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We present a notion of bisimulation that induces a reduced network which issemantically equivalent to the given neural network. We provide a minimizationalgorithm to construct the smallest bisimulation equivalent network. Reductionsthat construct bisimulation equivalent neural networks are limited in the scaleof reduction. We present an approximate notion of bisimulation that providessemantic closeness, rather than, semantic equivalence, and quantify semanticdeviation between the neural networks that are approximately bisimilar. Thelatter provides a trade-off between the amount of reduction and deviations inthe semantics.

Bisimulations for Neural Network Reduction