Neural Network Verification via Complementary Constraints
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Solution Overview
Problem
Current methods for verifying the transformational robustness of neural networks, especially in large and complex systems, often terminate inconclusively due to computational resource limitations, failing to provide definitive guarantees on output tolerance under input transformations.
Innovation Solution
A method that systematically verifies transformational robustness by introducing complementary constraints to reduce the complexity of child verification problems, allowing for a more efficient determination of counter-examples and ensuring neural networks remain within specified output tolerances under input transformations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If decompositional verification techniques are applied to large neural networks, then verification completeness is improved, but computational resource requirements worsen
Solution Approach 1:
The verification problem is segmented by decomposing the neural network into multiple sub-networks based on structural characteristics (such as separating convolutional layers from fully connected layers, or dividing by activation function types). Each sub-network is verified independently using specialized techniques, which reduces the computational burden compared to verifying the entire network as a single unit while maintaining comprehensive verification coverage.
Solution Approach 2:
Different verification techniques and constraint sets are applied to different parts of the neural network based on their specific characteristics. For example, convolutional layers may use one set of verification constraints optimized for spatial transformations, while fully connected layers use constraints optimized for their computational structure. This localized approach allows each region to be verified using the most efficient method for its specific properties, reducing overall computational requirements.
2Measurement precision
If the number of child verification problems is increased to reduce search space, then verification precision is improved, but device complexity worsens
Solution Approach 1:
The verification system dynamically adjusts the number and complexity of child verification problems based on the specific neural network being verified and the transformation class in question. Rather than using a fixed number of decomposition levels, the system adapts the decomposition strategy in real-time, creating only as many child problems as necessary to achieve conclusive verification results. This dynamic adjustment prevents unnecessary complexity while maintaining high verification precision.
Solution Approach 2:
The system changes key parameters of the verification problems (such as the tightness of constraints, the granularity of decomposition, and the selection criteria for child problems) based on the network architecture and transformation characteristics. By optimizing these parameters adaptively, the system achieves high verification precision without requiring a proportional increase in system complexity or the number of problems to be solved.
Data Source
AI summary
Systems and methods are provided for verifying the transformational robustness of a neural network. Data is obtained representing a trained neural network, a set of algebraic constraints on the output of the network, and a range of inputs to the neural network over which the algebraic constraints are to be verified, such that the data defines a transformational robustness verification problem. A set of complementary constrains on the pre-activation of a node in the network are then determined such that for any input in the range of inputs, at least one of the complementary constraints is satisfied. A plurality of child verification problems are generated based on the transformational robustness verification problem and the set of complementary constraints. For each child verification problem, it is determined whether a counter-example to the child verification problem exists. Based on the determination of whether counter-examples to the child verification problems exist, it is determined whether the neural network is transformationally robust.