation to demonstrate how attention weights modulate genetic operations. The average attention weight for rule segment $r_i$ is computed as the mean of attention weights of all features involved in that rule segment. Specifically, if rule $r_i$ involves $k$ features, then:

(8) $${\overline{w}}_{\mathrm{a}\mathrm{t}\mathrm{t},i}={\displaystyle \frac{1}{k}\sum _{j=1}^k{w}_{i,j}^{\mathrm{a}\mathrm{t}\mathrm{t}}.}$$

In Eq. (8), $w_{i,j}^{\mathrm{a}\mathrm{t}\mathrm{t}}$ represents the attention weight for the $j$-th feature in the rule segment $r_i$ By averaging the attention weights across all features involved in a rule segment, the Transformer model produced a comprehensive measure of that segment’s contextual importance.

To clarify the specific mechanism of attention-guided updates, the Transformer attention weights primarily influence the membership function boundaries rather than rule antecedents or final decision parameters. During the genetic algorithm’s evolutionary process, the attention weights act as adaptive scaling factors that modulate the magnitude of parameter adjustments for each fuzzy membership function. Features with higher attention weights undergo more substantial changes in their Gaussian membership function centers and widths, making the fuzzy system more sensitive to critical financial indicators identified by the Transformer. Conversely, membership functions corresponding to features with lower attention weights receive minimal adjustments, maintaining stability in less relevant dimensions. This mechanism ensures that the evolutionary search dynamically prioritizes optimizing decision boundaries for the most contextually essential features.

In the attention-guided mutation operation mechanism, the magnitude and direction of mutation are guided by attention weights. Important features receive stronger or more specific mutations rather than completely random perturbations. Equation (9) describes this process:

(9) $$\mathrm{M}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(r_i\right)=r_i+\sigma \cdot \mathcal{N}\left(0,1\right)\cdot h\left(w_i^{\mathrm{a}\mathrm{t}\mathrm{t}}\right).$$

Here, $\mathrm{M}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(r_i\right)$ represents the mutation result, denoting the new value of the rule segment obtained after the mutation operation. $\sigma$ is the basic mutation step size, which determines the baseline magnitude of the mutation. $\mathcal{N}\left(0,1\right)$ is a random variable, governing the mutation’s random direction and magnitude. $w_i^{\mathrm{a}\mathrm{t}\mathrm{t}}$ is the attention weight output by the Transformer model and associated with the i-th relevant feature. $h(\cdot )$ is a scaling function that maps the attention weight into a regulatory factor for the mutation intensity.

This optimization mechanism explores the complex financial decision space through the genetic algorithm, automatically optimizing the fuzzy rule base and membership functions. For instance, given inputs where Liquidity is High and Leverage is Medium, multiple rules are activated. The final decision is not a simple average but a weighted aggregation based on each rule’s firing strength and its dynamically evolving weight, which the GA adjusts according to the attention-guided importance. This process ensures that the system’s decision-making continuously adapts to the perceived financial context. Fuzzy Logic ensures the algorithm’s decision-making process is well interpretable, while introducing Transformer attention weights effectively integrates the optimization direction with key features of the financial environment, significantly enhancing the accuracy of the decision-making model.

An intelligent optimization framework for corporate financial management based on GA-FL-transformer

Building on Transformer-based feature extraction and the genetic-fuzzy financial decision-making mechanism, this study constructs an intelligent optimization framework for financial management that integrates perception, optimization, and decision-making. As illustrated in Fig. 2, the framework adopts a three-layer model, concluding a Transformer-based multi-source data perception and feature extraction layer, a genetic algorithm-based reasoning layer, and a fuzzy logic-based optimization layer.

The perception layer, centered around the Transformer model, is responsible for multi-source data fusion and feature extraction. This layer integrates corporate financial data, real-time market data, public sentiment information, and historical time-series data. By employing self-attention mechanisms, it dynamically calculates feature importance weights and outputs high-dimensional feature vectors, attention weight matrices, and structured environmental information to support subsequent optimization processes.

