📈 economics

A Multi-Input Approach for SME Default Using Explainable Deep Learning

This paper presents a novel multi-input deep learning model that integrates financial time series, governance features, and regional data to outperform traditional methods in predicting SME default risk while maintaining interpretability through Shapley values.

Original authors: Belinda Laura Del Gaudio, Raffaele Clemente Petrella, Salvatore Scognamiglio, Paolo Zanetti

Published 2026-10-23

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Belinda Laura Del Gaudio, Raffaele Clemente Petrella, Salvatore Scognamiglio, Paolo Zanetti

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the complex machinery of a modern economy, small and medium-sized businesses act as the essential gears that keep everything turning. They employ millions, drive innovation, and form the backbone of national wealth. Yet, these companies face a constant, high-stakes gamble: the risk of default, or the inability to pay back their debts. For banks and lenders, predicting which business might fail before it actually happens is a matter of financial stability. For decades, experts have tried to solve this puzzle using mathematical models that look at a company's financial statements—its assets, debts, and profits—to guess its future. These traditional methods work reasonably well, but they often treat a company's history as a single snapshot in time, ignoring how that company has changed over the years. They also tend to overlook other crucial details, such as who is running the company or where it is located, focusing almost exclusively on the numbers in the ledger.

A team of researchers from the University of Naples "Parthenope" in Italy has developed a new way to look at this problem, one that treats a business more like a living story than a static photograph. Instead of relying on a single, rigid formula, they built a sophisticated computer system capable of reading multiple types of information at once. This system, which they call a multi-input neural network, is designed to digest three distinct streams of data: the company's financial history over several years, the characteristics of its leadership and management structure, and the economic conditions of the specific region where it operates. By weaving these different threads together, the researchers created a model that can see patterns and connections that older methods miss. Their work suggests that to truly understand the risk of a business failing, one must look at its past trajectory, its current leadership, and its surroundings, not just its balance sheet.

The researchers tested their new approach using a massive dataset of Italian small and medium-sized enterprises, covering the period from 2013 to 2022. They focused on established companies that had been in business for at least three years, excluding very small micro-enterprises because their financial records are often too brief or their management structures too simple to provide the detailed history needed for this type of analysis. The team gathered information on thousands of companies, including their yearly profits, debts, and assets, as well as details about their board members, such as their age, gender, and experience. They also noted the specific region where each company was based, recognizing that local economic conditions can influence a business's success.

To process this diverse information, the researchers constructed a digital architecture with three specialized pathways, or "sub-networks," that feed into a central decision-making unit. The first pathway was designed to handle the financial data, which changes every year. Instead of just looking at the most recent year's numbers, this part of the system uses a type of artificial intelligence known as a Long Short-Term Memory network. This technology is particularly good at remembering sequences; it looks at the financial history of a company over several years to understand its trend, much like a doctor might look at a patient's health records over a decade rather than just their temperature on a single day. The second pathway processes the governance data, which describes the people in charge. Since leadership teams do not change as frequently as financial numbers, this part of the system treats that information as a stable set of facts about the company's structure. The third pathway handles the regional data, converting the name of a region into a numerical code that allows the system to learn how different geographic areas affect business risk.

Once these three streams of information are processed, they are combined into a single, unified picture of the company. This combined view is then passed to a final layer that calculates the probability of the company defaulting in the coming year. The researchers compared this new multi-input system against three other methods commonly used in the industry: a traditional statistical model known as logistic regression, a powerful machine learning tool called XGBoost, and a standard deep learning model that does not account for time sequences. They tested these models by asking them to predict which companies would fail in 2021 and 2022, based on data available the year before.

The results showed that the new multi-input approach was the most accurate predictor. In tests designed to see how well the models could distinguish between companies that would survive and those that would fail, the new system consistently outperformed the others. It achieved the highest scores in correctly identifying both the companies that would survive and those that would fail, striking a better balance than the other models. While the traditional statistical model and the standard machine learning tools made more errors, the new system demonstrated a superior ability to adapt to new data and avoid the common pitfall of overfitting, where a model memorizes past data so perfectly that it fails to predict the future.

Beyond simply predicting who would fail, the researchers wanted to understand why their model made the decisions it did. Deep learning systems are often criticized for being "black boxes," meaning their internal logic is so complex that humans cannot easily explain how they reached a conclusion. To address this, the team used a technique called Shapley values, which acts like a fairness calculator to measure how much each piece of information contributed to the final prediction. They found that the financial and economic indicators were, as expected, the strongest drivers of the prediction. However, the analysis revealed something important: the characteristics of the company's governance and its geographic location also played a significant, non-negligible role. While financial data carried the most weight, the model showed that ignoring the people in charge or the local economic context would lead to less accurate predictions. The regional data, for instance, contributed less than 20 percent to the final decision, but that small amount was still meaningful enough to improve the overall accuracy.

This study confirms that looking at a business through a single lens is no longer sufficient for accurate risk assessment. By integrating financial history, leadership details, and regional context into a single, flexible system, the researchers have created a tool that offers a more complete and reliable view of corporate health. Their work suggests that the future of predicting business failure lies in models that can handle different types of data simultaneously, respecting the unique way each piece of information evolves over time. While the model was tested specifically on Italian companies, the approach offers a blueprint for how lenders and analysts elsewhere might better understand the complex realities of the businesses they support. The findings do not eliminate the risk of failure, but they provide a clearer, more nuanced map for navigating it.

