Abstract Interpretation of ReLU Neural Networks with Optimizable Polynomial Relaxations
Primary Area: societal considerations including fairness, safety, privacy
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Keywords: Neural Network Verification, Abstract Interpretation, Symbolic Interval Propagation
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Abstract: Neural networks have shown to be highly successful in a wide range of applications. However, due to their black box behavior, their applicability can be restricted in safety-critical environments, and additional verification techniques are required.
Many state-of-the-art verification approaches use abstract interpretation based on linear overapproximation of the activation functions.
Linearly approximating non-linear activation functions clearly incurs loss of precision. One way to overcome this limitation is the utilization of polynomial approximations.
A second way shown to improve the obtained bounds is to optimize the slope of the linear relaxations.
Combining these insights, we propose a method to enable similar parameter optimization for polynomial relaxations.
Given arbitrary polynomials parameterized by their monomial coefficients, we can obtain valid polynomial overapproximations by appropriate upward or downward shifts.
Leveraging automatic differentiation, we optimize the choice of the monomial coefficients via gradient-based techniques.
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Submission Number: 5227
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