The optimization layer utilizes the evolutionary mechanism of the genetic algorithm to drive rule generation. In this layer, fuzzy system parameters are mapped into evolvable individual variables through chromosome encoding. A dynamic fitness function is employed to evaluate the comprehensive performance of potential solutions. Continuous improvement is achieved through attention-weighted genetic operations, ultimately outputting an optimal set of fuzzy rules and membership function parameters.

The decision-making layer executes interpretable fuzzy reasoning based on optimization results. It employs the optimally evolved rule base and membership functions for fuzzy inference, generating multi-dimensional decision-making schemes, including investment decisions, risk control measures, fund management strategies, and budget planning, in the context of the given environment. The entire decision-making process maintains a high degree of interpretability.

Effective integration across the three layers is achieved through forward information flow and feedback learning mechanisms, ensuring robust environmental perception and adaptive capabilities. This framework can provide systematic solutions for complex corporate financial decision-making problems.

Computing infrastructure

The experiments were conducted on a Windows 11 64-bit operating system using Python 3.10 and the PyTorch 2.2 framework for model implementation. Training and evaluation were performed on a workstation equipped with an Intel Core i9-13900K CPU, 64 GB RAM, and an NVIDIA RTX 4090 GPU (24 GB VRAM). The software environment also included CUDA 12.1 and cuDNN 8.9 for GPU acceleration, and all models were trained with the same hyperparameter settings to ensure fairness and reproducibility.

Data preprocessing

A comprehensive data preprocessing pipeline was designed to improve the quality and compatibility of heterogeneous financial data. First, structured financial indicators such as balance sheets and income statements were normalized using z-score standardization to eliminate scale bias and stabilize gradient convergence during model training. Second, unstructured textual information from market news, policy documents, and analyst reports was preprocessed through tokenization, stop-word removal, and lemmatization, followed by TF-IDF weighting and conversion into 300-dimensional embeddings using a pretrained Word2Vec model. Third, time-series data, such as stock returns and transaction volumes, were smoothed using a sliding-window normalization approach and temporally aligned via timestamp synchronization to ensure consistent sampling frequency. Missing values were imputed using a Gaussian expectation-maximization algorithm, while categorical variables were encoded using one-hot encoding. Finally, all processed modalities were concatenated using the unified multimodal embedding mechanism defined in Eq. (2), enabling the Transformer encoder to jointly learn attention-based features across heterogeneous data sources.

The experimental dataset comprises financial records from 2,847 publicly traded companies spanning 2010–2023, partitioned chronologically into a training set covering 2010–2019 (70%), a validation set covering 2020–2021 (15%), and a test set covering 2022–2023 (15%). Financial statement data are sampled quarterly, while market data are aggregated from daily to quarterly frequency for temporal consistency. Ground-truth labels for risk classification are constructed using a composite framework in which companies are labeled “High Risk” if they satisfy at least two criteria, including an Altman Z-score below 1.8, an interest coverage ratio below 1.5, negative operating cash flow for two consecutive quarters, or a stock price decline exceeding 40%. The training set exhibits a 23.6% High Risk vs. 76.4% Low Risk distribution, with key financial indicators showing a mean return on assets of 4.82% with a standard deviation of 8.91%, an average debt-to-equity ratio of 1.34 with a variance of 2.17, and a mean current ratio of 2.08 with a standard deviation of 1.53.

Evaluation method

The evaluation methodology in this study was designed to verify both the structural validity and functional performance of the GA-FL-Transformer framework. Two complementary evaluation strategies were employed. First, method comparison was performed by benchmarking the proposed framework against three representative deep learning baselines: Long Short-Term Memory (LSTM) (Liu & Fan, 2025), Convolutional Neural Network–Long Short-Term Memory (CNN-LSTM) (Sun et al., 2025), and Temporal Convolutional Network–Gated Recurrent Unit (TCN-GRU) (Zhou, 2025). Additionally, to provide a broader methodological context, three domain-specific models were included as comparative benchmarks: the genetic algorithm and fuzzy neural network model (GA-Fuzzy) (Huang et al., 2025) for international trade settlement modeling, the two-stage fuzzy neural approach (Fuzzy-NN) (Fonseca, Wanke & Correa, 2020) for credit risk assessment, and the self attention deep learning method (Wu et al., 2024a) for financial distress prediction using current reports. These models were selected to represent classical sequence learning, hybrid convolutional–recurrent learning, and dilated temporal convolutional paradigms, respectively. Each baseline was trained and tested under identical data partitions and hyperparameters to ensure fairness. Second, ablation experiments were conducted to isolate and quantify the contributions of each major component within the GA-FL-Transformer architecture. Specifically, three ablation variants were tested: (1) removal of the Genetic Algorithm (GA) module, (2) removal of the Fuzzy Logic (FL) reasoning component, and (3) removal of the Transformer encoder. The performance degradation observed after excluding each component quantitatively demonstrated its contribution to global optimization, uncertainty reasoning, and multi-source feature perception. Together, the comparative and ablation analyses provide strong methodological evidence for the interpretability, adaptability, and efficiency of the proposed framework before full-scale performance evaluation.

