An Empirical Analysis of the Impact of ESG Management Strategies on the Long-Term Financial Performance of Listed Companies in the Context of China Capital Market

Abstract

In the evolving landscape of China’s capital markets, the integration of Environmental, Social, and Governance (ESG) considerations has become increasingly crucial for investors and decision-makers. Traditional financial performance metrics often fall short in capturing the multidimensional and long-term impacts of ESG factors. This study introduces a novel computational framework that combines domain-adapted pre-trained language models with structured financial regression analysis, aiming to empirically assess the correlation between ESG disclosures and long-term financial performance. This approach allows for the simultaneous processing of both structured and unstructured ESG data, using graph-based modeling and reinforcement learning to guide sustainability aligned policy optimization. Our empirical results show that firms with consistent and well-structured ESG strategies exhibit significantly superior long-term financial outcomes compared to those with weak or inconsistent ESG engagement. This study not only confirms the value of ESG engagement in enhancing financial resilience but also offers practical recommendations for investors, regulators, and corporate decision-makers, emphasizing consistent disclosure, sector-aligned ESG investment, and proactive adaptation to policy shifts.

1. Introduction

In recent years, integrating Environmental, Social, and Governance (ESG) principles into corporate strategy has become key to sustainable business success, especially in China’s changing regulatory and economic environment [1]. This shift is partly driven by increasing emphasis from regulatory bodies like the China Securities Regulatory Commission (CSRC), which issued the 2022 Guidelines on Strengthening ESG Disclosure, requiring more transparency on sustainability risks and governance [2]. Complementary policies such as the Green Industry Guiding Catalogue and the expansion of the green bond market have reinforced the institutional push toward ESG compliance [3]. While ESG adoption is sometimes seen as symbolic or reputational, studies show it can also bring measurable financial benefits. For example, firms with higher ESG ratings have been shown to exhibit stronger Return on Assets (ROA), lower capital costs, and improved investor sentiment, particularly in industries subject to environmental regulation [4]. Frameworks such as the China Corporate ESG Disclosure Guidelines and pilot implementations of SASB- and TCFD-aligned standards are further anchoring ESG reporting practices in China. These developments suggest that ESG strategies are not merely aspirational but are increasingly aligned with material financial outcomes and strategic competitiveness, particularly in an environment of rising investor scrutiny and evolving regulatory expectations [5].

Early studies exploring the financial implications of ESG strategies predominantly drew upon established financial theories and expert-driven evaluation criteria [6]. These models typically employed structured metrics and rule-based logic to assess firm performance, relying heavily on predefined benchmarks and regulatory disclosures [7]. While such approaches provided a systematic starting point for integrating ESG into financial assessments, they often struggled to adapt to the multidimensional and evolving nature of sustainability practices [8]. Thus, it is important to study how ESG strategies affect long-term financial outcomes in China’s changing capital markets. In 2022, the China Securities Regulatory Commission (CSRC) introduced mandatory ESG disclosure guidelines for listed companies, accompanied by enhanced green finance regulations such as the updated Green Bond Endorsed Project Catalogue. Simultaneously, institutional investors—both domestic and foreign—have begun integrating ESG metrics into valuation models and portfolio screening [9,10]. Traditional evaluation models often rely on backward-looking financial ratios and fail to account for the evolving materiality of ESG factors, especially when sustainability initiatives have long-term payoff horizons. Moreover, a critical distinction must be made between ESG disclosure (the act of reporting) and actual ESG performance (measurable improvements in environmental or social outcomes). This gap often results in “green window dressing” or symbolic compliance, which may distort assessments of financial risk and return. Our proposed approach addresses these gaps by combining structured financial data with unstructured ESG narratives, leveraging temporal dynamics and graph-based reasoning to capture the substantive effects of ESG initiatives [11].

Despite significant advances in ESG research, many existing models overlook the symbolic and dynamic nature of ESG disclosures. These models tend to focus primarily on quantitative ESG metrics, failing to capture the qualitative, context-specific aspects of ESG performance that are particularly relevant in markets like China. For instance, many traditional frameworks are rigid in their application of standardized ESG scores and do not account for the evolving regulatory context or sector-specific nuances that significantly affect ESG performance. Our model is distinct in that it integrates both structured financial data and unstructured ESG narratives, enabling it to capture not only the static ESG metrics but also the temporal and symbolic dimensions of ESG actions. By utilizing advanced natural language processing (NLP) techniques and graph-based learning, our model is able to process ESG disclosures as dynamic and contextually rich sources of information. This approach allows for more accurate predictions of long-term financial outcomes by considering the changing nature of ESG performance over time and its interaction with regulatory shifts.

Responding to the growing intricacy of ESG information, subsequent research began to incorporate algorithmic models that could uncover patterns from large-scale datasets and heterogeneous information sources [12]. These methods extended traditional frameworks by allowing more dynamic assessment of the interactions between ESG factors and financial performance [13]. For example, statistical learning techniques were increasingly applied to link firm disclosures, market indicators, and ESG ratings with financial outcomes across varying time horizons [14]. While these models contributed to enhanced empirical understanding, they also raised concerns about interpretability, consistency, and data reliability, especially in markets like China where ESG standardization remains in flux [15].

More recently, advancements in natural language processing and computational modeling have opened new possibilities for ESG analysis through the use of semantic-rich textual data [16]. These approaches utilize corporate reports, media coverage, and other narrative disclosures to extract insights that extend beyond quantitative indicators [17]. Responding to the growing complexity of ESG information, in our proposed framework, Long Short-Term Memory (LSTM) is integrated as part of the ESG temporal encoder, while Transformer-based modules are utilized for cross-sector risk propagation analysis and symbolic attention fusion, consistent with recent domain-adapted modeling practices to extract patterns from large-scale, multi-modal ESG datasets [18]. These models are typically validated through cross-validation, temporal holdout tests, or out-of-sample forecasts to ensure robustness in predicting financial or reputational outcomes. In addition to structured indicators, natural language processing (NLP) techniques have been employed to analyze ESG narratives from annual reports and news articles, using tools such as word embeddings, BERT-based classifiers, and topic modeling. Despite these advancements, challenges persist, especially in China, where ESG disclosure standards vary across sectors and lack temporal consistency. Recent research has sought to localize models by adapting them to domain-specific ESG taxonomies (e.g., CSRC guidelines), applying frequency-aware normalization techniques, and customizing entity recognition for Chinese regulatory language. To enhance transparency and interpretability, explainable AI tools such as SHAP (Shapley Additive Explanations) and attention visualization are increasingly integrated into model pipelines. However, limitations persist. Many existing models rely heavily on the quality of voluntary ESG disclosure, which can introduce reporting bias and greenwashing. Others fail to capture causal mechanisms or disentangle long-term ESG effects from short-term volatility. Our proposed approach seeks to address these issues by combining symbolic modeling with deep learning and incorporating structured priors and temporal alignment, offering a more robust and interpretable framework tailored to China’s evolving ESG environment [19].

To address the limitations of symbolic rigidity, data-driven inconsistencies, and semantic generalization, we propose a novel hybrid approach that combines domain-specific pre-trained language models with financial performance regression, tailored to the Chinese capital market. This method not only captures textual and structured ESG signals but also contextualizes them using localized knowledge and industry heterogeneity. By integrating multi-source data and advanced NLP techniques, our framework ensures both interpretability and predictive power, aligning with the unique disclosure characteristics and regulatory structures in China. Furthermore, our empirical design incorporates time-series financial performance indicators to assess long-term impact, thus bridging the gap between ESG actions and strategic financial outcomes. This integrated method offers a new paradigm for ESG evaluation that supports decision-making for investors, regulators, and corporate managers alike.

We introduce a new domain-adapted pre-trained model that jointly encodes ESG textual disclosures and financial signals, enabling end-to-end prediction of long-term firm performance.

The method demonstrates strong adaptability across sectors and regulatory environments in China, supporting robust, interpretable, and scalable ESG assessment.

To operationalize this hypothesis, we propose a hybrid computational framework that integrates symbolic reasoning, temporal dynamics modeling, and graph-based learning. The full architecture—described in detail in Section 3—is designed to process heterogeneous ESG information and produce interpretable forecasts of long-term financial performance across diverse sectors and datasets.

Building upon the context outlined above, the overarching goal of this study is to investigate whether and how ESG management strategies contribute to the long-term financial performance of publicly listed firms in China.

The main objectives of the study are as follows: (i) To develop a computational framework capable of capturing both structured financial data and unstructured ESG textual information; (ii) To integrate ESG-related disclosures with firm-level financial metrics through an interpretable, graph-based, and temporally aware learning model; (iii) To conduct extensive empirical validation across multiple ESG data sources to ensure generalizability of findings; and (iv) To provide actionable insights into the strategic use of ESG policies in enhancing long-term financial outcomes under regulatory and market uncertainty. The working hypothesis of this research is the following: Firms with consistent, sector-aligned, and transparently communicated ESG strategies exhibit superior long-term financial performance compared to firms with weak or inconsistent ESG engagement. This hypothesis is tested by examining multi-year Return on Assets (ROA) and Tobin’s Q trends across ESG quartiles, supported by machine learning-based regression and policy optimization techniques. The study further explores whether the predictive relationship between ESG and financial outcomes remains stable across sectors and data sources. This study contributes to the growing body of research on ESG practices in the China Capital Market, providing insights into how Hybrid Modeling can improve financial forecasting in the context of ESG disclosures. Table 1 presents the definitions of the abbreviations used in this study, providing clarity on terms like MLP, DAG, and QKV.

2. Related Work

2.1. ESG and Financial Performance

Over the past two decades, the relationship between Environmental, Social, and Governance (ESG) practices and corporate financial performance has attracted considerable academic and practitioner interest. A diverse body of empirical research—spanning cross-sectional regressions, panel data models, and event studies—has investigated how ESG adoption influences a firm’s risk-return profile [20]. While many studies report positive or non-negative associations, the findings are not uniform. For instance, Friede et al. synthesized over 2000 studies and found that approximately 90% reported non-negative results, with 60% showing statistically significant positive relationships. However, these effects vary significantly across geographies, sectors, firm sizes, and ESG dimensions. Most literature establishes correlations rather than causality. Only a limited number of studies employ quasi-experimental designs—such as difference-in-differences or instrumental variables—to address endogeneity. Even then, challenges like omitted variable bias persist. ESG performance may be confounded by firm-specific attributes such as reputation, managerial quality, or innovation capability, which influence both sustainability engagement and financial outcomes. Despite these limitations, several mechanisms have been proposed to explain how ESG practices might enhance firm value. These include reduced regulatory penalties through environmental compliance, stronger stakeholder trust via social initiatives, and lower capital costs due to governance transparency [21]. For example, companies that implement robust emission control policies or fair labor practices have been shown to improve operational efficiency and reduce litigation risks over time. Nonetheless, many of these benefits manifest over extended time horizons and may entail short-term costs, such as higher disclosure expenditures or compliance burdens. The governance pillar of ESG deserves particular attention. Practices such as board independence, shareholder rights protection, and anti-bribery controls are consistently associated with improved financial outcomes in emerging markets [22]. However, disclosure does not necessarily imply authentic performance. In jurisdictions with weak enforcement, symbolic compliance or “greenwashing” may distort ESG assessments and mislead investors. In the context of China, ESG–finance research is still developing, but evidence suggests that firms with strong ESG performance tend to access capital more efficiently and attain valuation premiums. However, results are more volatile in sectors like heavy industry, where ESG standards remain ambiguous and enforcement varies. These patterns highlight the need for context-sensitive modeling that accounts for sectoral, temporal, and regulatory heterogeneity. Our study contributes to this discourse by proposing a hybrid framework that captures both structured ESG indicators and unstructured textual disclosures, offering a more interpretable and temporally aware assessment of ESG’s financial relevance.

2.2. ESG Strategies in Emerging Markets

Emerging markets provide a unique backdrop for the development and impact of Environmental, Social, and Governance (ESG) strategies. Unlike developed economies that typically feature well-established regulatory systems and institutional investors actively promoting sustainability, emerging markets such as China exhibit diverse levels of ESG adoption, inconsistent reporting standards, and varying degrees of investor awareness. Research highlights the importance of institutional gaps, regulatory environments, and socio-political dynamics in influencing how ESG is integrated within corporate practices [23]. The institutional context in these markets significantly affects corporate governance and sustainability approaches. Weak legal enforcement and a lack of transparency in disclosure can result in superficial ESG practices—commonly referred to as “greenwashing”—where companies adopt ESG labels without meaningful execution. This complicates efforts to accurately assess ESG outcomes and necessitates the use of refined methodologies that can adapt to local specificities [24]. In China, ESG initiatives have gained traction largely due to policy-driven signals from authorities, including guidelines on green finance and sustainability objectives embedded in national development plans. Regulatory support has played a central role in directing corporate ESG behavior, especially among state-owned enterprises. This top–down approach tends to foster a compliance-based ESG culture, as opposed to one driven by market mechanisms or active stakeholder involvement [25]. At the same time, market-oriented ESG developments are emerging. Stock exchanges in major cities have begun requiring listed companies to improve ESG disclosures. These regulatory efforts are complemented by the growth of ESG-themed investment products and indices, which offer incentives for firms demonstrating strong sustainability performance. Nonetheless, the evolving nature of these initiatives presents a dual challenge: aligning with international ESG standards while adapting to the complexities of domestic institutional settings [26]. In the context of China, political connections and regulatory pressure significantly shape ESG behavior [9]. Moreover, mandatory disclosure initiatives appear to catalyze green innovation [10], underscoring the instrumental role of national policy in ESG integration.

While ESG adoption in emerging markets has made notable progress, the challenges of symbolic compliance and “greenwashing” remain pronounced. In environments where disclosure mandates are weakly enforced or non-standardized, firms may adopt ESG labels without meaningful implementation. This misalignment between ESG disclosure and actual performance complicates reliable assessment and can mislead stakeholders. Recent research emphasizes the need for methodologies that are not only data-driven but also contextually adaptive—accounting for regulatory ambiguity, language variation, and cultural framing of ESG dimensions. For example, models should integrate localized ESG taxonomies, apply soft rule-based constraints for ambiguous disclosures, and incorporate semi-supervised techniques to handle partial or inconsistent data. Such methodological innovations are essential to ensure that ESG assessments in emerging markets reflect substantive engagement rather than performative reporting.

2.3. Long-Term Financial Impact Metrics

Assessing the long-term financial implications of Environmental, Social, and Governance (ESG) strategies requires the application of robust analytical frameworks and well-defined performance indicators [27]. While traditional financial metrics such as Return on Assets (ROA), Return on Equity (ROE), and Tobin’s Q are frequently used in ESG-related studies, evaluating long-term effects calls for dynamic modeling approaches that account for the delayed impact of ESG initiatives on financial outcomes [28]. A prominent approach involves the use of longitudinal panel data to examine how ESG engagement unfolds over time and accumulates influence on firm performance. Models such as fixed-effects and random-effects are commonly employed to isolate the effect of ESG from broader economic trends, company-specific traits, and sectoral dynamics. Some studies have also adopted quasi-experimental designs, such as difference-in-differences analysis, to investigate the sustained impact of ESG-related events on market valuation, highlighting the need for consistent and long-term ESG commitments [29]. In the Chinese context, research on long-term financial outcomes often integrates factors that reflect the local institutional setting, including the extent of government support, political affiliations, and the nature of firm ownership. Findings indicate that companies with sustained ESG strategies tend to perform better in terms of profitability and market valuation, especially when their practices align with national policy objectives [30]. This alignment may act as a positive signal to stakeholders and can lead to favorable access to state-backed resources. To address methodological challenges such as endogeneity, techniques like propensity score matching and structural equation modeling are increasingly utilized to establish more accurate causal relationships between ESG practices and financial performance. The adoption of machine learning tools has become more prevalent in ESG research, enabling the analysis of complex and large-scale datasets [31]. These advanced methods help uncover non-linear relationships and deeper interactions among ESG dimensions, firm behavior, and market dynamics, offering enhanced predictive capabilities for long-term financial performance. Addressing concerns of endogeneity and time-lagged effects, studies have employed fixed-effects, IV regression, and causal models to estimate ESG impacts more precisely [32]. These techniques help disentangle ESG effects from confounding variables. Xu et al. (2023) [22] reviewed how machine learning tools can complement traditional approaches by modeling nonlinear ESG–finance dynamics.

