The Complexity of Verifying Feedforward Neural Networks in Quantised Settings

2026-05-28

AI Summary

This study investigates the verification complexity of quantized feedforward neural networks under various weight representations—rational numbers, fixed-precision quantization, and dynamic quantization—and formal specifications expressed in linear programming (LP) and bit-vector (BV) logics. Leveraging computational complexity theory and formal verification techniques, the work employs reduction-based analyses to systematically map the complexity landscape of this verification problem. The primary contributions include proving that verifying fixed-precision quantized networks is NP-complete under both LP and BV specifications, and establishing the first explicit upper bound on the complexity of verifying dynamically quantized networks under BV specifications, thereby completing the known PSPACE-hardness result and sharpening the theoretical boundaries of quantized neural network verification.

Abstract

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights come from a finite-width arithmetic, and dynamically quantised FNNs in which rational networks are evaluated with respect to a given finite-width arithmetic. We consider two types of specifications used in the literature. Linear programming (LP) specifications are conjunctions of linear constraints, while bit-vector (BV) specifications allow reasoning at the bit level and can express non-linear constraints. Our results give a complexity landscape of these verification problems. For quantised FNNs with fixed arithmetic precision, we show that verification under both LP and BV specifications remains NP-complete, matching the complexity of the rational case. For dynamically quantised FNNs with BV specifications, we establish upper bounds, complementing a previously known PSPACE-hardness result.

Problem

• neural network verification
• quantised neural networks
• computational complexity
• bit-vector specifications
• feedforward neural networks

Innovation

• quantised neural networks
• verification complexity
• feedforward neural networks
• bit-vector specifications
• computational complexity