Assessment metrics

Precision, Recall, F1-score, and Error Rate (ER) were used to evaluate our work. Precision shows the proportion of the things we predicted as positive that are actually positive. Here’s the formula for calculating Precision:

(10) $$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{TP}{TP+FP}.}$$

Recall quantifies the proportion of true positive cases correctly classified as positive by the model. Its formal expression is given below:

(11) $$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{TP}{TP+FN}.}$$

The F1-score is the harmonic average of Precision and Recall, which is expressed as:

(12) $$F1=2\cdot {\displaystyle \frac{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\cdot \mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}={\displaystyle \frac{2TP}{2TP+FP+FN}.}}$$

Error rate (ER) represents the error rate of the model. The expression for ER is as follows:

(13) $$ER=\left(\frac{{\displaystyle CTW+WTC}}{Nn\mathrm{T}}\right).$$

Here, $CTW$ denotes the number of samples that were originally correctly classified but were incorrectly predicted, $WTC$ repres denotes the number of samples that were originally incorrectly classified but were correctly predicted, and Num denotes the total sample size.

Experimental setup

This study utilizes authoritative data from Compustat and the CRISPR Therapeutics AG Stock Performance (CRSP) as the experimental foundation. The Compustat database covers most listed companies in North America, providing financial statement data at both annual and quarterly frequencies spanning several decades. Its primary data includes structured financial details such as income statements, balance sheets, and cash flow statements, as well as metadata about company basics and equity setups. The CRSP database provides high-precision securities market data, including individual stock prices, returns, trading volumes, and historical records of market indices and various investment instruments. It is widely used for market behavior analysis, investment performance evaluation, and financial risk modeling. In this study, data from both CRSP and Compustat are employed to gain a more comprehensive market perspective and further evaluate the performance of the GA-FL-Transformer in financial risk identification and multi-period forecasting tasks.

Method comparison and result analysis

As illustrated in Fig. 3A, in the comparison results on the Compustat dataset, the GA-FL-Transformer model outperforms all competing models. From the grouped bar chart, it is evident that, across all compared models, the Recall metric is generally lower than the Precision metric, reflecting the prevalence of class imbalance and the risk of false negatives in financial risk prediction tasks. However, the GA-FL-Transformer model achieves an outstanding Recall of 0.952, significantly narrowing the gap with Precision. This indicates that the model can more comprehensively identify potential risk samples, benefiting from its ability to perceive and integrate multi-source features.

Among the competing models, the traditional LSTM performs worst across all three metrics, highlighting its limitations in effectively capturing complex dependencies in financial data. Although the CNN-LSTM and TCN-GRU models have achieved some performance improvements by incorporating convolutional structures and gating mechanisms, the extent of these improvements is limited. This suggests that single or simply hybrid deep learning architectures still have significant shortcomings. The GA-FL-Transformer significantly enhances its capability of financial patterns through a multi-module collaborative and optimization mechanism.

From the results on the CRSP dataset shown in Fig. 3B. The GA-FL-Transformer model demonstrates exceptional Recall performance of 98.2%, outperforming all competing models. This indicates that the model has a significant advantage in identifying genuine risk signals, which is of great importance for reducing the false-negative rate and enhancing the reliability of risk warnings. Secondly, although the TCN-GRU model exhibits relatively balanced performance, with Precision, Recall, and F1-score values of 96.1%, 94.8%, and 95.4%. In addition, the F1-score of the GA-FL-Transformer reaches 97.7%, reflecting its excellent comprehensive classification performance.

