In this post, I am excited to introduce ** Xequation**.

Generally, machine learning (ML) based applications are required to be
generalized such that they can work correctly with unseen samples. However,
ML algorithms, including highly trained and smooth neutral networks optimized for
perception tasks, have been shown to lack `robustness to small changes of inputs`

,
known as `perturbations`

. ** Xequation** is a new framework for verifying
the

`robustness of ML-based safety-critical applications`

. The analysis is fully
automatic and derives the estimated probability of how robust a model is w.r.t
perturbations, called `statistical robustness`

.The new technique combines the `temporal logics with time bounds`

, a method for formalizing program specifications, with an adaptation of `multi-level splitting`

, a method for estimating the probability of rare events to
the statistical robustness. As a result, the framework provides a unifying `formalization of the perturbation`

generation process and a definition of robustness from a formal methods perspective.
An advantage of the technique is that it has an ability to scale to `much larger ML models`

, e.g. deep neutral networks used in autonomous driving software stack, than
formal methods approaches such as using an automated theorem prover.
The effectiveness of the technique is demonstrated with a prototype implementation
that is able to automatically verify on benchmark problems, while scaling to larger
deep neutral networks. Experimental results indicate that the derived probability
is reliable and accurate.

The objective of ** Xequation** is to provide

*solutions and tool development for verifying the robustness and reliability from a formal methods perspective for machine learning (ML)-based safety-critical applications such as localization, perception, and planning modules in autnomous driving software stack*