On the Decompositionality of Neural Networks

2026-04-09

AI Summary

Neural networks are often treated as monolithic black boxes, lacking maintainability and systematic verifiability. This work formally defines the notion of “decomposability” for neural networks, establishing semantic contracts between the original model and its components based on decision boundary semantics preservation. To realize semantic-aware, verification-driven decomposition, the authors propose the SAVED framework, which integrates boundary-aware counterexample mining, low logical margin input analysis, probabilistic coverage evaluation, and structure-aware pruning. Experiments across CNNs, language Transformers, and vision Transformers reveal a fundamental architectural disparity: language models tend to satisfy decomposability more readily, whereas vision models frequently violate this property, highlighting intrinsic differences in their structural amenability to semantic decomposition.

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.

Problem

• decompositionality
• neural networks
• semantic preservation
• decision boundary
• modular reasoning

Innovation

• neural decompositionality
• decision boundary semantics
• modular neural networks
• SAVED framework
• semantic-preserving decomposition