Syntactic vs Semantic Linear Abstraction and Refinement of Neural Networks
This work addresses scalability issues in neural network verification for researchers and practitioners, though it is incremental as it builds on existing abstraction techniques.
The paper tackles the limited scalability of neural network verification by introducing a flexible abstraction framework where neurons can be replaced with linear combinations of others, applied to both syntactic and semantic methods, and includes a refinement technique to balance reduction and precision, achieving improved reductions as evaluated experimentally.
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that is similar enough. We can classify the similarity as defined either syntactically (using quantities on the connections between neurons) or semantically (on the activation values of neurons for various inputs). Unfortunately, the previous approaches only achieve moderate reductions, when implemented at all. In this work, we provide a more flexible framework where a neuron can be replaced with a linear combination of other neurons, improving the reduction. We apply this approach both on syntactic and semantic abstractions, and implement and evaluate them experimentally. Further, we introduce a refinement method for our abstractions, allowing for finding a better balance between reduction and precision.