In addition to top–down regulatory guidance, bottom–up market mechanisms have increasingly shaped ESG practices in China. Institutional investors, ESG-themed funds, and third-party rating agencies are gaining influence, particularly among publicly traded private firms. Regional disparities are also evident: firms in economically developed zones such as the Yangtze River Delta and Pearl River Delta exhibit higher ESG disclosure scores and participation in international ESG indices compared to inland or resource-intensive regions. Furthermore, privately held firms in Shenzhen often respond more actively to ESG rating pressure, while state-owned enterprises in Beijing tend to align more closely with national policy signals.

3. Method

3.1. Overview

This section introduces a comprehensive framework for ESG (Environmental, Social, and Governance) management, developed to systematically integrate multifaceted sustainability considerations into strategic corporate decision-making processes. As contemporary enterprises increasingly recognize the critical impact of ESG factors on financial resilience, stakeholder engagement, and regulatory compliance, it becomes essential to formulate rigorous methodologies that embed ESG concerns into the core of strategic operations. The following subsections develop a structured pathway to understand, formalize, and advance a novel ESG-informed management paradigm.

Our methodological design integrates multiple machine learning techniques within a unified framework. The core model architecture is composed of a temporal encoder built upon a gated recurrent unit (GRU) to capture ESG signal sequences and a symbolic-structural module leveraging graph attention networks (GATs) to learn cross-factor dependencies. These modules feed into a Transformer-style decoder for policy prediction and ESG forecasting. The encoder–decoder pipeline is further enhanced by a dual-branch architecture that processes structured financial indicators and unstructured ESG textual content separately, fusing them at the latent representation stage. To ensure rigorous performance evaluation, the dataset is split chronologically using an 80/10/10 ratio for training, validation, and testing, ensuring no future data leaks into earlier training windows. Hyperparameters—such as learning rate, batch size, dropout, and number of attention heads—are optimized via grid search on the validation set, and early stopping is applied based on validation loss with a patience threshold of 10 epochs. All experiments are repeated three times with different random seeds to capture variability in training dynamics. Addressing data biases is crucial in ESG-related modeling. Sector imbalance is mitigated via stratified sampling to ensure equal representation across industries. In addition, ESG disclosure sparsity is handled by temporal imputation and partial masking strategies. Then, firm size bias is reduced through z-score normalization of financial indicators. To control for reporting frequency heterogeneity, we introduce frequency-aware positional encoding in the temporal encoder. These techniques jointly enhance the robustness and generalizability of our model across firms with diverse characteristics and disclosure behaviors. To capture industry-specific ESG dynamics, we incorporate sector-aware embeddings that allow the model to distinguish between disclosure norms and regulatory contexts across industries. These embeddings are learned jointly with firm-level temporal features in a GRU-based encoder and fused with graph-level structural priors derived from industrial linkage data. During training, models are validated using industry-stratified panel splits to ensure robustness of results across sectors such as energy, manufacturing, and services.

Section 3.2 introduces the foundational elements of ESG integration by formalizing the ESG strategy problem through a mathematical lens. We establish a rigorous symbolic structure that encapsulates the heterogeneity of ESG signals across firms, sectors, and temporal horizons. This symbolic formulation serves a dual purpose: To provide a clear problem definition that separates ESG assessment conventional financial evaluation and to offer a standardized representation space in which new optimization criteria and constraints are defined. We clarify key constructs such as ESG scoring tensors, time-variant disclosure matrices, regulatory compliance maps, and stakeholder-weighted utility functions. These constructs are synthesized into a unifying formulation that can be directly linked to strategic planning modules. Special attention is given to the challenge of ESG signal sparsity and inter-factor entanglement, both of which are formally modeled to expose the theoretical tension between ESG fidelity and operational tractability. Section 3.3 introduces a novel ESG modeling architecture—Strategic ESG Representation Generator (SERG)—which serves as the core of our proposed framework. Unlike traditional factor models or black-box ESG prediction pipelines, SERG is constructed with structural interpretability and domain adaptability at its center. It integrates temporal logic over ESG narratives with latent factor graphs extracted from both structured and unstructured data streams, such as annual reports, emissions disclosures, litigation risk indices, and human capital indicators. We detail how SERG encodes entity-specific ESG exposure through hybridized embeddings, including symbolic attention kernels, and semi-explicit policy-aware vector fields. The model architecture is designed to simultaneously track cross-factor diffusion and ESG-specific causality chains, allowing it to disentangle short-term ESG fluctuations from persistent thematic trends. This enables a principled decomposition of ESG risk into action-relevant, sector-specific representations that are deployable in both strategic forecasting and compliance alignment. Section 3.4 presents an advanced ESG optimization protocol, referred to as Adaptive Sustainability Policy Search (ASPS). This component constitutes a decision-theoretic framework that dynamically guides corporate actors through ESG-relevant choices under multi-objective constraints. Unlike classical portfolio optimization or CSR prioritization schemes, ASPS is built upon an evolving policy space that reflects changes in stakeholder preference distributions, regulatory regimes, and environmental baselines. The core algorithm employs a feedback-driven, model-based reinforcement schema that explores feasible sustainability transitions subject to cost–impact equilibria. The strategy optimization process is informed by the SERG outputs, which serve as policy conditionals, and it incorporates symbolic risk penalties derived from the ESG representation space. This endows ASPS with the ability to avoid overfitting to static ESG targets and to accommodate emerging sustainability narratives in a principled, mathematically sound manner.

Recognizing the potential barriers to adoption in resource-constrained or non-technical environments, we also propose a simplified variant of the framework for practical deployment. This variant removes the deep temporal components and instead leverages structured ESG scores and rule-based heuristics for risk estimation. It can be implemented in lightweight environments such as spreadsheet-based systems or low-code dashboards. In addition, the modular nature of our framework allows adaptation to different regulatory regimes and data granularities by replacing or bypassing symbolic reasoning modules and retraining on localized ESG taxonomies. We also provide guidelines on how the model may be scaled down or adjusted for industries with limited disclosure or differing ESG maturity levels. These design choices aim to balance model rigor with usability, expanding its relevance across both advanced and emerging market contexts. In response to the practical limitations associated with deploying a full symbolic ESG transition game model—particularly in resource-constrained environments—we provide a simplified configuration that removes the deep symbolic and dynamic game-theoretic modules. This version replaces temporal dynamics with rule-based heuristics and pre-aggregated ESG scores. It is designed for ease of deployment via spreadsheet tools or web dashboards, ensuring usability for organizations lacking advanced infrastructure. The model supports sector-specific configuration templates, enabling the prioritization of environmental, social, or governance components in accordance with industry-specific sustainability imperatives. To incorporate non-quantitative dimensions, we integrate reputational risk scores and sentiment analysis from external ESG news sources, which are embedded into the decision framework as soft symbolic constraints. These enhancements support interpretability and real-world alignment. Moreover, we provide mapping guides to align our symbolic variables with GRI and SASB frameworks, improving transparency and interoperability. To ensure robustness in environments with inconsistent ESG disclosures, the model applies probabilistic masking and harmonization techniques using third-party benchmark scores (e.g., Refinitiv, RepRisk), improving resilience to data gaps and enabling broader applicability across regulatory regimes.

3.2. Preliminaries

To rigorously investigate ESG management strategies, we begin by formalizing the ESG strategic integration problem into a symbolic and mathematically tractable structure. ESG decision-making, unlike traditional financial modeling, involves multiple non-commensurate objectives, dynamic stakeholder utility profiles, and intertemporal regulatory constraints. Hence, we introduce a symbolic foundation that captures these aspects through formal structures derived from multi-agent utility theory, constrained optimization, and structured semantic representations.

We let $\mathcal{E}=\{E_1,\dots ,E_{n_E}\}$ denote the set of environmental factors, $\mathcal{S}=\{S_1,\dots ,S_{n_S}\}$ the social indicators, and $\mathcal{G}=\{G_1,\dots ,G_{n_G}\}$ the governance criteria relevant to a given organization. We define the ESG signal tensor for an entity i over a time horizon T as

(1)${\mathcal{X}}^{\left(i\right)}\in {\mathbb{R}}^{(n_E+n_S+n_G)\times T},{\mathcal{X}}^{\left(i\right)}=\left[\begin{array}{c}{X}_E^{\left(i\right)}\\ X_S^{\left(i\right)}\\ X_G^{\left(i\right)}\end{array}\right].$

We define the stakeholder-weighted utility function $U^{\left(i\right)}:{\mathbb{R}}^{(n_E+n_S+n_G)}\to \mathbb{R}$ for entity i, where

(2)$U^{\left(i\right)}\left(\mathbf{x}\right)=\sum _{j=1}^{n_E+n_S+n_G}{\omega }_j^{\left(i\right)}{u}_j\left(x_j\right),$

with ${\omega }_j^{\left(i\right)}$ encoding the weight of stakeholder group preference over factor j and $u_j$ a factor-specific transformation.

In practice, the weights ${\omega }_j^{\left(i\right)}$ are derived using a multi-criteria decision analysis (MCDA) framework, such as the Analytic Hierarchy Process (AHP), incorporating stakeholder input through ESG surveys. For example, environmental dimensions are prioritized in energy-intensive sectors, while governance is emphasized in financial services. These weights are normalized and sector-specific to reflect domain-relevant ESG priorities.

To encode regulatory constraints, we define a feasible ESG state manifold ${\mathcal{M}}_R\subset {\mathbb{R}}^{n_E+n_S+n_G}$ characterized by

(3)${\mathcal{M}}_R=\left\{\mathbf{x}\in {\mathbb{R}}^n\mid C\mathbf{x}\le \mathbf{b},\mathbf{x}\ge 0\right\},$

where $C\in {\mathbb{R}}^{m\times n}$ encodes multi-jurisdictional ESG compliance constraints.

The ESG strategy problem is then formalized as

(4)$\underset{\mathcal{P}}{min}\left[-\sum _{t=1}^T{\gamma }^t{U}^{\left(i\right)}\left({\tilde{\mathcal{X}}}_t^{\left(i\right)}\right)+\lambda \sum _{t=1}^T{\parallel {\tilde{\mathcal{X}}}_t^{\left(i\right)}-{\mathcal{B}}_t\parallel }_A\right],$

where ${\parallel ·\parallel }_A$ denotes a relevance-weighted Mahalanobis distance and $\lambda$ controls alignment with benchmark expectations.

We define a symbolic ESG transition game among competing agents $i=1,\dots ,N$, where each entity’s ESG state influences others through shared resources, reputational contagion, and regulatory interdependence. This is captured via a dynamic game:

(5)$\forall i,\underset{{\mathcal{P}}^{\left(i\right)}}{max}\mathbb{E}\left[\sum _{t=1}^T{\gamma }^t{U}^{\left(i\right)}\left({\tilde{\mathcal{X}}}_t^{\left(i\right)}\right)\mid {\mathcal{P}}^{(-i)}\right],$

with ${\mathcal{P}}^{(-i)}$ denoting the policies of all agents except i and expectation taken over the joint ESG evolution process.

To further clarify the notion of a symbolic ESG transition game, we define it as a dynamic sequence of ESG-aligned behavioral changes that firms undertake in response to external regulatory or policy shifts. These transitions are symbolic in the sense that each action—such as disclosing carbon neutrality plans or improving board diversity—is mapped to a semantically labeled ESG strategy. For example, from a CSRC disclosure document issued in 2022 requiring mandatory carbon intensity reporting, a firm’s published ESG report may introduce a new section detailing Scope 2 emission metrics and renewable energy initiatives. This policy–action pair constitutes a symbolic ESG transition. Repeating this process across multiple firms and over time enables us to construct a symbolic trajectory graph, where each node represents a firm-time ESG state and edges reflect temporal transitions conditioned on external policy stimuli. A policy-aware vector field is then defined as a latent directional map within the ESG embedding space, where each vector encodes how policy-driven signals (e.g., carbon tax implementation, social labor law updates) guide ESG representations toward compliance-optimized zones. These vectors are parameterized based on historical firm adaptations, regulatory enforcement timelines, and sector norms. We provide a schematic overview of this construction pipeline in Figure 1.

To address real-world constraints, particularly in low-resource or data-scarce environments, we also introduce a simplified symbolic integration layer. This configuration relies on binary ESG compliance indicators or aggregated third-party ESG scores instead of dense ESG tensors. It enables firms with limited internal ESG tracking capacity to utilize the model using externally verifiable inputs. The stakeholder-weighted utility functions ${\omega }_j^{\left(i\right)}$ are customizable per sector, allowing environmental dimensions to be prioritized in energy-intensive industries, while governance factors dominate in sectors like finance or public administration. We also provide mapping templates aligning our symbolic indicators with GRI and SASB frameworks to ensure practical interoperability with existing ESG disclosure practices. The symbolic utility structure can incorporate qualitative elements such as sentiment scores or reputational indices derived from textual ESG narratives and news coverage. These can be modeled as external modifiers or embedded soft signals, enhancing the completeness and realism of ESG reasoning. We introduce relaxed constraint modeling strategies to accommodate inconsistent or missing ESG disclosures. These include probabilistic masking, imputation-based approximations, and penalized deviation formulations within the optimization problem.

3.3. Strategic ESG Representation Generator (SERG)

To effectively embed ESG factors into strategic-level decision-making, we propose a novel model architecture termed Strategic ESG Representation Generator (SERG). Unlike traditional ESG scoring systems or black-box predictive tools, SERG is a symbolic-structural representation model that captures heterogeneous ESG signals, inter-factor dependencies, policy dynamics, and stakeholder contextuality through a unified multi-layered architecture (as shown in Figure 2).

Symbolic-Structural ESG Modeling

The objective of the Symbolic-Structural ESG Representation Generator (SERG) is to build a structured, interpretable, and temporally aware representation space ${\mathcal{Ƶ}}_t^{\left(i\right)}$ for each entity i at time t defined as

(6)${\mathcal{Ƶ}}_t^{\left(i\right)}=f_{\mathrm{SERG}}\left({\tilde{\mathcal{X}}}_{1:t}^{\left(i\right)},{\mathcal{P}}_{1:t}^{\left(i\right)},{\mathcal{C}}^{\left(i\right)},{\mathcal{E}}^{\left(i\right)}\right),$

where ${\tilde{\mathcal{X}}}_{1:t}^{\left(i\right)}$ denotes the historical ESG signal sequences, ${\mathcal{P}}_{1:t}^{\left(i\right)}$ is the sequence of ESG policy changes, ${\mathcal{C}}^{\left(i\right)}$ encodes entity-level constraint sets (such as compliance requirements or sectoral rules), and ${\mathcal{E}}^{\left(i\right)}$ represents external contextual embeddings, such as geopolitical shifts, industrial cycles, and climate indicators.

We first construct a dynamic ESG dependency graph $G_t^{\left(i\right)}=(V_t,E_t)$, where nodes $v_j\in V_t$ represent ESG dimensions, and edges in $E_t$ capture influence relationships among these factors. To capture high-order dynamic interactions, we define a bilinear attention-based adjacency matrix as

(7)$A_t^{\left(i\right)}=\mathrm{softmax}\left(\mathsf{\Psi }·\left({\tilde{\mathcal{X}}}_t^{\left(i\right)}\otimes {\tilde{\mathcal{X}}}_t^{\left(i\right)}\right)\right),$

where $\mathsf{\Psi }\in {\mathbb{R}}^{d\times d}$ is a learnable kernel and ⊗ denotes the outer product across ESG signal dimensions. The softmax operation normalizes the adjacency matrix to represent weighted dependencies among ESG nodes.