Technical Summary: A Multi-Input Approach for SME Default Using Explainable Deep Learning

Problem Statement
The prediction of default risk for Small and Medium-sized Enterprises (SMEs) remains a critical challenge in corporate finance. While traditional models, such as logistic regression and linear discriminant analysis, offer interpretability, they often fail to capture the nonlinear, multidimensional dynamics inherent in SME behavior. Furthermore, existing literature frequently relies on static snapshots of financial data, neglecting the temporal evolution of a firm's condition and the heterogeneity of non-financial variables (e.g., governance structures and regional contexts). Although recent Machine Learning (ML) and Deep Learning (DL) approaches have improved predictive accuracy, many remain "black boxes" lacking transparency, and few are explicitly designed to integrate heterogeneous data modalities—specifically time-series financial data, static governance attributes, and categorical regional information—into a unified framework.

Methodology
The authors propose a novel Multi-Input Neural Network (MI-NET) architecture designed to process heterogeneous data sources through a pillar-based structure. The model is formulated as a supervised binary classification task to predict default one year in advance ( $T$ ) using information available at $T-1$ .

The architecture consists of three specialized sub-networks (subnets) that process distinct data types before aggregating them:

Financial-Economic Subnet (Temporal): This component handles balance sheet and income statement indicators (e.g., assets, liabilities, revenues) that evolve over time. To capture temporal dependencies and evolutionary patterns, the authors employ Long Short-Term Memory (LSTM) networks. The model utilizes a lookback period ( $\tau$ ) to process sequences of financial data, allowing the network to learn from the firm's historical trajectory rather than a single static point.
Governance Subnet (Static): This component processes quasi-static attributes describing corporate governance, such as board composition, executive tenure, and diversity metrics. Since these features exhibit limited variation over time, they are processed using a standard Feed-Forward Neural Network (FFNN) using data from the evaluation date $T-1$ .
Regional Subnet (Categorical): This component incorporates the geographical context (region) where the firm operates. Categorical variables are transformed into continuous, low-dimensional vector representations using Entity Embedding (EE) layers. This technique allows the model to learn latent relationships between regions based on their impact on default probability.

Aggregation and Classification:
The latent representations generated by the three subnets are concatenated to form a unified feature vector. This aggregated vector is fed into a final Decoder (a sequence of FFNN layers) which outputs the probability of default.

Explainability Framework:
To address the "black box" nature of deep learning, the authors integrate Shapley Values (from game theory) to quantify the marginal contribution of each input pillar to the final prediction. Rather than applying Shapley values to every individual raw feature (which is computationally prohibitive), the authors apply the technique to the three aggregated sub-network outputs. This allows for a transparent decomposition of the model's decision-making process into three distinct contributions: financial-economic history, governance structure, and regional context.

Data and Experimental Setup
The study utilizes a large dataset of Italian SMEs from the AIDA database, covering the period 2013–2022. The sample includes 81,186 units, excluding micro-enterprises to ensure data granularity and stability. The dataset includes financial statements, governance records (aggregated by decision-maker roles), and regional data derived from ZIP codes. The models were evaluated in two out-of-sample forecasting scenarios: predicting 2021 defaults based on 2020 data, and predicting 2022 defaults based on 2021 data.

Key Results
The MI-NET model was compared against three benchmarks: Logistic Regression (LR), XGBoost, and a standard FFNN (based on the work of Crosato et al., 2023).

Predictive Performance: MI-NET consistently achieved the highest ROC-AUC scores in both training and test sets across both scenarios. In the 2022 test set, MI-NET achieved an AUC of 0.927, outperforming XGBoost (0.920), FFNN (0.897), and LR (0.855).
Balanced Metrics: MI-NET demonstrated superior Accuracy (0.920 in 2022) and maintained a more efficient balance between Sensitivity (0.765) and Specificity (0.920) compared to XGBoost, which showed higher sensitivity but significantly lower specificity (indicating a higher rate of false positives).
Interpretability Findings: The Shapley value analysis revealed that financial-economic indicators are the dominant driver of default risk. However, governance characteristics provided a significant, complementary contribution, and regional context, while contributing less than 20% on average, offered non-negligible explanatory power.

Significance and Claims
The paper claims that the proposed approach offers a significant advancement over traditional linear models and standard non-linear ML methods by explicitly modeling the heterogeneous and dynamic nature of SME data. The key contributions are:

Architectural Innovation: The integration of LSTM for temporal financial data, FFNN for static governance, and Embeddings for categorical regional data within a single multi-input framework allows for the effective exploitation of complementary information sources that are often treated separately or ignored.
Improved Generalization: The model's superior performance in out-of-sample testing suggests that the structured exploitation of heterogeneous data sources mitigates overfitting and enhances adaptability to new data compared to benchmarks.
Responsible AI: By leveraging the modular design to apply Shapley values at the subnet level, the study provides a practical framework for interpretability. This mitigates the opacity of deep learning, making the model suitable for regulatory-sensitive contexts like credit risk assessment.

The authors conclude that while financial fundamentals remain the primary predictors of default, the inclusion of governance and regional context significantly enhances predictive performance. They note that future work will explore extending this framework to micro-enterprises and younger firms, as well as investigating Transformer-based architectures and transfer learning.

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