Soft voting robustness in neural network ensembles with empirical analysis and formal verification

Kovács, Ádám and Gunics, Roland and Kovásznai, Gergely and Tajti, Tibor (2025) Soft voting robustness in neural network ensembles with empirical analysis and formal verification. ANNALES MATHEMATICAE ET INFORMATICAE, 61. pp. 171-185. ISSN 1787-6117

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Abstract

Neural network ensembles with soft voting improve accuracy and stability by aggregating multiple models; however, their reliability under individual model failure remains a critical concern. This paper addresses the robustness of soft-voting ensembles in safety-critical settings by combining empirical analysis and formal verification. We evaluate the impact of singlemodel failures on ensemble performance and find that soft voting yields graceful degradation, with only minimal loss in accuracy when one component model is removed or corrupted. In parallel, we develop a formal verification framework to investigate whether the ensemble’s final prediction remains unchanged under any single-model failure scenario. The results demonstrate that soft-voting ensembles can maintain reliable outputs despite individual model failures, providing both empirical evidence and provable guarantees of fault tolerance in neural network ensembles.

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