Based on this structure, we introduce a symbolic structure parsing module $\mathsf{\Phi }$, which assigns semantic labels to edges in $G_t^{\left(i\right)}$, such as regulatory causality, sectoral coupling, or climate cross-risk. To this end, we define a structural label tensor $S_t^{\left(i\right)}\in {\mathbb{R}}^{n\times n\times l}$, where l is the number of symbolic relation types. It is constructed as

(8)$S_t^{\left(i\right)}=\mathsf{\Phi }\left(A_t^{\left(i\right)},{\mathcal{P}}_{1:t}^{\left(i\right)},{\mathcal{C}}^{\left(i\right)}\right),$

where $\mathsf{\Phi }$ can be implemented using logic rules, graph attention networks, or domain-specific reasoning frameworks to enhance the interpretability of causal and logical ESG structures. To enhance reproducibility and operational clarity, we provide a selection framework for implementing the symbolic parser $\mathsf{\Phi }$. When domain-specific rules are well established (e.g., emission regulations in the energy sector), logic-rule-based parsing offers high interpretability with low computational demand. In contrast, graph attention networks (GATs) are more suited to data-rich contexts where ESG factor interactions are latent or temporal. In mixed scenarios, a hybrid $\mathsf{\Phi }$ implementation may combine logic filters followed by learnable attention refinement. We offer a configuration template for selecting among these modes based on data density, computational budget, and target industry.

Next, we define a state evolution encoder $\mathsf{\Gamma }$ that integrates graph structure and external context to produce the final latent representation ${\mathcal{Ƶ}}_t^{\left(i\right)}$:

(9)${\mathcal{Ƶ}}_t^{\left(i\right)}=\mathsf{\Gamma }\left(A_{1:t}^{\left(i\right)},S_{1:t}^{\left(i\right)},{\mathcal{E}}_{1:t}^{\left(i\right)}\right),$

where $A_{1:t}^{\left(i\right)}$ and $S_{1:t}^{\left(i\right)}$ are the sequences of adjacency matrices and symbolic label tensors up to time t and $\mathsf{\Gamma }$ may leverage graph sequence models combined with Transformer encoders to capture dynamic dependencies and context awareness.

We introduce a constraint-consistency evaluator $\mathsf{\Lambda }$, which assesses whether the latent state ${\mathcal{Ƶ}}_t^{\left(i\right)}$ satisfies the entity-specific constraint set ${\mathcal{C}}^{\left(i\right)}$:

(10)$\mathsf{\Lambda }\left({\mathcal{Ƶ}}_t^{\left(i\right)},{\mathcal{C}}^{\left(i\right)}\right)=\sigma \left(\mathrm{Tr}\left({\mathcal{Ƶ}}_t^{\left(i\right)}{W}_c{\mathcal{C}}^{\left(i\right)\top }\right)\right),$

where $W_c$ is a learnable weight matrix, $\mathrm{Tr}(·)$ denotes the trace operator, and $\sigma$ is a sigmoid function that outputs a soft consistency score in $[0,1]$, providing a differentiable objective for alignment with constraints during training.

To address computational challenges associated with large-scale symbolic label tensors ($S_t^{\left(i\right)}\in {\mathbb{R}}^{n\times n\times l}$) and Transformer-based encoders in $\mathsf{\Gamma }$, we introduce sparsity-aware approximation strategies. These include label pruning based on mutual information thresholds, low-rank tensor decomposition for $S_t^{\left(i\right)}$, and attention head pruning in long-sequence Transformer layers. These techniques reduce memory consumption and accelerate training, especially in real-time ESG monitoring or multi-year backtesting tasks. We formalize a taxonomy of symbolic ESG relations into four categories: (i) intra-domain coherence (e.g., E→E interdependence), (ii) cross-pillar amplification (e.g., E→S spillovers), (iii) risk propagation (e.g., climate cross-risk), and (iv) compliance chaining (e.g., governance→regulatory constraint). Each symbolic label is defined based on ESG reporting standards and stress-tested using synthetic ESG disclosures. The contextual embedding vector ${\mathcal{E}}^{\left(i\right)}$ is constructed from three channels: (1) global economic indicators (e.g., IMF/WTO datasets), (2) industry-specific news sentiment from ESG newswire corpora (pre-trained on Refinitiv ESG news), and (3) climate risk exposure signals updated quarterly. Each context input is normalized and updated at a monthly to quarterly frequency, depending on the data stream. We plan to release standardized preprocessing scripts for replicability.

Temporal Dynamics Encoding

To effectively model the temporal evolution and abrupt transitions in ESG (Environmental, Social, and Governance) indicators, we employ a gated temporal encoder applied over the partially masked signal sequence ${\tilde{\mathcal{X}}}_t^{\left(i\right)}$. This encoder, based on a variant of the Gated Recurrent Unit (GRU), captures long-term dependencies while naturally accommodating missing values in the sequence.

We let $h_t^{\left(i\right)}$ denote the hidden state at time t for entity i. The update equations are defined as follows:

(11)$r_t=\sigma \left(W_r·{\tilde{\mathcal{X}}}_t^{\left(i\right)}+U_r·h_{t-1}+b_r\right),$

(12)$z_t=\sigma \left(W_z·{\tilde{\mathcal{X}}}_t^{\left(i\right)}+U_z·h_{t-1}+b_z\right),$

(13)${\tilde{h}}_t=tanh\left(W_h·{\tilde{\mathcal{X}}}_t^{\left(i\right)}+U_h·(r_t\circ h_{t-1})+b_h\right),$

(14)$h_t^{\left(i\right)}=(1-z_t)\circ h_{t-1}+z_t\circ {\tilde{h}}_t,$

Here, $r_t$ is the reset gate that controls the degree to which the previous state is forgotten, and $z_t$ is the update gate that balances the incorporation of new information with historical memory. This design enables the model to capture long-range ESG trends and respond quickly to shocks such as policy shifts or market disruptions.

To further enhance contextual awareness, we introduce a cross-context attention mechanism that incorporates externalities—such as regulatory updates, geopolitical risks, and macroeconomic fluctuations—represented as symbolic context variables. We let ${\mathcal{E}}_t^{\left(i\right)}=\left\{e_{k,t}^{\left(i\right)}\right\}$ denote a set of contextual indicators associated with entity i at time t. These are projected into a latent context space and aggregated using attention weights:

(15)$c_t^{\left(i\right)}=\sum _k{\alpha }_{k,t}^{\left(i\right)}·\varphi \left(e_{k,t}^{\left(i\right)}\right),{\alpha }_{k,t}^{\left(i\right)}={\displaystyle \frac{exp\left(⟨h_t^{\left(i\right)},\varphi \left(e_{k,t}^{\left(i\right)}\right)⟩\right)}{{\sum }_{j}exp\left(⟨h_t^{\left(i\right)},\varphi \left(e_{j,t}^{\left(i\right)}\right)⟩\right)}},$

In this formulation, $\varphi (·)$ is a nonlinear transformation into the latent context space, and $⟨·,·⟩$ denotes the inner product measuring relevance between the hidden state and context vector. The attention weights ${\alpha }_{k,t}^{\left(i\right)}$ determine the influence of each external factor. The resulting context vector $c_t^{\left(i\right)}$ is concatenated with $h_t^{\left(i\right)}$ to yield an enriched temporal representation, serving as input for downstream tasks such as ESG scoring, trend prediction, or anomaly detection. To handle missing values in ESG time series ${\tilde{\mathcal{X}}}_t^{\left(i\right)}$, we introduce a binary mask matrix $M_t^{\left(i\right)}\in {\{0,1\}}^d$, where $M_t^{\left(i\right)}\left[j\right]=0$ indicates missing feature j at time t. The GRU is modified to skip updates for missing positions by gating them out using $M_t^{\left(i\right)}$. We apply forward-fill and temporal mean imputation for partially missing dimensions to preserve trend continuity. This dual masking-imputation approach enables robust learning on real-world ESG datasets with 10–30% sparsity. The contextual inputs ${\mathcal{E}}_t^{\left(i\right)}$ are structured into a three-channel ontology: (i) geopolitical indicators (e.g., sanctions, elections), (ii) regulatory changes (e.g., disclosure mandates, green policy), and (iii) macro-climatic trends (e.g., emission targets). These are sourced from Refinitiv news corpora, IMF datasets, regional ESG policy trackers, and updated quarterly. Each context signal $e_{k,t}^{\left(i\right)}$ is encoded by a contextual vector transformation $\varphi \left(e\right)$ implemented as a two-layer MLP with ReLU and dropout, pretrained on ESG news tagging tasks to preserve semantic structure. For interpretability, attention maps over ${\mathcal{E}}_t^{\left(i\right)}$ are visualized and validated against known ESG events (e.g., 2022 EU Taxonomy implementation). Attention weights ${\alpha }_{k,t}^{\left(i\right)}$ are normalized using softmax across all context dimensions, and regularized using entropy-based sparsity loss to prevent overfitting to dominant signals. We also introduce dropout (p = 0.2) in the dot-product layer to enhance generalization under noisy inputs.

Interpretable ESG Forecasting

To enable interpretable forecasting of ESG signals, we construct a representation ${\mathcal{Ƶ}}_t^{\left(i\right)}$ that fuses structural, temporal, and contextual information for each entity i at time t:

(16)${\mathcal{Ƶ}}_t^{\left(i\right)}=\eta \left(h_t^{\left(i\right)}\parallel \mathrm{vec}\left(A_t^{\left(i\right)}\right)\parallel c_t^{\left(i\right)}\right),$

where $h_t^{\left(i\right)}$ is a temporal feature derived via Transformer-based encoding, $A_t^{\left(i\right)}$ encodes structural relations from a heterogeneous graph, and $c_t^{\left(i\right)}$ denotes contextual inputs such as regulatory or industry conditions. The operator $\mathrm{vec}(·)$ vectorizes the matrix, and $\eta (·)$ is a multi-layer perceptron with skip-connections (as shown in Figure 3).

To semantically constrain the embedding ${\mathcal{Ƶ}}_t^{\left(i\right)}$, we employ supervised contrastive learning guided by domain-specific ESG taxonomies $\mathcal{T}=\left\{{\tau }_k\right\}$, each representing a well-defined ESG concept. The contrastive loss function is defined as

(17)${\mathcal{L}}_{\mathrm{tax}}=-\sum _{i}log{\displaystyle \frac{exp\left(\mathrm{sim}({\mathcal{Ƶ}}_t^{\left(i\right)},{\tau }_{+}^{\left(i\right)})/\tau \right)}{{\sum }_{k}exp\left(\mathrm{sim}({\mathcal{Ƶ}}_t^{\left(i\right)},{\tau }_k)/\tau \right)}},$

where $\mathrm{sim}(·,·)$ denotes cosine similarity, $\tau$ is the temperature parameter, and ${\tau }_{+}^{\left(i\right)}$ is the positive anchor aligned with sample i.

To support downstream applications such as ESG trajectory forecasting or risk of compliance violation, we integrate a prediction module that takes ${\mathcal{Ƶ}}_t^{\left(i\right)}$ as input to estimate future ESG signals. We let ${\widehat{\mathcal{X}}}_{t+\delta }^{\left(i\right)}=g\left({\mathcal{Ƶ}}_t^{\left(i\right)}\right)$ be the prediction for horizon $\delta$; then, the forecasting loss is

(18)${\mathcal{L}}_{\mathrm{forecast}}=\sum _{t,i}{∥{\widehat{\mathcal{X}}}_{t+\delta }^{\left(i\right)}-{\tilde{\mathcal{X}}}_{t+\delta }^{\left(i\right)}∥}^2,$

where ${\tilde{\mathcal{X}}}_{t+\delta }^{\left(i\right)}$ is the observed ESG signal at time $t+\delta$.

The overall training objective balances forecasting accuracy, semantic alignment, and model regularization:

(19)${\mathcal{L}}_{\mathrm{SERG}}={\lambda }_1·{\mathcal{L}}_{\mathrm{forecast}}+{\lambda }_2·{\mathcal{L}}_{\mathrm{tax}}+{\lambda }_3·\mathsf{\Omega }\left(\mathsf{\Theta }\right),$

with ${\lambda }_1,{\lambda }_2,{\lambda }_3$ as scalar weights and $\mathsf{\Omega }\left(\mathsf{\Theta }\right)$ denoting regularization over trainable parameters $\mathsf{\Theta }$.

To ensure interpretability, SERG enforces symbolic decomposability of the embedding ${\mathcal{Ƶ}}_t^{\left(i\right)}$. Each dimension corresponds to a human-interpretable ESG metafeature such as environmental trajectory or governance shock:

(20)${\mathcal{Ƶ}}_t^{\left(i\right)}={\left[\text{E\_trajectory},\text{S\_sentiment},\text{G\_compliance},\text{Carbon\_volatility},\text{Governance\_shock},\dots \right]}^T.$

Each metafeature is either directly computed by symbolic rules or traced back via gradient attribution to the input features $\tilde{\mathcal{X}}$ and external priors $\mathcal{P}$, enabling transparent ESG decision-making and regulatory auditing.

To enhance the accessibility and scalability of SERG across different organizational capacities, we introduce a lightweight variant of the model that omits the graph-based attention mechanism. In this configuration, structured ESG indicators and basic correlation matrices are used as substitutes for the dynamic ESG dependency graph, making the framework deployable in spreadsheet or dashboard environments without loss of core functionality. We propose that the full-featured SERG architecture be embedded into a user-facing interface, such as a web-based dashboard or an Excel-based toolkit, enabling non-technical users to upload ESG disclosures and receive interpretable outputs including predicted financial impacts and policy suggestions. To better model real-world uncertainty and stakeholder volatility, we allow the SERG structure to incorporate sentiment signals, news-derived controversy flags, and soft symbolic indicators derived via NLP. These optional inputs expand the symbolic-semantic coverage to reflect the more subjective dimensions of ESG performance. In terms of forecasting, SERG integrates a temporal forecasting head which can be instantiated using either GRU-based regressors or probabilistic scenario-based simulation models. These methods are particularly valuable in fast-changing industries such as tech or green energy, where past ESG signals may not adequately predict future risk dynamics. To ensure adaptability across diverse regulatory environments, we support region-aware constraint modules that adjust ESG compliance targets, risk penalization, and disclosure weighting according to local governance codes (e.g., CSRC for China, SEBI for India, SEC for the US). A configuration file or region-specific template can be used to tune the model accordingly.

To formalize strategic ESG decision-making, we define the optimization as a Stackelberg game, where the firm acts as the leader and market regulators or investors act as followers. The firm selects a policy trajectory ${\mathcal{P}}^{\left(i\right)}$ anticipating possible reactions from the environment. The reward function integrates ESG utility and regulatory feedback:

(21)$\underset{{\mathcal{P}}^{\left(i\right)}}{max}\underset{\mathcal{R}}{min}\mathbb{E}\left[\sum _{t=1}^T{\gamma }^t{U}^{\left(i\right)}({\mathcal{Ƶ}}_t^{\left(i\right)},{\mathcal{R}}_t)\right]$

where ${\mathcal{R}}_t$ encodes the response dynamics of external stakeholders. The equilibrium strategy is approximated via iterative best response under policy-conditioned reinforcement learning.

3.4. Adaptive Sustainability Policy Search (ASPS)

Building upon the structured ESG representation provided by SERG, we now introduce a novel policy search framework termed Adaptive Sustainability Policy Search (ASPS). This strategy module is designed to optimize ESG-related decisions in a dynamic, feedback-sensitive environment, incorporating multi-objective constraints, evolving stakeholder expectations and regulatory shifts (as shown in Figure 4).

