Static analysis of ReLU neural networks with tropical polyhedra
summary
Claims a concrete static-analysis method that uses tropical polyhedra to abstract ReLU feedforward nets, representing ReLU layers exactly and approximating linear layers via a zone abstraction and optional zone subdivision to regain precision. Presents closed-form formulas for best zone bounds in low dimensions, encodes final checks as linear or mixed-integer programs, and ships a prototype evaluation showing it can prove nontrivial range properties (classification and safety) while exposing a cost tradeoff from switching internal/external representations.
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chapters (8)
- 0:00Tropical geometry analysis
- 3:18Tropical polyhedra for ReLU
- 8:21Linear layers with tropical
- 13:40Computing tropical abstractions
- 17:19Multi-layer analysis with trop. polyhedra
- 20:06Future work and challenges
- 22:51Performance and scalability
- 26:17Q&A
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