Abstract Neural Networks
summary
The paper introduces Abstract Neural Networks that soundly overapproximate a DNN while using far fewer nodes by replacing weight matrices with elements of an abstract numerical domain and merging nodes via convex combinations (including a scaling factor equal to the number merged). It gives an algorithm parameterized by abstract domain and activation functions and proves soundness under a weakened intermediate value property for activations and non‑negative post‑activation values. Works for intervals + ReLU and generalizes to octagons, polyhedra, Leaky ReLU, Sigmoid, Tanh; noncontinuous activations or mixed signs break soundness and practical evaluation remains open.
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chapters (8)
- 0:00Abstract neural networks intro
- 3:12Verification challenges
- 8:10Defining abstract neural networks
- 12:48Converting DNNs to abstract NNs
- 16:43Proving abstraction soundness
- 21:38When abstraction fails
- 25:27Open questions and future work
- 27:19Q&A
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