Probabilistic verification of neural networks is concerned with formally
analysing the output distribution of a neural network under a probability
distribution of the inputs. Examples of probabilistic verification include
verifying the demographic parity fairness notion or quantifying the safety of a
neural network. We present a new algorithm for the probabilistic verification
of neural networks based on an algorithm for computing and iteratively refining
lower and upper bounds on probabilities over the outputs of a neural network.
By applying state-of-the-art bound propagation and branch and bound techniques
from non-probabilistic neural network verification, our algorithm significantly
outpaces existing probabilistic verification algorithms, reducing solving times
for various benchmarks from the literature from tens of minutes to tens of
seconds. Furthermore, our algorithm compares favourably even to dedicated
algorithms for restricted subsets of probabilistic verification. We complement
our empirical evaluation with a theoretical analysis, proving that our
algorithm is sound and, under mildly restrictive conditions, also complete when
using a suitable set of heuristics.

用具有适当启发式条件的一组算法基于神经网络的输出分布来验证其概率，同时计算和迭代优化神经网络输出概率的下界和上界，并通过应用非概率性神经网络验证中的最先进的边界传播和分支约束技术，显著提高了解决时间。

使用分支界限法对神经网络进行概率验证

Probabilistic Verification of Neural Networks using Branch and Bound

A robotic behavior model that can reliably generate behaviors from natural
language inputs in real time would substantially expedite the adoption of
industrial robots due to enhanced system flexibility. To facilitate these
efforts, we construct a framework in which learned behaviors, created by a
natural language abstractor, are verifiable by construction. Leveraging recent
advancements in motion primitives and probabilistic verification, we construct
a natural-language behavior abstractor that generates behaviors by synthesizing
a directed graph over the provided motion primitives. If these component motion
primitives are constructed according to the criteria we specify, the resulting
behaviors are probabilistically verifiable. We demonstrate this verifiable
behavior generation capacity in both simulation on an exploration task and on
hardware with a robot scooping granular media.

构建了一个能够从自然语言输入中可靠生成行为的机器人行为模型，通过构建自然语言抽象器所创建的学习行为的验证构架，在实时中合成了基于给定动作基元的有向图来生成行为，并借助运动基元和概率验证的最新进展，如果按照约定的标准构造这些基本运动元件，则生成的行为是可概率验证的，通过模拟探索任务和实际机器人操作来展示了这种可验证行为生成的能力。