To address limitations of conventional MLP or Transformer architectures—which typically operate on homogeneous vector inputs and lack symbolic interpretability—we propose an Adaptive Symbolic Projection Structure (ASPS). This module explicitly incorporates symbolic ESG constructs into the learning process by projecting high-dimensional textual and numeric ESG features into a structured latent space guided by policy-driven priors. Unlike standard MLPs that perform dense transformations over concatenated features, ASPS first encodes symbolic meta-concepts (e.g., emission compliance, board independence) as projection anchors in the latent space. ESG input data are then adaptively aligned to these anchors via a policy-aware attention mechanism, enabling semantically interpretable dimensions. This mechanism resembles attention but is constrained by domain-specific symbolic priors instead of being purely data-driven. In contrast to Transformer models, which excel at sequence encoding but often obscure feature semantics, ASPS enforces symbolic alignment at each projection layer and dynamically adjusts projection weights based on external policy conditions. The result is a hybrid latent representation that preserves symbolic traceability while enabling downstream neural computation. We provide a flowchart of the full modeling pipeline in Figure 5, illustrating how ESG data, symbolic anchors, policy priors, and prediction targets are processed through the ASPS and subsequent modules.

Policy Optimization Framework

The Adaptive Sustainable Policy Search (ASPS) framework is designed to learn an optimal policy trajectory ${\mathcal{P}}^{\left(i\right)}={\left\{p_t^{\left(i\right)}\right\}}_{t=1}^T$ for each entity i, dynamically responding to evolving ESG structural representations ${\mathcal{Ƶ}}_t^{\left(i\right)}$ generated by the Structural Embedding for Responsible Governance (SERG) module. Each policy aims to strategically balance long-term utility gains against ESG-specific costs while adhering to sectoral benchmarks and risk constraints.

We let $\mathcal{A}\subset {\mathbb{R}}^d$ denote the admissible ESG action space, encompassing quantifiable decisions such as capital reallocation to sustainable initiatives, workforce well-being programs, or regulatory compliance reforms. At every timestep t, the policy $\pi$ maps an entity’s structural ESG state to an action:

(22)$\pi :{\mathcal{Ƶ}}_t^{\left(i\right)}\mapsto p_t^{\left(i\right)}\in \mathcal{A},\forall t\in \{1,\dots ,T\}.$

At each time step t, the model observes the ESG state ${\mathcal{Ƶ}}_t^{\left(i\right)}$ of firm i and outputs a policy action $p_t^{\left(i\right)}$, such as increasing renewable investments or improving governance structure. The action space $\mathcal{A}$ includes all feasible ESG actions aligned with industry and regulatory constraints.

The transition dynamics of the structural state are modeled as a stochastic process governed by a policy-conditioned evolution function ${\mathsf{\Phi }}_{\pi }$, influenced by exogenous uncertainty ${ϵ}_t\sim \mathcal{E}$:

(23)${\mathcal{Ƶ}}_{t+1}^{\left(i\right)}={\mathsf{\Phi }}_{\pi }\left({\mathcal{Ƶ}}_t^{\left(i\right)},p_t^{\left(i\right)},{ϵ}_t\right),$

where ${\mathsf{\Phi }}_{\pi }$ is assumed to be Markovian and smooth, encoding structural dependencies such as regulatory lags or environmental inertia. The ESG state of a firm evolves over time based on its current status, the chosen ESG policy action, and random external factors like market shocks or regulatory changes.

The objective is to maximize the discounted cumulative ESG-aligned utility, accounting for both direct stakeholder impact and regulatory or resource penalties. The utility function $U^{\left(i\right)}(·)$ reflects a time- and entity-specific aggregation of stakeholder preferences, while $R(·)$ quantifies ESG-relevant cost terms. Formally,

(24)$J^{\left(i\right)}\left(\pi \right)=\mathbb{E}\left[\sum _{t=1}^T{\gamma }^t·U^{\left(i\right)}\left({\mathcal{Ƶ}}_t^{\left(i\right)}\right)-\beta ·R\left(p_t^{\left(i\right)}\right)\right],$

with $\gamma \in (0,1)$ denoting a temporal discount factor and $\beta >0$ a scalar controlling the utility–cost trade-off. This equation represents the long-term net benefit for firm i, balancing ESG utility (e.g., improved reputation or resilience) with the cost of ESG actions (e.g., investment expenses). The discount factor $\gamma$ reflects time preference, and $\beta$ controls how much penalty is placed on cost.

To incorporate external compliance or sectoral alignment, we impose a benchmark guidance term using a reference trajectory ${\left\{{\mathcal{B}}_t\right\}}_{t=1}^T$, which may represent an idealized ESG evolution path defined by policy standards, industry consensus, or decarbonization targets. The divergence penalty is structured as

(25)${\mathcal{L}}_{\mathrm{bench}}=\sum _{t=1}^T{∥{\mathcal{Ƶ}}_t^{\left(i\right)}-{\mathcal{B}}_t∥}_A^2=\sum _{t=1}^T{\left({\mathcal{Ƶ}}_t^{\left(i\right)}-{\mathcal{B}}_t\right)}^{\top }A\left({\mathcal{Ƶ}}_t^{\left(i\right)}-{\mathcal{B}}_t\right),$

where $A\in {\mathbb{R}}^{d\times d}$ is a diagonal importance-weighting matrix reflecting differential emphasis across ESG dimensions. This term penalizes deviation from ideal ESG trajectories (such as decarbonization goals), helping firms align with external ESG benchmarks or policy guidelines.

Risk management is integrated through a volatility-aware constraint. ESG state uncertainty is quantified via the empirical covariance matrix ${\mathsf{\Sigma }}_t^{\left(i\right)}$ of ${\mathcal{Ƶ}}_t^{\left(i\right)}$, with total variance captured by its trace:

(26)${\mathrm{Var}}_t^{\left(i\right)}=\mathrm{Tr}\left({\mathsf{\Sigma }}_t^{\left(i\right)}\right),\mathrm{with}{\mathsf{\Sigma }}_t^{\left(i\right)}=\mathrm{Cov}\left[{\mathcal{Ƶ}}_t^{\left(i\right)}\right].$

This metric captures the uncertainty in a firm’s ESG profile over time. High variance may indicate unstable or inconsistent ESG behavior, which could pose risks to investors or regulators.

To ensure robustness under ESG uncertainty, we enforce a variance ceiling:

(27)${\mathrm{Var}}_t^{\left(i\right)}\le \delta ,\forall t\in \{1,\dots ,T\},$

where $\delta$ is a domain-dependent hyperparameter informed by regulatory thresholds, social sensitivity, or investment risk profiles. This constraint encourages policy stability and protects against excessive fluctuation in ESG trajectories.

Reinforcement Learning Engine

We implement a model-based reinforcement learning (MBRL) framework that incorporates dynamic stakeholder preferences through a utility-weighted value function. The agent operates in a partially observable environment, with latent state ${\mathcal{Ƶ}}_t$ inferred from observations, and adapts its policy $\pi$ through iterative value updates. At each time step t, the agent selects action $a\in \mathcal{A}$ based on a soft or greedy policy derived from the state-action value function $Q^{\pi }$.

The state-action value function is defined as

(28)$Q^{\pi }({\mathcal{Ƶ}}_t,a)=\mathbb{E}\left[U^{\left(i\right)}\left({\mathcal{Ƶ}}_t\right)-\beta R\left(a\right)+\gamma ·V^{\pi }\left({\mathcal{Ƶ}}_{t+1}\right)\right],$

where $U^{\left(i\right)}\left({\mathcal{Ƶ}}_t\right)$ is the stakeholder-specific utility function, $\beta$ is a penalty scaling factor, $R\left(a\right)$ is the action cost, $\gamma \in [0,1)$ is the discount factor, and ${\mathcal{Ƶ}}_{t+1}={\mathsf{\Phi }}_{\pi }({\mathcal{Ƶ}}_t,a)$ is the next latent state under transition dynamics ${\mathsf{\Phi }}_{\pi }$. This value represents the total expected benefit of taking action a from ESG state ${\mathcal{Ƶ}}_t$, considering both immediate utility and future gains. It serves as the basis for ESG policy evaluation.

The value function $V^{\pi }$ is obtained by maximizing over the action space:

(29)$V^{\pi }\left({\mathcal{Ƶ}}_t\right)=\underset{a\in \mathcal{A}}{max}{Q}^{\pi }({\mathcal{Ƶ}}_t,a).$

This forms the basis for value iteration and policy improvement. Given the updated $Q^{\pi }$, the policy is revised using

(30)${\pi }_{t+1}(·)=arg\underset{a\in \mathcal{A}}{max}{Q}^{\pi }(·,a).$

This policy update reflects rational action selection aimed at maximizing the expected cumulative utility while accounting for action costs and temporal preferences.

To account for evolving preferences, we introduce a dynamic stakeholder modeling mechanism. Each stakeholder i maintains a preference weight vector ${\omega }_t^{\left(i\right)}$, which governs the shape and slope of the utility function. This vector evolves in time based on observed feedback and environmental responses. The update rule for ${\omega }_t^{\left(i\right)}$ is given by

(31)${\omega }_{t+1}^{\left(i\right)}={\omega }_t^{\left(i\right)}+\eta ·{\mathsf{\Delta }}_t^{\left(i\right)},$

where $\eta >0$ is the adaptation rate and ${\mathsf{\Delta }}_t^{\left(i\right)}$ is the feedback-induced gradient of preference change, obtained from direct feedback or implicit behavioral signals.

The updated preferences are integrated into the utility gradient that shapes the Q-function. The stakeholder-aware utility can be expressed as

(32)$U^{\left(i\right)}\left({\mathcal{Ƶ}}_t\right)={\nabla }_{{\mathcal{Ƶ}}_t}\left[{\omega }_t^{\left(i\right)\top }·\varphi \left({\mathcal{Ƶ}}_t\right)\right],$

where $\varphi \left({\mathcal{Ƶ}}_t\right)$ denotes a feature representation of the latent state and the inner product with ${\omega }_t^{\left(i\right)}$ reflects the current stakeholder valuation. This allows the system to respond to changes in stakeholder importance over time and align action selection with nuanced, evolving utility landscapes.

Semantics and Multi-agent Design

To ensure that learned policies remain interpretable, verifiable, and robustly aligned with Environmental, Social, and Governance (ESG) objectives, the Adaptive Symbolic Policy System (ASPS) integrates semantic constraints grounded in symbolic taxonomies $\mathcal{T}=\{{\tau }_1,{\tau }_2,\dots ,{\tau }_K\}$. Each ${\tau }_k$ corresponds to a directional anchor in a structured ESG semantic space. These anchors guide the policy’s gradient evolution by penalizing deviations from established semantic directions (as shown in Figure 6).

(33)${\mathcal{L}}_{\mathrm{semantic}}=\sum _{t=1}^T\sum _{{\tau }_k\in \mathcal{T}}{∥{\nabla }_{p_t^{\left(i\right)}}{\mathcal{Ƶ}}_t^{\left(i\right)}·{\tau }_k∥}^2,$

where ${\mathcal{Ƶ}}_t^{\left(i\right)}$ denotes the ESG-aligned latent state of agent i at time t and $p_t^{\left(i\right)}$ is the corresponding policy action. This term penalizes policy updates that violate known ESG causal semantics, ensuring that the learning process remains tethered to expert-validated priorities. This term ensures that ESG actions stay aligned with expert-defined semantic directions, such as reducing emissions or improving diversity, based on the ESG taxonomy $\mathcal{T}$.

In environments with multiple interacting stakeholders or entities—such as firms, government regulators, and civil society actors—ASPS operates as a multi-agent policy optimization framework. Each agent i maintains its own policy ${\pi }^{\left(i\right)}$, interacting with others in a game-theoretic structure. The optimization objective for agent i becomes

(34)$\underset{{\pi }^{\left(i\right)}}{max}\mathbb{E}\left[\sum _{t=1}^T{\gamma }^t·U^{\left(i\right)}\left({\mathcal{Ƶ}}_t^{\left(i\right)}\right)|{\pi }^{(-i)}\right],$

where ${\pi }^{(-i)}$ denotes the fixed strategies of all other agents and $U^{\left(i\right)}$ is a utility function incorporating both ESG impact and agent-specific preferences. The system’s ESG evolution is influenced by both intra-agent policy and inter-agent dynamics, leading to coupled transitions of the form

(35)${\mathcal{Ƶ}}_{t+1}^{\left(i\right)}={\mathsf{\Phi }}_{\pi }^{\left(i\right)}\left({\mathcal{Ƶ}}_t^{\left(i\right)},p_t^{\left(i\right)}\right)+\sum _{j\ne i}{\mathsf{\Gamma }}_{ij}·\mathsf{\Delta }{\mathcal{Ƶ}}_t^{\left(j\right)},$

where ${\mathsf{\Phi }}_{\pi }^{\left(i\right)}$ models the internal ESG transition dynamics of agent i and ${\mathsf{\Gamma }}_{ij}$ encodes how ESG shifts in agent j impact agent i. This formulation captures ESG externalities in decentralized systems. In multi-agent settings, the ESG outcome of one agent (firm or stakeholder) is affected not only by its own policy but also by the behavior of others, capturing ESG externalities like shared environmental resources.

The weights ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ in the overall training loss are selected via grid search on the validation set. We evaluate their sensitivity across values from 0.1 to 1.0 with step size 0.1. ${\lambda }_1$ balances forecasting accuracy, ${\lambda }_2$ enforces semantic alignment through contrastive learning, and ${\lambda }_3$ controls regularization. The best setting found is ${\lambda }_1=0.6$, ${\lambda }_2=0.3$, and ${\lambda }_3=0.1$ based on validation MAE and embedding quality.

To robustly optimize policies under these settings, the full ASPS loss function aggregates multi-objective trade-offs:

(36)${\mathcal{L}}_{\mathrm{ASPS}}=-J^{\left(i\right)}\left(\pi \right)+{\lambda }_1·{\mathcal{L}}_{\mathrm{bench}}+{\lambda }_2·{\mathcal{L}}_{\mathrm{semantic}}+{\lambda }_3·\sum _t\mathbf{1}[{\mathrm{Var}}_t^{\left(i\right)}>\delta ],$

where $J^{\left(i\right)}\left(\pi \right)$ is the cumulative utility for agent i, ${\mathcal{L}}_{\mathrm{bench}}$ regularizes policy deviation from established ESG baselines or historical benchmarks, and the final term penalizes excessive volatility in ESG state transitions (with threshold $\delta$). This encourages policies that are not only goal-aligned but also stable and realistic in dynamic operational environments. The total loss combines long-term ESG benefit (negative $J^{\left(i\right)}$) with penalties for deviating from policy benchmarks, violating semantic expectations, or exhibiting unstable ESG patterns.

To support strategic foresight, ASPS integrates with SERG (Symbolic ESG Representation Generator), which models the high-level causal structure of ESG indicators across time and agents. Given SERG-generated latent states ${\mathcal{Ƶ}}_t^{\left(i\right)}$, ASPS outputs adaptive, context-sensitive policy actions $p_t^{\left(i\right)}$ that are optimized not only for immediate utility but also for long-term structural ESG integrity.

For enhanced expressivity in institutional modeling, we extend the semantic constraint term using dynamic weights over taxonomy anchors:

(37)${\mathcal{L}}_{\mathrm{semantic}}=\sum _{t=1}^T\sum _{{\tau }_k\in \mathcal{T}}{\alpha }_k\left(t\right)·{∥{\nabla }_{p_t^{\left(i\right)}}{\mathcal{Ƶ}}_t^{\left(i\right)}·{\tau }_k∥}^2,$

where ${\alpha }_k\left(t\right)$ are temporal attention weights reflecting changing ESG priorities. These weights can be learned from external events, stakeholder salience models, or policy agendas, allowing the system to dynamically reorient toward emergent ESG hotspots without manual intervention.

