Dear Ali Amiri ,
The term formal verification refers to theory and practice of computer-supported mathematical analysis methods for ensuring correctness of software (and hardware) systems. The modeling and verification of such systems is an important issue. In particular, safety-critical systems are ones in which errors can be disastrous: loss of life, major financial losses, etc. Techniques to safeguard against such scenarios are essential for such systems. Testing can identify problems, especially if done in a rigorous fashion, but is generally not sufficient to guarantee a satisfactory level of quality. The latter (additionally) requires proving correctness of systems via automated deduction, e.g., using theorem proving or model checking as a core reasoning method.
https://moves.rwth-aachen.de/teaching/ss-18/fvmml/
Regards,
Shafagat
Another answer. Formally verifying machine learning algorithms, including deep learning ones, is a challenging and complex task. The key reason is the non-linear nature and the complexity of the mathematical models used. However, there are a few techniques that researchers have been exploring to provide some degree of formal verification for these algorithms.
Here's an overview of some methods that have been applied to this problem:
However, these methods are generally quite computationally expensive and may not scale well to large, complex deep learning models. Also, they often provide guarantees that are only valid under specific assumptions, such as the absence of numerical errors during computation. Therefore, the development of practical formal verification methods for deep learning remains an active area of research.
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