Abstract Neural network verification is an active and rapidly maturing research area, with a growing ecosystem of solvers and tools. The VNN-LIB standard was introduced to support interoperability in this ecosystem, but Version 1.0 has several serious short-comings as a formal foundation: it lacks a precise syntax, semantics, and type system, offers limited expressivity, and relies on externally defined ONNX models whose semantics are informal and constantly evolving. The latter distinguishes VNN-LIB from established standards such as SMT-LIB, where queries are self-contained and have fixed semantics. In this paper we address these challenges by developing the theoretical foundations of VNN-LIB 2.0. Our key contribution is the introduction of the notion of a network theory , which abstractly characterises the minimal semantic interface required from a neural network model format. This abstraction enables VNN-LIB to be defined independently of any specific ONNX version while remaining compatible with evolving model representations. Building on this foundation, we present a formal syntax for a more expressive query language, a type system for it over the numeric domains provided by the network theory, and finally a formal semantics. To ensure internal consistency, the standard is mechanised in the Agda theorem prover. VNN-LIB 2.0 therefore provides robust and rigorous foundations for trustworthy neural network verification.

Formal verification of neural networks is a crucial technique to increase their dependability in safety critical applications. In this paper we address some scalability challenges in our verification tool NEVER2 by proposing strategies to enhance speed and overall performances. First, we apply a precomputation technique based on symbolic bounds propagation in order to improve the network analysis by determining neuron stability a priori. Second, we combine the strengths of different levels of abstraction towards a refinement strategy. We experiment with the proposed techniques on some verification benchmarks from the annual competition of verification tools for neural networks (VNN-COMP).