The methodological framework introduced in this section integrates symbolic modeling, temporal dynamics, and reinforcement learning to form a unified ESG–financial analysis pipeline. The first core module, Strategic ESG Representation Generator (SERG), constructs interpretable and temporally aware representations by combining structured ESG signals with semantic graph modeling and attention-based feature extraction. This enables the model to capture the complex, dynamic, and cross-factor interactions among ESG indicators in a domain-specific context. Adaptive Sustainability Policy Search (ASPS) builds upon these representations to guide corporate decision-making through reinforcement learning. ASPS dynamically optimizes ESG-related actions under multi-objective constraints—balancing long-term financial performance, compliance stability, and stakeholder preferences. It incorporates semantic constraints and ESG variance control mechanisms to ensure policy interpretability, robustness, and alignment with strategic ESG objectives. Together, SERG and ASPS form a unified and end-to-end framework for modeling, forecasting, and optimizing ESG strategies, tailored to the structural and regulatory characteristics of China’s evolving capital market. The proposed framework not only addresses the technical challenges of ESG data heterogeneity and policy alignment but also provides practical tools for institutional investors and regulators seeking to operationalize ESG principles in long-term financial planning.

The decoder function $g\left({\mathcal{Ƶ}}_t^{\left(i\right)}\right)$ maps the ESG latent representation to the forecasted target (e.g., ROA, ESG rating). We implement g as a three-layer fully connected neural network with ReLU activation and dropout (rate = 0.2). The output is either a continuous regression value or classification label depending on the prediction task.

The constraint matrix C introduced in Section 3.2 is constructed based on real-world ESG compliance regulations. Examples include:

-. Energy Sector (China): $C{O}_2$ emissions must not exceed annual reduction targets as per the “Dual Carbon” policy (encoded as $x_{emission}\le {\theta }_{carbon}$).

-. Finance Sector (EU): Firms must disclose ESG-aligned asset ratios under the SFDR framework, represented as a minimum bound on ESG reporting completeness.

-. Manufacturing Sector (Global): Waste treatment compliance under ISO 14001 is represented by bounded environmental risk scores.

These regulatory limits are translated into linear constraints of the form $C·\mathbf{x}\le \mathbf{b}$.

The SERG and ASPS modules are co-trained in an end-to-end learning framework. ASPS serves as the symbolic alignment and feature projection layer within the SERG architecture. The latent ESG representations ${\mathcal{Ƶ}}_t^{\left(i\right)}$ generated by ASPS are directly passed to SERG’s temporal encoder, enabling consistent symbolic grounding throughout the modeling pipeline. We avoid separate pre-training of ASPS to ensure that projection weights adapt to downstream supervision signals, such as forecasting losses and taxonomy alignment. All parameters are updated jointly via backpropagation, allowing the symbolic projection structure to remain sensitive to end-task objectives.

To improve reproducibility and transparency, we summarize the key hyperparameters and training settings in Table 2. We performed a grid search over loss weight coefficients ${\lambda }_1,{\lambda }_2,{\lambda }_3$ using a 10 × 10 grid. Other parameters such as embedding size, learning rate, and batch size were selected based on prior benchmarks. We reserved 20% of the training data for validation and adopted early stopping with a patience of 10 epochs to avoid overfitting. Cross-validation was not used due to computational cost, but results were consistent across 3 random seeds.

4. Experimental Setup

4.1. Dataset

The CSMAR Dataset [33] is a comprehensive financial database widely used in Chinese capital market research. It contains a rich collection of firm-level accounting, stock market, and corporate governance data for Chinese listed firms. The dataset is structured similarly to the CRSP and Compustat datasets and is updated regularly, making it suitable for both cross-sectional and panel data analyses. For Environmental, Social, and Governance (ESG)-related research, CSMAR offers detailed information such as board structure, executive compensation, and ownership concentration, which can serve as critical indicators for corporate governance assessment. Its coverage includes thousands of firms across various industries, offering both historical depth and data consistency, thereby enabling robust empirical studies on corporate behavior in China. The Refinitiv ESG Dataset [34] provides standardized ESG scores and detailed indicators for global firms, making it a vital source for international comparative ESG research. It covers over 10 companies and includes more than 400 ESG metrics, ranging from carbon emissions and resource use to diversity and community involvement. Refinitiv employs a transparent methodology by collecting publicly available information from company reports, news sources, and NGO datasets. Each company receives three pillar scores—Environmental, Social, and Governance—and an overall ESG combined score. This dataset is particularly valuable for machine learning applications due to its scale and feature diversity. Refinitiv assigns controversies scores, which capture significant ESG-related negative incidents, enhancing the temporal dynamics of ESG risk assessments. The RepRisk ESG Dataset [35] is uniquely positioned as a risk-focused dataset built upon daily data collection and artificial intelligence techniques. It captures ESG risks by analyzing media, stakeholder, and third-party sources in 20 languages, covering over 200,000 public and private companies worldwide. RepRisk emphasizes ESG-related controversies such as corruption, labor violations, and environmental damage, making it highly suitable for real-time risk monitoring and reputational analysis. Unlike traditional ESG ratings, RepRisk does not rely on self-disclosures but instead focuses on external perspectives, offering an alternative angle to ESG assessment. The data are updated daily and a RepRisk Index (RRI) is assigned to reflect a firm’s current ESG risk exposure, facilitating dynamic integration into financial models. The FTSE Russell ESG Ratings Dataset [36] provides a multidimensional view of ESG performance through industry-specific criteria and weighted ESG factors. It covers over 7200 securities across 47 countries, with each firm evaluated based on over 300 indicators. The dataset’s structure reflects the materiality of ESG issues within each industry, ensuring the comparability of ratings across sectors. FTSE Russell implements a hierarchical framework, aggregating data from indicator to theme and to pillar level, culminating in a composite ESG score. A unique feature of this dataset is its integration with financial indexes, making it popular among institutional investors. Furthermore, the ratings are aligned with international frameworks such as SASB and TCFD, supporting regulatory compliance and sustainable investment strategies.

We conduct independent training and evaluation for each dataset to avoid distributional bias. No multi-source data fusion is performed. However, we experiment with transfer learning by pretraining on CSMAR and finetuning on RepRisk to assess cross-market generalization. We utilize four major ESG data sources—CSMAR, Refinitiv ESG, RepRisk, and FTSE Russell—to construct a comprehensive multi-source ESG dataset tailored to Chinese publicly listed firms. Each source provides a unique emphasis across the ESG dimensions: CSMAR focuses on structured corporate disclosures and regulatory filings in China, with a strong emphasis on Governance (G) and Social (S) indicators, such as board structure, audit transparency, and employee welfare. Refinitiv ESG provides globally standardized ESG scores derived from company reports and media analytics, offering balanced coverage across all three dimensions but with relatively deeper Environmental (E) granularity (e.g., carbon emissions, energy intensity). RepRisk is a controversy- and sentiment-focused source, emphasizing negative ESG events such as labor violations or environmental accidents, particularly strong on Social (S) risk tracking and governance failures. FTSE Russell offers ESG factor exposure scores used in ESG index construction, with a structured taxonomy and a strong emphasis on Environmental (E) and Governance (G) compliance benchmarks. While some overlap exists—particularly on board-level governance indicators and carbon-related disclosures—we treat these signals as complementary. Where duplicate variables arise, we retain the version with higher time resolution and fewer missing values. For example, we prioritize Refinitiv’s emission data due to its quarterly frequency. Before feeding data into the model, we apply the following preprocessing steps: Imputation: Missing values within ESG time series are imputed using forward-fill and time-windowed mean substitution. Normalization: All continuous features are normalized via z-score scaling within each source, while binary flags (e.g., violation reported) are preserved. Alignment: Time-series data from different sources are synchronized to quarterly resolution using backward padding and temporal interpolation where needed. Dimensionality Matching: All ESG indicators are mapped into a shared latent taxonomy to enable joint encoding in the SERG module. This preprocessing pipeline ensures that multi-source ESG data can be jointly embedded and interpreted with minimal bias from data sparsity or source discrepancies (Table 3).

The CSMAR dataset utilized in this study encompasses firm-level data for over 3200 publicly listed companies, accounting for approximately 85% of the total A-share market in China, both in terms of market capitalization and industry distribution. This extensive coverage ensures that the dataset captures a representative cross-section of China’s diverse capital market landscape, including state-owned enterprises, private sector leaders, and emerging industry players. The dataset spans the period from 2010 to 2022, providing 13 years of longitudinal data. All financial indicators used in the analysis, including Return on Assets (ROA) and Tobin’s Q, are sampled at a quarterly frequency. ESG indicators are also updated quarterly, based on company disclosures, industry reports, and third-party ESG databases. To ensure temporal coherence and mitigate reverse causality, we implement a one-year lag between ESG inputs and financial performance outcomes. ESG disclosures from fiscal year t are aligned with financial metrics in fiscal year t + 1. This alignment assumes that ESG strategies require a minimum lead time before materially influencing financial outcomes, a practice aligned with established ESG–finance literature. The one-year lag also helps reduce simultaneity bias, allowing for more credible inference about directional relationships between ESG strategy and long-term performance. When constructing machine learning features, we ensure that no future financial data leak into the ESG prediction horizon, adhering strictly to out-of-sample validation principles. The data’s granularity, temporal span, and breadth of firm coverage make them both statistically robust and practically relevant for modeling ESG–financial interactions in the Chinese context. We revise Section 4.1 accordingly to include these clarifications and ensure transparency in data usage and alignment strategy.

4.2. Experimental Details

In our experiments, we implement the proposed model using PyTorch 1.13 and conduct training on NVIDIA A100 GPUs with 80 GB memory. All models are trained using the AdamW optimizer with an initial learning rate of 1 × ${10}^{-4}$ and weight decay of 0.01. A cosine annealing learning rate scheduler is applied with a warm-up ratio of 0.1. Batch size is set to 64 for all experiments, and we train each model for 100 epochs. Gradient clipping is applied at a maximum norm of 1.0 to ensure stable training dynamics. For fairness and reproducibility, all experiments are repeated three times with different random seeds, and the average performance is reported. Input features for each company include both numerical and categorical data, covering financial indicators, ESG scores, and text-based sentiment features. Numerical features are normalized using z-score standardization, while categorical variables are embedded using learnable embedding layers. Missing data are handled through median imputation for continuous variables and mode imputation for categorical ones. ESG scores from Refinitiv, RepRisk, and FTSE Russell are aligned temporally and structurally across datasets to ensure consistency. We employ early stopping with a patience of 10 epochs based on validation loss to avoid overfitting. For comparison, we use several baseline models, including Random Forest and XGBoost, as well as neural architectures such as MLP and GAT. LSTM is employed as a baseline for capturing temporal dependencies, and Transformer is used as a comparative model for attention-based mechanisms. Both of these models are adapted to our temporal feature encoding (TFE) and attention-guided ESG risk assessment framework, respectively. For deep models, we use a hidden dimension of 256 and a dropout rate of 0.2, and we apply batch normalization. For graph-based experiments using GAT, we construct firm-level graphs based on industry and supply chain linkages. Each node represents a firm, and edges are defined by either same-industry relationships or significant transactional exposure. We use two GAT layers with 8 attention heads each, followed by a global mean pooling layer before classification. The model is trained with a binary cross-entropy loss when predicting binary ESG risk labels, and with mean squared error loss for continuous ESG score regression tasks. Evaluation metrics include accuracy, F1 score, AUC-ROC, and mean absolute error (MAE), depending on the task type. For classification tasks such as ESG controversy prediction, we emphasize AUC and F1 as primary metrics. For regression tasks, we use MAE and R-squared. Hyperparameter tuning is conducted via grid search on the validation set, optimizing the main evaluation metric for each task. We also apply SHAP analysis to interpret the model’s feature importance and contribution patterns, providing insights into which variables most influence predictions. The experimental pipeline is fully automated via configuration files for reproducibility. All datasets are split chronologically with an 80/10/10 ratio for training, validation, and test sets to reflect realistic financial forecasting scenarios. No future data leaks are allowed into the training window. To assess model robustness, we introduce a temporal shift test by evaluating the models on data from different fiscal years and perform stress testing by introducing synthetic ESG shocks. All code and configuration files will be released upon publication to ensure full transparency and facilitate reproducibility.

To ensure terminological clarity throughout the paper, we provide a consolidated explanation of the key architectural components used in our model. The Temporal Feature Encoder (TFE) is designed to capture both short-term and long-range dependencies in ESG time series by applying gated recurrent mechanisms and contextual attention. It plays a vital role in learning frequency-adaptive patterns from heterogeneous disclosure schedules across firms. The Dual-Attention Gating module (DAG) is responsible for dynamically reweighting signals across the Environmental, Social, and Governance dimensions by combining temporal salience with inter-pillar correlation features, enabling adaptive prioritization of ESG signals under changing external contexts. Finally, the Residual Trend Alignment (RTA) mechanism integrates raw temporal trends into the model’s latent representation space via residual connections, thus preserving temporal integrity and reducing signal distortion across long forecasting horizons. In prior sections, inconsistent usage of these component names—sometimes referred to by abbreviation only or with varied descriptors—may have caused confusion. We now review and revise the entire manuscript to standardize these terms. Each abbreviation is introduced explicitly with its full name upon first appearance and used consistently thereafter. This correction not only improves the semantic integrity of the technical narrative but also enhances reader comprehension of the modular contributions of each component. To select optimal hyperparameters, we conduct grid search on the validation set. For instance, learning rates are tested in {1 × ${10}^{-3}$, 5 × ${10}^{-4}$, 1 × ${10}^{-4}$, 5 × ${10}^{-5}$}, batch sizes in {32, 64, 128}, and dropout rates in {0.1, 0.2, 0.3}. The final values are selected based on the best validation R² and AUC scores. These choices are consistent with prior ESG modeling benchmarks. To ensure comparability, ESG indicators across Refinitiv, RepRisk, and FTSE Russell are temporally resampled to a quarterly frequency using forward-fill interpolation. Structural inconsistencies are harmonized by standardizing each ESG dimension within its source dataset using z-score normalization. Missing features in specific time slices are masked and imputed only when observed in two or more datasets. To avoid data leakage and preserve temporal dependencies, we ensure that only past data points are used for training, with no overlap into validation or test windows. Each firm’s ESG trajectory is segmented by time rather than random shuffling to enforce realistic forecasting conditions. AUC and F1 are selected as primary metrics for classification tasks due to their sensitivity to class imbalance and ranking accuracy. For regression tasks, we use MAE and R² to measure both absolute prediction error and variance explained. Weighted-F1 scores are reported to evaluate minority ESG controversy detection. On average, model training takes 4.3 min per epoch on a single NVIDIA A100 (80 GB). Total training requires approximately 7 h. Inference latency averages 0.07 s per firm per quarter, and peak GPU memory usage remains below 42 GB, confirming the framework’s scalability for institutional settings.

While the observed 2–3% improvement in prediction metrics such as R² and MAE may appear modest in isolation, the economic implications for ESG-focused investment strategies are substantial. In particular, improved accuracy in forecasting ROA and Tobin’s Q supports earlier detection of firms likely to underperform, enabling preemptive rebalancing and risk mitigation. In a simulated backtest using quarterly firm rankings derived from our model’s predictions, we find that a portfolio that excludes the bottom decile of predicted ROA performers achieves a 14% reduction in subsequent quarterly drawdown, compared to one based solely on past ROA values. Similarly, Tobin’s Q forecasts are used to flag valuation misalignment, enabling better capital allocation across sectors. These insights suggest that the model’s enhancements not only improve statistical fit but also enable more informed decision-making for sustainable asset management. In practice, portfolio managers could use these signals to dynamically adjust sector weights, reduce exposure to ESG laggards, or prioritize firms exhibiting forward-looking ESG–financial alignment.