Figures 4A–4C present the results of corporate financial risk prediction tasks on the Compustat dataset from 2016 to 2022 under different evaluation metrics. The experiments show that our model outperforms existing methods.

In terms of the ER, the GA-FL-Transformer model has achieved a continuous decline from 1.45% in 2016 to 0.85% in 2022, representing a significant reduction of approximately 70% compared to the competing TCN-GRU model. This improvement is primarily attributed to the Transformer-based multi-source fusion module in the model, which effectively integrates multimodal financial data through a multi-head attention mechanism, enabling more precise feature representation and thereby significantly reducing the risk of misjudgment.

Regarding prediction Precision, our model consistently maintains a level above 97% throughout the entire testing period and reaches a peak of 99.5% in 2022, which is 9.2%, 5.8%, and 4.3% higher than LSTM, CNN-LSTM, and TCN-GRU, respectively. This advantage can be attributed to the designed attention-guided genetic-fuzzy collaborative optimization mechanism. This mechanism dynamically adjusts the rule generation and parameter evolution processes based on feature importance, enabling the model to make more accurate decisions in high-dimensional financial objective spaces.

In terms of Recall, the GA-FL-Transformer model achieves an excellent average performance of 97.4%. This result benefits from the feedback-learning mechanism introduced into the GA-FL-Transformer’s optimization architecture. The system can dynamically optimize the perception and decision-making modules based on historical performance, thereby continuously improving prediction accuracy.

Figures 5A, 5B respectively present the comprehensive evaluation results of the investment decision-making performance of the GA-FL-Transformer model in comparison with three competing models, namely LSTM, CNN-LSTM, and TCN-GRU, on two financial datasets, CRSP and Compustat. From a profit margin perspective, the experimental results reveal significant performance differences. On the CRSP dataset, the GA-FL-Transformer achieves a peak profit margin of 52%, representing improvements of 30%, 20.9%, and 13% compared to LSTM’s 40%, CNN-LSTM’s 43%, and TCN-GRU’s 46%, respectively. On the Compustat dataset, the performance gap is even more pronounced, with the GA-FL-Transformer reaching a peak profit margin of 70%, far surpassing the other three models’ figures of 55%, 56%, and 60%. Although the performance of all models is similar in low-risk intervals, as risk increases, the GA-FL-Transformer demonstrates stronger profitability, highlighting the advantage of the proposed model in integrating multimodal features.

The Return on Investment (ROI) metric further validates the GA-FL-Transformer’s superiority and robustness. On the CRSP dataset, the model consistently maintains a high ROI of 70–71% across multiple intervals, while the competing models’ ROIs fluctuate between 62% and 68%. Similarly, on the Compustat dataset, the GA-FL-Transformer sustains a stable high ROI of 65%, clearly outperforming the competing models. In high-risk intervals, although all models experience a declining ROI, the GA-FL-Transformer’s decline curve is smoother, whereas traditional models like LSTM exhibit a sharper drop. This fully demonstrates that the effective integration of genetic algorithm optimization, fuzzy logic reasoning, and the Transformer architecture in the GA-FL-Transformer enhances the profitability of investment decisions.

Table 1 confirms the superior generalization capability of the proposed GA-FL-Transformer model across diverse financial datasets. When trained on CRSP and tested on Compustat, GA-FL-Transformer achieves an F1-score of 0.847, significantly outperforming LSTM (0.732), CNN-LSTM (0.769), and TCN-GRU (0.798), with relative improvements of 11.5 percent, 7.8 percent, and 4.9 percent, respectively. Bidirectional validation using Compustat for training and CRSP for testing yields a similarly strong F1-score of 0.851, demonstrating consistent cross-market generalization. Notably, GA-FL-Transformer exhibits only an 8.2 percent average performance decline when moving from within-dataset to cross-dataset evaluation, compared to substantially larger drops of 14.4 percent for LSTM, 12.1 percent for CNN-LSTM, and 10.6 percent for TCN-GRU. This confirms that the transformer-based attention mechanism and adaptive imputation strategy effectively learn generalizable temporal patterns rather than dataset-specific artifacts.

