Amin Arab NajafabadiNg Keng YapZahra Nazemi AshaniFaranak NejatiMohamed Abdullahi Ali2026-10-142026-10-14202510.1109/ACCESS.2025.3606472https://dspace-cris.utar.edu.my/handle/123456789/11748Ensemble learning plays a crucial role in deep learning (DL) by improving classification accuracy through the aggregation of multiple classifiers. However, traditional methods, such as bagging, boosting, and stacking, face limitations when combining heterogeneous classifiers trained on unrelated tasks, owing to their reliance on closely aligned objectives. To address these challenges, we propose Adjusted Exponential Scaling (AES), a novel approach that combines diverse classifiers using probabilistic outputs, such as those generated by the Softmax function. AES eliminates the need to modify DL architectures or interfere with their training processes, thereby significantly reducing computational costs while ensuring compatibility with existing systems. We demonstrate AES scalability in simulations, successfully combining the outputs of up to 40 classifiers while maintaining probabilistic integrity. A formal verification using the Z3 Satisfiability Modulo Theories (SMT) solver confirmed its accuracy and reliability. AES is designed for simplicity and adaptability, making it particularly well suited for dynamic applications such as deepfake detection and medical diagnostics, where real-time combination is critical. By providing a scalable and computationally efficient solution, AES expands the applicability of ensemble learning and establishes a foundation for future extensions to sequential and binary tasks, further enhancing its versatility in machine learning challenges. © 2013 IEEE.en-USadjusted exponential scaling (AES)classifier integrationEnsemble learningformal verificationmulticlass classificationClassification (of information)Computational efficiencyDeep learningDiagnosisFormal logicLearning systemsAdjusted exponential scalingClassification accuracyClassifier integrationsExponentialsInnovative approachesMulti-class classificationMultiple-classifiersScalingsStackingsFormal verificationjournal-article