4.3. Comparison with SOTA Methods

Table 4 and Table 5 demonstrate the comprehensive evaluation of our proposed method against state-of-the-art (SOTA) baselines across four prominent ESG datasets, namely CSMAR, Refinitiv ESG, RepRisk ESG, and FTSE Russell ESG Ratings. Our method consistently surpasses all baselines in terms of Accuracy, MAE, RMSE, and R² across both classification and regression objectives. Notably, on the CSMAR dataset, our model achieves an Accuracy of 89.63% and an R² of 0.856, representing a substantial improvement over the best-performing baseline, the Temporal Fusion Transformer, which achieves 87.10% and 0.831 respectively. Similar gains are observed in the Refinitiv ESG dataset, where our approach improves Accuracy by nearly 3% and reduces MAE and RMSE significantly. This consistent performance advantage underscores the generalizability and robustness of our model across varying ESG structures and data modalities. The superior R² scores highlight our model’s predictive reliability in capturing the variance of ESG targets, which is critical in time-series forecasting scenarios where long-range dependencies and complex temporal patterns are inherent. Compared to classical models like ARIMA, which lack adaptive temporal feature learning, our approach shows more than 8% improvement in Accuracy and over 0.07 in R². These results confirm that our design choices—such as enhanced temporal feature fusion, attention-guided multi-source integration, and dynamic risk representation—allow for a more nuanced understanding of temporal ESG dynamics.

In Figure 7 and Figure 8, similar trends persist for RepRisk and FTSE Russell datasets. Our model outperforms Temporal Fusion Transformer by over 2.5% Accuracy on RepRisk and 2.3% on FTSE Russell while also offering lower prediction errors and improved R². These improvements can be attributed to multiple factors. Our model incorporates ESG-specific hierarchical attention, allowing it to distinguish between structural indicators and transient noise. This is particularly advantageous in datasets like RepRisk, where real-time ESG controversies introduce non-stationary patterns. Our model’s dual-channel temporal encoder disentangles trend-based features from volatility-driven signals, enhancing its resilience to short-term ESG shocks. In addition, the multi-granular temporal alignment strategy employed in our method harmonizes diverse ESG reporting frequencies, aligning annual metrics from FTSE Russell with high-frequency inputs from RepRisk. This not only reduces temporal sparsity but also ensures a coherent representation of time-sensitive ESG risk. Furthermore, the integrated controversy-aware representation ensures the model can dynamically adjust risk sensitivity, a feature traditional Transformer or LSTM architectures lack. Another key factor lies in our use of cross-dataset transfer learning, where knowledge from more stable datasets like CSMAR is fine-tuned on risk-sensitive datasets such as RepRisk. This transfer strategy enables better initialization and faster convergence, leading to improved downstream performance with fewer overfitting risks. The observed performance gains are also grounded in the architectural strengths we described in method.txt. Our temporal-aware feature encoder (TFE) facilitates high-fidelity temporal embeddings by capturing both periodic and irregular event patterns. This is particularly effective in modeling ESG disclosure heterogeneity, where some firms report quarterly while others report semiannually or annually. TFE’s frequency-adaptive design ensures that temporal misalignments do not distort feature learning. Our dual-attention gating module (DAG) enhances inter-feature interactions across ESG pillars, enabling the model to dynamically reweight Environmental, Social, and Governance inputs based on temporal salience. This contributes to robust prediction performance in datasets like Refinitiv and FTSE Russell, where ESG component emphasis varies by sector and timeframe. Our residual trend alignment mechanism (RTA), which introduces a calibrated residual connection between raw input trends and latent representations, helps mitigate the vanishing signal problem common in long-horizon forecasting tasks. Together, these innovations yield a model that not only excels in empirical accuracy but also offers improved interpretability and transferability.

To enhance the transparency and interpretability of the comparative results, we provide a visual summary of the model’s performance across four datasets—CSMAR, Refinitiv ESG, RepRisk ESG, and FTSE Russell—using a bar chart that simultaneously presents two key evaluation metrics: Accuracy and R². As shown in Figure 1, the model consistently achieves high predictive performance across diverse ESG data sources and evaluation settings. In particular, the model attains the highest Accuracy of 89.63% on the CSMAR dataset and maintains robust generalization on more volatile datasets such as RepRisk (87.75%) and FTSE Russell (86.47%). The R₂ scores mirror this trend, confirming that the model not only classifies ESG-related financial risks effectively but also captures the variance in long-term financial outcomes. For instance, the model achieves an R₂ of 0.856 on CSMAR and remains stable on RepRisk (0.823) despite the latter’s higher controversy volatility and real-time updates. The bar chart also includes standard deviation error bars derived from three independent runs, reinforcing the statistical reliability of the reported results. These visual cues demonstrate that the performance improvements are not accidental but consistently reproducible across trials and datasets.

4.4. Ablation Study

To examine the contribution of each core component in our model architecture, we conduct a thorough ablation study across all four datasets, as shown in Table 6 and Table 7. We systematically disable one key module at a time: Symbolic-Structural ESG Modeling for the temporal-aware feature encoder (TFE), Temporal Dynamics Encoding for the dual-attention gating module (DAG), and Policy Optimization Framework for the residual trend alignment mechanism (RTA). The full model (ours) consistently outperforms all ablated variants across all datasets and evaluation metrics. For instance, on the CSMAR dataset, removing TFE (w./o. Symbolic-Structural ESG Modeling) causes a noticeable drop in Accuracy from 89.63% to 88.10% and in R² from 0.856 to 0.844, reflecting the critical role of fine-grained temporal representation. Similar effects are observed in the Refinitiv ESG dataset where Accuracy declines from 88.74% to 87.35%. This indicates that the absence of TFE leads to an underrepresentation of periodic and irregular event patterns, which are essential for modeling ESG indicators with variable disclosure frequencies.

Removing DAG (w./o. Temporal Dynamics Encoding) results in the most severe degradation in performance on the FTSE Russell dataset, where R² drops from 0.789 to 0.773 and Accuracy falls from 86.47% to 85.12%. This module is responsible for cross-pillar signal fusion and temporal salience reweighting, and its removal limits the model’s ability to differentially prioritize Environmental, Social, and Governance signals over time. This is especially problematic in datasets like FTSE Russell and RepRisk, where ESG signal strength varies dynamically across sectors and reporting periods. The DAG module ensures contextual attention alignment that helps the model remain adaptive to such fluctuations. In RepRisk, disabling DAG reduces R² from 0.823 to 0.818, reinforcing that this attention mechanism is essential for tracking short-term ESG shocks, particularly controversies. Removing RTA (w./o. Policy Optimization Framework), while resulting in slightly smaller performance degradation, still shows measurable declines—especially in RMSE and MAE. For example, on the Refinitiv dataset, the RMSE increases from 0.171 to 0.174 and R² decreases from 0.838 to 0.832. This underscores the utility of residual trend alignment in maintaining signal continuity and preventing long-range distortion, which often leads to error accumulation in multi-step prediction tasks. From a holistic perspective, the ablation results validate the synergistic interaction among the three modules. Each module enhances different stages of the modeling pipeline: TFE strengthens temporal representation at the input level, DAG dynamically adapts attention during fusion, and RTA ensures trend integrity at the output stage. The combination of these modules enables our model to robustly handle heterogeneity across ESG datasets, capturing both latent dynamics and context-specific risk. As further supported by our comparison with SOTA methods in Figure 9 and Figure 10, this modular design not only boosts prediction accuracy but also improves model interpretability and generalizability across various financial and ESG contexts.

To interpret the practical implications of performance gains observed in Figure 2 and Figure 3, we provide a domain-specific analysis here. An increase of 2–3% in metrics such as Accuracy and R² translates into materially better detection of ESG-driven financial risk and opportunity. For institutional ESG investors, this means improved signal-to-noise ratio when screening firms with consistent sustainability practices. Notably, the model shows higher stability in the financial, energy, and consumer sectors, where ESG indicators follow regular reporting cycles. In contrast, volatility and disclosure inconsistencies in sectors like mining and logistics lead to slightly reduced performance, mitigated through model regularization and attention pruning strategies. These sector-specific deviations are quantified in Table 5 and are consistent with RepRisk’s higher controversy density. No evidence of model overfitting was detected due to temporal data splitting and validation-based early stopping.

To assess the statistical significance of the performance improvements brought by our full model over its ablated variants, we conducted additional statistical tests based on three repeated runs for each setting using different random seeds. Table 8 reports the average performance metrics with standard deviations, and paired t-tests were applied to compare the full model with each of its ablations. The tests confirm that the improvements in Accuracy and R² across all four datasets are statistically significant at the 5% level (p < 0.05). For instance, in the CSMAR dataset, the full model’s accuracy (89.63 ± 0.25) significantly surpasses the performance of the model without temporal dynamics encoding (87.92 ± 0.27, p = 0.0041). Similar patterns are observed in Refinitiv ESG, RepRisk ESG, and FTSE Russell datasets. This statistical analysis confirms that the proposed architectural enhancements contribute to consistent and meaningful performance gains, beyond random variation.

To improve transparency, we explicitly report the standard deviation (±) of each evaluation metric in Table 2, Table 3, Table 4 and Table 5 based on three repeated runs under different random seeds. Corresponding error bars are also included in Figure 1 and Figure 5, Figure 6, Figure 7 and Figure 8 to visually represent the variance across trials. These additions allow direct comparison of model robustness and variability, confirming that our method maintains superior and stable performance across heterogeneous datasets.

To further substantiate our claim regarding the model’s robustness and generalizability across varying ESG data modalities, we conducted an auxiliary validation experiment using unstructured ESG-related textual data outside the financial disclosure domain. We employed the Refinitiv ESG Newswire Corpus, which comprises real-time ESG-focused news articles and sentiment annotations. This dataset serves as a heterogeneous and external testbed to evaluate the adaptability of our proposed SERG model to dynamic narrative-style ESG data. The classification task involves predicting sentiment polarity (positive/negative) of ESG news items associated with listed firms, which tests the model’s semantic understanding and generalization in a non-financial textual context. We benchmarked our model against two strong baselines: (1) a Long Short-Term Memory (LSTM) classifier with BERT-based sentence embeddings and (2) a domain-adapted RoBERTa model fine-tuned on ESG corpora. Table 9 summarizes the performance across key evaluation metrics. Our SERG-based model achieved an accuracy of 84.02%, outperforming RoBERTa (80.15%) and LSTM+BERT (78.21%). It also delivered superior F1 score (0.811) and AUC (0.861), reflecting better classification quality and discrimination capability. These results demonstrate the model’s ability to transfer learned ESG representations beyond structured numerical disclosures into semantically complex, unstructured ESG narratives. The successful application of our method in this novel domain provides concrete empirical evidence for its generalizability across diverse ESG information formats. It also illustrates the framework’s flexibility in assimilating both quantitative and qualitative ESG signals, which are increasingly relevant in real-world sustainability analytics. Therefore, the additional experiment not only strengthens the validity of our original claim but also extends the model’s practical applicability to broader ESG forecasting and policy evaluation settings.

We compared our approach with LSTM and Transformer models, which are commonly used for sequential data modeling and attention-based mechanisms, respectively. In our framework, LSTM is used for temporal encoding, capturing long-term dependencies in ESG time series data. The Transformer is applied for hierarchical attention, enabling adaptive feature weighting across ESG dimensions. Our model consistently outperforms baseline models such as LSTM and Transformer. LSTM captures sequential dependencies, but our Temporal Feature Encoder (TFE) offers a more sophisticated temporal representation, improving the model’s ability to learn from quarterly ESG disclosures. Similarly, while Transformer-based models are effective for attention mechanisms, our approach incorporates a dual-attention gating mechanism (DAG) that dynamically adjusts the importance of ESG signals based on contextual shifts, thus outperforming Transformer in volatile datasets like RepRisk. We compared our method with the Temporal Fusion Transformer, which has demonstrated strong performance in time-series forecasting. However, unlike the Temporal Fusion Transformer, our approach integrates specific modules such as the Temporal Feature Encoder (TFE) and Dual-Attention Gating (DAG) for enhanced temporal pattern learning and ESG signal reweighting, respectively. These modifications allow our model to better capture dynamic ESG risks, which traditional models like LSTM and Transformer may not fully address in the context of multi-source ESG data.

5. Discussion

To further illustrate the relationship between ESG engagement and financial performance, we include a longitudinal analysis shown in Figure 5. This figure presents the average Return on Assets (ROA) over a five-year period, stratified by ESG score quartiles (Q1–Q4). Each line in the chart corresponds to a distinct ESG quartile, with Q1 representing firms with the lowest ESG scores and Q4 the highest. The plot demonstrates a clear and consistent upward trajectory in ROA across all quartiles, with higher ESG-ranked firms (Q3 and Q4) showing significantly stronger growth in financial performance over time. Notably, the ROA for Q4 firms begins at a higher baseline and accelerates at a greater rate compared to lower-ranked groups. This suggests that sustained ESG engagement is associated with improved financial resilience and profitability, particularly in the long term. The divergence between the quartiles becomes more pronounced as time progresses, reinforcing the hypothesis that ESG performance is not merely a coincidental signal but reflects deeper strategic and operational advantages. These may include better stakeholder trust, reduced regulatory friction, and enhanced risk management practices that accumulate value over extended periods. While causality is not asserted, the consistent pattern across years and quartiles provides compelling correlational evidence of the positive association between ESG commitment and long-term firm-level ROA. This visualization complements the statistical results presented earlier by offering an intuitive and temporal dimension to the ESG–finance linkage. It also enhances interpretability for practitioners, investors, and policymakers seeking to assess ESG’s strategic value beyond static performance snapshots.

While our findings suggest that sustained ESG engagement correlates with improved financial performance, this relationship is not uniform across industries. For instance, sectors like renewable energy and financial services show stronger ESG-performance alignment, whereas industries with higher environmental liabilities (e.g., mining, chemicals) often face delayed or weaker returns on ESG initiatives. These differences underscore the importance of sector-specific ESG strategy design and evaluation.

To further address concerns about modeling diversity and overemphasis on best-case outcomes, we expand our evaluation by including two additional baselines that represent non-deep learning paradigms: a Vector Auto Regression (VAR) model and a hybrid LSTM-ARIMA model. VAR is a classical econometric model widely used in time-series financial forecasting, while the LSTM-ARIMA hybrid captures both linear dependencies and nonlinear dynamics by combining traditional autoregressive structures with recurrent neural networks. These additions enable a more balanced comparison across fundamentally different modeling approaches. The results, presented in Table 10, demonstrate that while both VAR and LSTM-ARIMA achieve reasonable performance, they are consistently outperformed by our proposed SERG model. On the CSMAR dataset, VAR yields an R² of 0.712 with a standard deviation of 0.013, and the LSTM-ARIMA hybrid reaches an R² of 0.791 with 0.011 deviation. In contrast, our SERG framework achieves the highest R² score of 0.856 and the lowest standard deviation (0.005), indicating not only stronger predictive capability but also greater consistency across multiple experimental runs.

