Quantitative verification of neural networks requires reasoning about probabilities under substantial uncertainty in both input distributions and their dependence structure. In realistic settings, this information is often only partially specified, and assuming precise probabilistic models can lead to unreliable results. We propose a sound framework for quantitative verification under imprecise probabilistic information, combining interval belief structures to represent marginal uncertainty with imprecise copulas to model uncertain dependence. We develop a propagation method for imprecisely coupled interval belief structures through feed-forward neural networks. Using mixed imprecise copula volumes, we derive sound push-forward constructions through affine transformations and activation functions. The resulting output can provide guaranteed lower and upper bounds on probabilistic safety properties, valid for all probability models compatible with the specified imprecise inputs.
Neural network verification and data privacy are inherently in tension: verification demands full access to model parameters and input data, yet both are increasingly restricted by privacy regulations and intellectual property constraints. This tension has left robustness verific…
In this work, we investigate the effect of lookahead branching strategies in neural network verification. We present a general recipe to integrate lookahead into any branch-and-bound verifier and demonstrate how one of the current state-of-the-art branching heuristics, FSB, can b…
In distributed systems, the classical State Machine Replication (SMR) model assumes that correct replicas execute deterministic transitions to yield identical bitwise states. However, the rise of agentic distributed systems -- where autonomous, stochastic, and model-driven agents…
Existing approaches for reasoning about action and change provide expressive semantics for modeling dynamic systems, in most cases built on top of logic programming systems. We introduce a modular framework for transition and trajectory verification based on Tiles and implemented…
We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p…
Existing approaches to multi-agent belief combination have established mature foundations for combining uncertain beliefs under common assumptions: consensus methods use iterative averaging, logic-based methods resolve conflicting knowledge bases, and epistemic logic analyzes age…