On the Decompositionality of Neural Networks
2026-04-09 • Logic in Computer Science
Logic in Computer ScienceSoftware Engineering
AI summaryⓘ
The authors introduce a new way to break down neural networks into meaningful parts without changing how they make decisions, which they call neural decompositionality. Their method focuses on keeping the decision boundary—the line that separates different outcomes—the same in both the whole model and its parts. They create a tool called SAVED to help find these parts by testing tricky inputs and pruning the model carefully. When testing different types of models, they found that language models keep this property better than vision models, which often don’t. This work provides a clear way to think about and test if neural networks can be broken into useful modules.
neural decompositionalitydecision boundarysemantic behaviorcounterexample mininglogic marginprobabilistic coveragepruningCNNTransformersmodel decomposition
Authors
Junyong Lee, Baek-Ryun Seong, Sang-Ki Ko, Andrew Ferraiuolo, Minwoo Kang, Hyuntae Jeon, Seungmin Lim, Jieung Kim
Abstract
Recent advances in deep neural networks have achieved state-of-the-art performance across vision and natural language processing tasks. In practice, however, most models are treated as monolithic black-box functions, limiting maintainability, component-wise optimization, and systematic testing and verification. Despite extensive work on pruning and empirical decomposition, the field still lacks a principled semantic notion of when a neural network can be meaningfully decomposed. We introduce neural decompositionality, a formal notion defined as a semantic-preserving abstraction over neural architectures. Our key insight is that decompositionality should be characterized by the preservation of semantic behavior along the model's decision boundary, which governs classification outcomes. This yields a semantic contract between the original model and its components, enabling a rigorous formulation of decomposition. Building on this foundation, we develop a boundary-aware framework, SAVED (Semantic-Aware Verification-Driven Decomposition), which operationalizes the proposed definition. SAVED combines counterexample mining over low logic-margin inputs, probabilistic coverage, and structure-aware pruning to construct decompositions that preserve decision-boundary semantics. We evaluate our approach on CNNs, language Transformers, and Vision Transformers. Results show clear architectural differences: language Transformers largely preserve boundary semantics under decomposition, whereas vision models frequently violate the decompositionality criterion, indicating intrinsic limits. Overall, our work establishes decompositionality as a formally definable and empirically testable property, providing a foundation for modular reasoning about neural networks.