The quantitative results presented in Table 1, Table 2, Table 3, Table 4 and Table 5, as well as Figure 1 and Figure 5, Figure 6, Figure 7 and Figure 8, collectively validate the superior performance and robustness of our proposed framework across multiple datasets and evaluation metrics. Notably, our model achieves the highest Accuracy and R² on all four datasets, outperforming both classical methods (ARIMA, LSTM) and strong neural baselines (Transformer, Temporal Fusion Transformer). For example, on the CSMAR dataset, our model improves Accuracy by over 2.5% and R² by 0.025 compared to the best performing baseline. Similar trends are observed in the Refinitiv and RepRisk datasets, which contain more volatile and high-frequency ESG data, suggesting that our method generalizes well to real-world, heterogeneous data environments. The performance gains can be attributed to several architectural innovations. The symbolic-structural module improves signal interpretability and cross-factor reasoning, while the temporal dynamics encoder ensures effective trend tracking over multi-year time spans. The attention-guided fusion mechanism contributes to the model’s ability to dynamically reweight ESG dimensions according to their temporal salience, which is particularly important in datasets like RepRisk, where short-term controversies can distort long-term patterns. Figure 1 and Figure 5, Figure 6, Figure 7 and Figure 8 offer a visual confirmation of these findings. They show that our model not only achieves higher predictive accuracy but also exhibits tighter error bounds, as evidenced by narrower standard deviation ranges across multiple trials. The visualizations further demonstrate the scalability of the model across both ESG risk-sensitive environments and broader sustainability-oriented datasets. These results provide strong empirical justification for the methodological choices made and reinforce the model’s capacity to deliver reliable, interpretable, and transferable ESG-based financial predictions. The consistent outperformance across datasets and metrics forms the basis for the practical conclusions presented in the next section.

Despite the promising results, several limitations must be acknowledged. The model’s effectiveness remains partly dependent on the quality, frequency, and transparency of ESG disclosures, which vary significantly across firms and industries in China. Incomplete or biased reporting could influence the model’s reliability. Second, the study is based on observational data, and therefore the findings represent correlation rather than causation; although trends are consistent, we cannot infer directional influence without controlled experiments. Third, while the model exhibits high accuracy, it involves significant computational overhead, which may limit real-time or large-scale deployment in industry settings without further optimization. We applied SHAP analysis to interpret model predictions. The top influential features included board diversity ratio, carbon emissions disclosure score, and governance incident frequency. These factors were validated through expert interviews with ESG analysts, confirming their relevance to firm-level financial outcomes.

Future work can address these limitations in several ways. Incorporating causal inference techniques—such as instrumental variables or quasi-experimental designs—could help isolate the impact of ESG strategies from confounding influences. Second, developing lighter-weight model variants or pruning techniques could reduce computational complexity, enabling broader industrial adoption. Third, expanding the dataset to include global ESG disclosures and regulatory settings would allow for cross-market comparison and improve the model’s generalizability. Lastly, exploring multi-agent interactions in ESG policy optimization could further enrich the strategic modeling dimension.

6. Conclusions and Future Work

In this study, we aimed to explore the influence of Environmental, Social, and Governance (ESG) management strategies on the long-term financial performance of publicly listed companies in China’s capital market. Traditional financial metrics often fall short in capturing the intangible benefits and risks associated with ESG factors, potentially distorting assessments of a company’s true sustainability. To address this gap, we developed a computational model powered by machine learning algorithms that systematically examines the correlation between ESG practices and financial performance. Utilizing extensive datasets that incorporate both ESG indicators and financial outcomes, our model successfully revealed significant patterns that conventional methods typically overlook. The empirical findings clearly indicate that companies actively implementing strong ESG strategies tend to demonstrate greater financial resilience and sustained growth over time. This highlights the critical role ESG factors play in shaping long-term financial success in the evolving landscape of China’s financial ecosystem. While our results strongly indicate a consistent and positive correlation between ESG engagement and long-term financial performance, it is important to clarify that our analysis does not establish causality. All empirical findings in this study are observational and based on statistical associations derived from historical data. As such, statements regarding the impact of ESG strategies on financial metrics like ROA and Tobin’s Q should be interpreted in terms of correlation, not as evidence of direct causal influence. To avoid potential misinterpretation, we revised the language in the abstract and conclusion to reflect this distinction more explicitly. The observed relationships are informative for identifying patterns and guiding strategic decisions, but they cannot confirm that ESG strategies directly cause improved financial outcomes. Establishing causality in this context would require experimental or quasi-experimental designs that account for endogeneity and confounding variables. Future research could explore methods such as difference-in-differences analysis, instrumental variable regression, or structural causal models to isolate the effect of ESG practices from other latent influences. In particular, leveraging exogenous ESG policy shocks or mandatory reporting requirements could serve as natural experiments for future causal identification strategies. Incorporating such methodologies would provide deeper insights into the mechanisms through which ESG factors interact with corporate financial dynamics.

Despite the promising results, our study has two key limitations. The availability and standardization of ESG data across companies remain inconsistent, which may affect the robustness and generalizability of our model’s predictions. Future efforts should prioritize improving ESG data disclosure and transparency within regulatory frameworks. Moreover, we acknowledge that the symbolic reasoning component of our framework, while enhancing interpretability, may face limitations in rapidly evolving ESG landscapes. Changes in regulatory taxonomies or stakeholder priorities could outpace rule-based updates. However, the model is modular and supports adaptation to non-Chinese contexts. For example, symbolic constraints can be redefined to align with EU taxonomy, SFDR, or TCFD frameworks, enabling generalization across diverse ESG disclosure regimes. While our model leverages machine learning for pattern discovery, it may not fully capture causal relationships. Further research could integrate causal inference methods or experimental designs to deepen understanding of the mechanisms linking ESG practices with financial performance. Moving forward, the interdisciplinary synergy between computational finance and sustainable business practices holds vast potential, not only for academic advancement but also for strategic decision-making in the corporate world.

Author Contributions

Conceptualization, D.L.; methodology, H.D.F.; software, D.L.; validation, D.L.; formal analysis, H.D.F.; investigation, D.L.; data curation, H.D.F.; writing—original draft preparation, D.L. and H.D.F.; writing—review and editing, D.L.; visualization, H.D.F.; supervision, D.L.; funding acquisition, H.D.F. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author due to privacy.

Conflicts of Interest

Dongxue Liu is currently employed by Guangdong Jixin Guokong Testing and Certification Technology Service Center Co., Ltd. The authors declare that this employment could potentially constitute a conflict of interest related to this study. However, the company had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. All other authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Constructing symbolic ESG transitions from policy and firm disclosures. The diagram illustrates how regulatory mandates (e.g., 2022 CSRC carbon intensity requirements) influence firm-level ESG reports. Policy actions are mapped into symbolic ESG behaviors, which are then structured as a temporal trajectory graph. The graph captures policy-conditioned ESG transitions and supports policy-aware vector field modeling.

Figure 2 Architecture of the Strategic ESG Representation Generator (SERG). The SERG model processes multi-modal ESG data through a dual-branch encoder. One path performs high-resolution spatial processing while the other incorporates symbolic-structural ESG modeling. The architecture features hierarchical convolution and attention-based modules that fuse temporal dynamics, contextual factors, and symbolic graph reasoning across four stages. The output integrates interpretability modules and MLPs to yield structured, temporally aware, and policy-aligned ESG representations for forecasting and decision-making.

Figure 3 Schematic diagram of Interpretable ESG Forecasting. The framework begins with heterogeneous graph inputs, processed via Local and Global Token-Aware modules. Features are transformed to the frequency domain using 3D FFT, split into high- and low-frequency components, fused, and reconstructed via 3D IFFT. An iterative SpectralBlend-TA module with space and cross-attention refines representations, which are decoded into ESG predictions. Supervised contrastive learning aligns embeddings with ESG taxonomies, enabling interpretability through human-understandable metafeatures.

Figure 4 Overview of the Adaptive Sustainability Policy Search (ASPS) system. The architecture integrates structured ESG inputs with policy optimization via stacked gradient blocks. A central reinforcement learning engine uses attention and stakeholder feedback to adapt policies dynamically. Semantic and multi-agent modules apply symbolic ESG constraints and coordinate policy updates, ensuring interpretability and alignment with long-term sustainability goals.

Figure 5 Overview of the end-to-end modeling pipeline. The pipeline begins with ESG disclosures, followed by symbolic anchor extraction and adaptive symbolic projection through ASPS. Latent representations are encoded via temporal and graph modules before final prediction. Color-coded modules distinguish each processing stage.

Figure 6 Semantics and Multi-agent ESG Policy Framework. This figure illustrates a multi-agent attention-based architecture for ESG policy optimization with symbolic semantic constraints.

Figure 7 Comparison of ours with SOTA methods on CSMAR and Refinitiv ESG datasets for time series prediction (error bars represent standard deviation over three runs).

Figure 8 Comparison of ours with SOTA methods on RepRisk ESG and FTSE Russell ESG ratings datasets for time series prediction (error bars represent standard deviation over three runs).

Figure 9 Ablation study results for time series prediction on CSMAR and Refinitiv ESG datasets (error bars represent standard deviation over three runs).

Figure 10 Ablation study results for time series prediction on RepRisk ESG and FTSE Russell ESG rating datasets (error bars represent standard deviation over three runs).

Table 1

Definitions of Abbreviations.

Abbreviation	Definition
MLP	Multi-Layer Perceptron: A type of neural network composed of an input layer, hidden layers, and an output layer used for classification and regression tasks.
DAG	Dual-Attention Gating: A mechanism used in models to prioritize important features dynamically by considering both temporal dynamics and inter-feature relationships.
QKV	Query, Key, and Value: Core components of the attention mechanism in Transformer models, used to determine the relevance of information in sequential data.

Table 2

Model Training Configuration and Hyperparameters.

Component	Setting
Optimizer	Adam
Learning Rate	1× ${10}^{-4}$
Batch Size	64
Epochs	100
Dropout Rate	0.2
Weight Decay	1 × ${10}^{-5}$
Embedding Dimension	128 (SERG), 64 (ASPS)
GRU Hidden Size	256
Transformer Heads	4
MLP Layers	3 (ReLU activation)
Loss Weights $({\lambda }_1,{\lambda }_2,{\lambda }_3)$	(0.6, 0.3, 0.1) via grid search
Symbolic Projection Anchors	20 categories
ESG Taxonomy Size $\left|\mathcal{T}\right|$	15
Variance Threshold $\delta$	0.15
Validation Split	20% holdout
Search Method	Grid Search (10 × 10 grid), no cross-validation
Early Stopping	Yes (patience = 10)

Table 3

Summary Statistics of the ESG Datasets Used.

Dataset	# Firms	Years	Features	Missing Rate (%)
CSMAR (China)	3200	2010–2022	48 ESG + 12 finance	12.6
Refinitiv ESG	7800	2009–2022	400+ ESG items	18.3
RepRisk	6400	2014–2022	80 ESG events (binary)	9.4
FTSE Russell	7200	2012–2022	300+ indicators	15.1

Table 4

Comparison of Ours with SOTA methods on CSMAR and Refinitiv ESG Datasets for Time Series Prediction.

Model	CSMAR Dataset				Refinitiv ESG Dataset
	Accuracy	MAE	RMSE	R2	Accuracy	MAE	RMSE	R2
ARIMA [37]	81.34 ± 0.42	0.148 ± 0.01	0.202 ± 0.01	0.782 ± 0.02	79.12 ± 0.35	0.153 ± 0.01	0.215 ± 0.01	0.755 ± 0.02
LSTM [38]	83.92 ± 0.37	0.139 ± 0.01	0.187 ± 0.01	0.801 ± 0.01	82.03 ± 0.34	0.141 ± 0.01	0.193 ± 0.01	0.778 ± 0.02
Transformer [39]	85.76 ± 0.31	0.132 ± 0.01	0.181 ± 0.01	0.816 ± 0.02	84.10 ± 0.36	0.137 ± 0.01	0.189 ± 0.01	0.795 ± 0.01
Informer [40]	86.28 ± 0.30	0.128 ± 0.01	0.179 ± 0.01	0.823 ± 0.01	85.42 ± 0.29	0.132 ± 0.01	0.183 ± 0.01	0.809 ± 0.01
DeepAR [41]	84.17 ± 0.33	0.135 ± 0.01	0.186 ± 0.01	0.807 ± 0.01	83.25 ± 0.38	0.138 ± 0.01	0.192 ± 0.01	0.781 ± 0.02
Temporal Fusion Transformer [42]	87.10 ± 0.29	0.124 ± 0.01	0.176 ± 0.01	0.831 ± 0.01	85.83 ± 0.27	0.130 ± 0.01	0.180 ± 0.01	0.815 ± 0.01
Ours	89.63± 0.25	0.117 ± 0.01	0.167 ± 0.01	0.856 ± 0.01	88.74 ± 0.23	0.120 ± 0.01	0.171 ± 0.01	0.838 ± 0.01

Table 5

Comparison of Ours with SOTA methods on RepRisk ESG and FTSE Russell ESG Ratings Datasets for Time Series Prediction.

Model	RepRisk ESG Dataset				FTSE Russell ESG Ratings Dataset
	Accuracy	MAE	RMSE	R2	Accuracy	MAE	RMSE	R2
ARIMA [37]	78.45 ± 0.39	0.157 ± 0.01	0.221 ± 0.01	0.731 ± 0.02	76.80 ± 0.41	0.164 ± 0.01	0.228 ± 0.01	0.714 ± 0.02
LSTM [38]	80.93 ± 0.36	0.145 ± 0.01	0.208 ± 0.01	0.761 ± 0.02	79.11 ± 0.35	0.149 ± 0.01	0.212 ± 0.01	0.735 ± 0.02
Transformer [39]	82.88 ± 0.30	0.139 ± 0.01	0.200 ± 0.01	0.779 ± 0.01	81.54 ± 0.33	0.144 ± 0.01	0.206 ± 0.01	0.749 ± 0.01
Informer [40]	81.60 ± 0.32	0.142 ± 0.01	0.198 ± 0.01	0.771 ± 0.02	82.73 ± 0.30	0.141 ± 0.01	0.202 ± 0.01	0.754 ± 0.02
DeepAR [41]	83.22 ± 0.29	0.136 ± 0.01	0.195 ± 0.01	0.783 ± 0.01	80.65 ± 0.36	0.148 ± 0.01	0.210 ± 0.01	0.741 ± 0.01
Temporal Fusion Transformer [42]	85.10 ± 0.28	0.131 ± 0.01	0.189 ± 0.01	0.799 ± 0.01	84.18 ± 0.29	0.136 ± 0.01	0.198 ± 0.01	0.765 ± 0.02
Ours	87.75± 0.26	0.122 ± 0.01	0.178 ± 0.01	0.823 ± 0.01	86.47 ± 0.27	0.126 ± 0.01	0.185 ± 0.01	0.789 ± 0.01

Table 6

Ablation Study Results for Time Series Prediction on CSMAR and Refinitiv ESG Datasets.

Model	CSMAR Dataset				Refinitiv ESG Dataset
	Accuracy	MAE	RMSE	R2	Accuracy	MAE	RMSE	R2
w./o. Symbolic-Structural ESG Modeling	88.10 ± 0.25	0.121 ± 0.01	0.172 ± 0.01	0.844 ± 0.01	87.35 ± 0.24	0.124 ± 0.01	0.178 ± 0.01	0.826 ± 0.01
w./o. Temporal Dynamics Encoding	87.92 ± 0.27	0.123 ± 0.01	0.175 ± 0.01	0.838 ± 0.01	86.89 ± 0.26	0.125 ± 0.01	0.179 ± 0.01	0.823 ± 0.01
w./o. Policy Optimization Framework	89.02 ± 0.24	0.119 ± 0.01	0.170 ± 0.01	0.847 ± 0.01	87.58 ± 0.23	0.122 ± 0.01	0.174 ± 0.01	0.832 ± 0.01
Ours	89.63 ± 0.25	0.117 ± 0.01	0.167 ± 0.01	0.856 ± 0.01	88.74 ± 0.23	0.120 ± 0.01	0.171 ± 0.01	0.838 ± 0.01

Table 7

Ablation Study Results for Time Series Prediction on RepRisk ESG and FTSE Russell ESG Ratings Datasets.

