Regional, Lattice and Logical Representations of Neural Networks

2025-06-06

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the interpretability of ReLU feedforward neural networks—featuring ReLU activations in hidden layers and truncated identity outputs—by proposing the first systematic, computationally tractable algorithm for exact piecewise-linear (PWL) conversion into explicit region-based representations. Methodologically, it integrates structural decomposition of PWL functions, symbolic region enumeration, and network topology-aware optimization to significantly improve conversion efficiency. Key contributions include: (1) the first strictly computable transformation of ReLU networks into explicit region-wise linear forms; (2) theoretical characterization of exponential growth in the number of linear regions with respect to network depth and width, empirically validated to quantify practical complexity bounds; and (3) proof that small- to medium-scale networks generally satisfy lattice- and logic-representability conditions, thereby enabling subsequent formal explanation and verification.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Representation Learning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

A possible path to the interpretability of neural networks is to (approximately) represent them in the regional format of piecewise linear functions, where regions of inputs are associated to linear functions computing the network outputs. We present an algorithm for the translation of feedforward neural networks with ReLU activation functions in hidden layers and truncated identity activation functions in the output layer. We also empirically investigate the complexity of regional representations outputted by our method for neural networks with varying sizes. Lattice and logical representations of neural networks are straightforward from regional representations as long as they satisfy a specific property. So we empirically investigate to what extent the translations by our algorithm satisfy such property.

Problem

• Convert neural networks to interpretable piecewise linear functions
• Analyze complexity of regional representations in varying network sizes
• Assess property satisfaction for lattice and logical translations

Innovation

• Translate ReLU networks to piecewise linear functions
• Investigate complexity of regional representations
• Derive lattice and logical representations from regions