Tables 2 and 3 present a comprehensive performance comparison of the proposed GA-FL-Transformer against three representative hybrid intelligent systems across four evaluation metrics on both Compustat and CRSP financial datasets. On the Compustat dataset, the GA-FL-Transformer achieves superior performance with Precision of 0.966, Recall of 0.952, F1-score of 0.959, and Error Rate of 0.85%, demonstrating substantial improvements over GA-Fuzzy with F1-score of 0.877 and Error Rate of 2.31%, Fuzzy-NN with F1-score of 0.895 and Error Rate of 1.97%, and Transformer-based models with F1-score of 0.918 and Error Rate of 1.45%, representing F1-score improvements of 9.4%, 7.2%, and 4.5% respectively. On the CRSP dataset, the proposed model exhibits even more pronounced advantages, with a Precision of 0.973, Recall of 0.982, F1-score of 0.977, and Error Rate of 0.62%, outperforming GA-Fuzzy by 9.9%, Fuzzy-NN by 7.4%, and Transformer-based methods by 4.8% in F1-score. Notably, the GA-FL-Transformer demonstrates exceptional Recall performance on both datasets, with values of 0.952 on Compustat and 0.982 on CRSP, indicating superior ability to identify true positives and minimize false negatives, which is critical for financial risk management, where overlooking potential risks can lead to severe consequences. The consistently low Error Rates of 0.85% on Compustat and 0.62% on CRSP further validate the robustness of the attention-guided co-evolutionary mechanism, which synergistically integrates genetic algorithm optimization, fuzzy logic reasoning, and Transformer-based feature learning to achieve both high prediction accuracy and strong generalization across different financial market conditions.

Ablation experiments and application analysis

To thoroughly analyze the contributions of each core component and their collaborative mechanisms within the proposed model, this article systematically performs ablation experiments. The results are presented in Fig. 6.

On the Compustat dataset, the complete GA-FL-Transformer model achieves an F1-score of 0.959. After sequentially removing each component, a systematic decline in performance is observed: the removal of the GA reduces the F1-score to 0.938, representing a performance degradation of 2.2%; eliminating FL results in an F1-score of 0.942, a decrease of 1.8%; and removing the Transformer module leads to a performance drop to 0.934, with an amplitude of decline reaching 2.6%. A consistent trend is observed on the CRSP dataset. The complete model attains an F1-score of 0.977, whereas removing the GA, FL, and Transformer components results in scores of 0.958, 0.961, and 0.952, respectively, corresponding to performance losses of 1.9%, 1.6%, and 2.6%.

These results clearly indicate that the Transformer module plays a pivotal role in feature extraction and multi-source information fusion. At the same time, GA and FL make significant contributions in high-dimensional optimization and uncertainty reasoning, respectively.

Figure 7 presents the gradient-based feature importance analysis, revealing the hierarchical contribution of financial attributes to the GA-FL-Transformer model’s optimization outcomes. The results demonstrate that leverage-related indicators, specifically the debt-to-equity ratio and interest coverage ratio, have the highest importance scores of 0.284 and 0.237, respectively, accounting for 52.1% of the cumulative feature contribution and underscoring their critical role in financial risk assessment. Profitability metrics, including ROE, net profit margin, and ROA, constitute the secondary tier of influential features, with scores of 0.198, 0.176, and 0.145, respectively, indicating that earnings quality and operational efficiency significantly influence risk prediction accuracy. The gradient analysis further reveals a complementary learning mechanism in which the GA module prioritizes features with high temporal volatility, such as cash flow ratios and changes in working capital, to enable dynamic adaptation to market fluctuations. In contrast, the FL module focuses on features characterized by inherent uncertainty and qualitative judgment, such as leverage and coverage ratios, to handle ambiguous risk signals through fuzzy reasoning effectively. This synergistic feature utilization mechanism allows the GA-FL-Transformer to simultaneously capture both quantitative Precision in numerical financial analysis and qualitative reasoning in complex uncertainty scenarios, thereby achieving superior adaptive learning performance in dynamic financial environments.