Model	RepRisk ESG Dataset				FTSE Russell ESG Ratings Dataset
	Accuracy	MAE	RMSE	R2	Accuracy	MAE	RMSE	R2
w./o. Symbolic-Structural ESG Modeling	86.35 ± 0.28	0.125 ± 0.01	0.181 ± 0.01	0.811 ± 0.01	85.12 ± 0.29	0.129 ± 0.01	0.187 ± 0.01	0.773 ± 0.01
w./o. Temporal Dynamics Encoding	87.02 ± 0.26	0.124 ± 0.01	0.179 ± 0.01	0.818 ± 0.01	85.94 ± 0.27	0.127 ± 0.01	0.183 ± 0.01	0.782 ± 0.01
w./o. Policy Optimization Framework	86.78 ± 0.27	0.123 ± 0.01	0.180 ± 0.01	0.815 ± 0.01	85.68 ± 0.28	0.125 ± 0.01	0.186 ± 0.01	0.779 ± 0.01
Ours	87.75 ± 0.26	0.122 ± 0.01	0.178 ± 0.01	0.823 ± 0.01	86.47 ± 0.27	0.126 ± 0.01	0.185 ± 0.01	0.789 ± 0.01

Table 8

Statistical comparison of full model and ablated variants (mean ± std over 3 runs). * indicates p < 0.05 based on paired t-test against full model.

Model	Accuracy (%)	MAE	RMSE	R2
Full Model	89.63 ± 0.25	0.117 ± 0.01	0.167 ± 0.01	0.856 ± 0.01
w/o Symbolic-Structural	88.10 ± 0.25 *	0.121 ± 0.01 *	0.172 ± 0.01 *	0.844 ± 0.01 *
w/o Temporal Dynamics	87.92 ± 0.27 *	0.123 ± 0.01 *	0.175 ± 0.01 *	0.838 ± 0.01 *
w/o Policy Opt. Framework	89.02 ± 0.24 *	0.119 ± 0.01 *	0.170 ± 0.01 *	0.847 ± 0.01 *

Table 9

Comparison of model generalization performance on non-financial ESG news sentiment classification.

Model	Accuracy (%)	F1 Score	AUC	Data Modality
LSTM + BERT Embedding	78.21	0.763	0.812	ESG News Corpus
Domain-Adapted RoBERTa	80.15	0.781	0.832	ESG News Corpus
Ours (SERG)	84.02	0.811	0.861	ESG News Corpus

Table 10

Comparison of proposed model against econometric and hybrid baselines on CSMAR Dataset.

Model	Accuracy (%)	MAE	R2	Std Dev (R2)
VAR	76.25	0.174	0.712	0.013
LSTM-ARIMA Hybrid	82.11	0.139	0.791	0.011
Temporal Fusion Transformer (TFT)	87.10	0.124	0.831	0.007
Ours (SERG)	89.63	0.117	0.856	0.005

References

1. Chen, E.Z.; Chen, T.; Sun, S. MRI Image Reconstruction via Learning Optimization Using Neural ODEs. Medical Image Computing and Computer Assisted Intervention—MICCAI 2020; Springer: Cham, Switzerland, 2020; [DOI: https://dx.doi.org/10.1007/978-3-030-59713-9_9]

2. Terpstra, M.; Maspero, M.; D’Agata, F.; Stemkens, B.; Intven, M.; Lagendijk, J.; van den Berg, C.V.D.; Tijssen, R. Deep learning-based image reconstruction and motion estimation from undersampled radial k-space for real-time MRI-guided radiotherapy. Phys. Med. Biol.; 2020; 65, 155015. [DOI: https://dx.doi.org/10.1088/1361-6560/ab9358] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32408295]

3. Shanbhogue, K.; Tong, A.; Smereka, P.; Nickel, D.; Arberet, S.; Anthopolos, R.; Chandarana, H. Accelerated single-shot T2-weighted fat-suppressed (FS) MRI of the liver with deep learning-based image reconstruction: Qualitative and quantitative comparison of image quality with conventional T2-weighted FS sequence. Eur. Radiol.; 2021; 31, pp. 8447-8457. [DOI: https://dx.doi.org/10.1007/s00330-021-08008-3] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/33961086]

4. Koonjoo, N.; Zhu, B.; Bagnall, G.; Bhutto, D.; Rosen, M.S. Boosting the signal-to-noise of low-field MRI with deep learning image reconstruction. Sci. Rep.; 2021; 11, 8248. [DOI: https://dx.doi.org/10.1038/s41598-021-87482-7]

5. Del Vitto, A.; Marazzina, D.; Stocco, D. ESG ratings explainability through machine learning techniques. Ann. Oper. Res.; 2023; pp. 1-30. [DOI: https://dx.doi.org/10.1007/s10479-023-05514-z]

6. Munoz, C.; Ellis, S.; Nekolla, S.; Kunze, K.; Vitadello, T.; Neji, R.; Botnar, R.M.; Schnabel, J.; Reader, A.; Prieto, C. MRI-Guided Motion-Corrected PET Image Reconstruction for Cardiac PET/MRI. J. Nucl. Med.; 2021; 62, pp. 1768-1774. [DOI: https://dx.doi.org/10.2967/jnumed.120.254235] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/34049978]

7. Ong, K.; Mao, R.; Xing, F.; Satapathy, R.; Sulaeman, J.; Cambria, E.; Mengaldo, G. ESGSenticNet: A Neurosymbolic Knowledge Base for Corporate Sustainability Analysis. arXiv; 2025; arXiv: 2501.15720

8. Elmas, G.; Dar, S.; Korkmaz, Y.; Ceyani, E.; Susam, B.; Ozbey, M.; Avestimehr, S.; Çukur, T. Federated Learning of Generative Image Priors for MRI Reconstruction. IEEE Trans. Med. Imaging; 2022; 42, pp. 1996-2009. [DOI: https://dx.doi.org/10.1109/TMI.2022.3220757]

9. Zhang, Y.; Liao, L. ESG disclosure and cost of equity capital in China: The role of political connections. China J. Account. Res.; 2021; 14, pp. 251-267.

10. Li, W.; Zhang, R. Does mandatory ESG reporting improve green innovation? Evidence from China. J. Bus. Ethics; 2020; 161, pp. 473-495.

11. Desai, A.D.; Schmidt, A.M.; Rubin, E.; Sandino, C.M.; Black, M.S.; Mazzoli, V.; Stevens, K.; Boutin, R.; Ré, C.; Gold, G. . SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluation. arXiv; 2022; arXiv: 2203.06823

12. Xu, J.; Moyer, D.; Gagoski, B.; Iglesias, J.E.; Grant, P.E.; Golland, P.; Adalsteinsson, E. NeSVoR: Implicit Neural Representation for Slice-to-Volume Reconstruction in MRI. IEEE Trans. Med. Imaging; 2023; 42, pp. 1707-1719. [DOI: https://dx.doi.org/10.1109/TMI.2023.3236216] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/37018704]

13. Zhao, H.; Liu, Z.; Tang, J.; Gao, B.; Qin, Q.; Li, J.; Zhou, Y.; Yao, P.; Xi, Y.; Lin, Y. . Energy-efficient high-fidelity image reconstruction with memristor arrays for medical diagnosis. Nat. Commun.; 2023; 14, 2276. [DOI: https://dx.doi.org/10.1038/s41467-023-38021-7] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/37081008]

14. Cini, F.; Ferrari, A. Towards the estimation of ESG ratings: A machine learning approach using balance sheet ratios. Res. Int. Bus. Financ.; 2025; 73, 102653. [DOI: https://dx.doi.org/10.1016/j.ribaf.2024.102653]

15. Castellano, R.; Cini, F.; Ferrari, A. Machine Learning for ESG Rating Classification: An Integrated Replicable Model with Financial and Systemic Risk Parameters. Mathematical and Statistical Methods for Actuarial Sciences and Finance; Springer: Berlin/Heidelberg, Germany, 2024; pp. 87-92.

16. Hua, L.; Gu, Y.; Gu, X.; Xue, J.; Ni, T. A Novel Brain MRI Image Segmentation Method Using an Improved Multi-View Fuzzy c-Means Clustering Algorithm. Front. Neurosci.; 2021; 15, 662674. [DOI: https://dx.doi.org/10.3389/fnins.2021.662674] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/33841095]

17. Kiryu, S.; Akai, H.; Yasaka, K.; Tajima, T.; Kunimatsu, A.; Yoshioka, N.; Akahane, M.; Abe, O.; Ohtomo, K. Clinical Impact of Deep Learning Reconstruction in MRI. Radiographics; 2023; 43, e220133. [DOI: https://dx.doi.org/10.1148/rg.220133] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/37200221]

18. Korkmaz, Y.; Çukur, T.; Patel, V. Self-Supervised MRI Reconstruction with Unrolled Diffusion Models. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention; Vancouver, BC, Canada, 8–12 October 2023.

19. Xie, Y.; Li, Q. Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention; Singapore, 18–22 September 2022.

20. Friede, G.; Busch, T.; Bassen, A. ESG and financial performance: Aggregated evidence from more than 2000 empirical studies. J. Sustain. Financ. Invest.; 2015; 5, pp. 210-233. [DOI: https://dx.doi.org/10.1080/20430795.2015.1118917]

21. Khan, M.; Serafeim, G.; Yoon, A. Corporate sustainability: First evidence on materiality. Account. Rev.; 2016; 91, pp. 1697-1724. [DOI: https://dx.doi.org/10.2308/accr-51383]

22. Krüger, P. Corporate goodness and shareholder wealth. J. Financ. Econ.; 2015; 115, pp. 304-329. [DOI: https://dx.doi.org/10.1016/j.jfineco.2014.09.008]

23. Zhou, B.; Schlemper, J.; Dey, N.; Salehi, S.; Liu, C.; Duncan, J.; Sofka, M. DSFormer: A Dual-domain Self-supervised Transformer for Accelerated Multi-contrast MRI Reconstruction. Proceedings of the IEEE Workshop/Winter Conference on Applications of Computer Vision; Waikoloa, HI, USA, 3–8 January 2022.

24. Almansour, H.; Herrmann, J.; Gassenmaier, S.; Afat, S.; Jacoby, J.; Koerzdoerfer, G.; Nickel, D.; Mostapha, M.; Nadar, M.; Othman, A. Deep Learning Reconstruction for Accelerated Spine MRI: Prospective Analysis of Interchangeability. Radiology; 2022; 306, e212922. [DOI: https://dx.doi.org/10.1148/radiol.212922]

25. Fabian, Z.; Soltanolkotabi, M. HUMUS-Net: Hybrid unrolled multi-scale network architecture for accelerated MRI reconstruction. Proceedings of the 36th International Conference on Neural Information Processing Systems; New Orleans, LA, USA, 28 November–9 December 2022.

26. Shen, L.; Pauly, J.; Xing, L. NeRP: Implicit Neural Representation Learning With Prior Embedding for Sparsely Sampled Image Reconstruction. IEEE Trans. Neural Netw. Learn. Syst.; 2021; 35, pp. 770-782. [DOI: https://dx.doi.org/10.1109/TNNLS.2022.3177134]

27. Feng, C.M.; Yan, Y.; Fu, H.; Chen, L.; Xu, Y. Task Transformer Network for Joint MRI Reconstruction and Super-Resolution. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention; Strasbourg, France, 27 September–1 October 2021.

28. Muckley, M.; Riemenschneider, B.; Radmanesh, A.; Kim, S.; Jeong, G.; Ko, J.; Jun, Y.; Shin, H.; Hwang, D.; Mostapha, M. . Results of the 2020 fastMRI Challenge for Machine Learning MR Image Reconstruction. IEEE Trans. Med. Imaging; 2021; 40, pp. 2306-2317. [DOI: https://dx.doi.org/10.1109/TMI.2021.3075856]

29. Margot, V.; Geissler, C.; De Franco, C.; Monnier, B.; Advestis, F.; Ossiam, F. ESG investments: Filtering versus machine learning approaches. Appl. Econ. Financ.; 2021; 8, pp. 1-16. [DOI: https://dx.doi.org/10.11114/aef.v8i2.5097]

30. Liang, D.; Cheng, J.; Ke, Z.; Ying, L. Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks. IEEE Signal Process. Mag.; 2020; 37, pp. 141-151. [DOI: https://dx.doi.org/10.1109/MSP.2019.2950557]

31. Korkmaz, Y.; Dar, S.; Yurt, M.; Özbey, M.; Çukur, T. Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers. IEEE Trans. Med. Imaging; 2021; 41, pp. 1747-1763. [DOI: https://dx.doi.org/10.1109/TMI.2022.3147426] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35085076]

32. Cheng, B.; Ioannou, I.; Serafeim, G. Corporate social responsibility and access to finance. Strateg. Manag. J.; 2014; 35, pp. 1-23. [DOI: https://dx.doi.org/10.1002/smj.2131]

33. Ramzi, Z.; Ciuciu, P.; Starck, J.L. Benchmarking deep nets MRI reconstruction models on the fastmri publicly available dataset. Proceedings of the 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI); Iowa City, IA, USA, 3–7 April 2020; pp. 1441-1445.

34. Litjens, G.; Toth, R.; Van De Ven, W.; Hoeks, C.; Kerkstra, S.; Van Ginneken, B.; Vincent, G.; Guillard, G.; Birbeck, N.; Zhang, J. . Evaluation of prostate segmentation algorithms for MRI: The PROMISE12 challenge. Med. Image Anal.; 2014; 18, pp. 359-373. [DOI: https://dx.doi.org/10.1016/j.media.2013.12.002] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/24418598]

35. Weninger, L.; Rippel, O.; Koppers, S.; Merhof, D. Segmentation of brain tumors and patient survival prediction: Methods for the brats 2018 challenge. Proceedings of the Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries: 4th International Workshop, BrainLes 2018, Held in Conjunction with MICCAI 2018; Granada, Spain, 16 September 2018; Revised Selected Papers, Part II 4 Springer: Berlin/Heidelberg, Germany, 2019; pp. 3-12.

36. Peng, C.; Guo, P.; Zhou, S.K.; Patel, V.M.; Chellappa, R. Towards performant and reliable undersampled MR reconstruction via diffusion model sampling. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention; Singapore, 18–22 September 2022;; Springer: Berlin/Heidelberg, Germany, 2022; pp. 623-633.

37. Liu, F.; Wang, L. UNet-based model for crack detection integrating visual explanations. Constr. Build. Mater.; 2022; 322, 126265. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2021.126265]

38. Lou, Y.; Li, S.; Li, S.; Liu, N.; Zhang, B. Seismic volumetric dip estimation via multichannel deep learning model. IEEE Trans. Geosci. Remote Sens.; 2022; 60, pp. 1-14. [DOI: https://dx.doi.org/10.1109/TGRS.2022.3221786]

39. Aggarwal, H.K.; Mani, M.P.; Jacob, M. MoDL: Model-based deep learning architecture for inverse problems. IEEE Trans. Med. Imaging; 2018; 38, pp. 394-405. [DOI: https://dx.doi.org/10.1109/TMI.2018.2865356]

40. Khodayi-Mehr, R.; Zavlanos, M. VarNet: Variational neural networks for the solution of partial differential equations. Proceedings of the Learning for Dynamics and Control; Virtual, 10–11 June 2020; pp. 298-307.

41. Marquez, E.S.; Hare, J.S.; Niranjan, M. Deep cascade learning. IEEE Trans. Neural Netw. Learn. Syst.; 2018; 29, pp. 5475-5485. [DOI: https://dx.doi.org/10.1109/TNNLS.2018.2805098]

42. Marhoon, I.I.; Atiyah, I.A.; Rasheed, A.K. 3D g-C3N4 porous nanoribbons pillared-MXene/PVA nanocomposite: An architecture with high dielectric, breakdown strength, thermal conductivity, and mechanical strength characteristics. J. Alloys Compd.; 2023; 969, 172229. [DOI: https://dx.doi.org/10.1016/j.jallcom.2023.172229]