Geometric Path Enumeration for Equivalence Verification of Neural Networks

Counterexample Guided Neural Network Quantization Refinement

“…Definition 2.1 is a strict form of equivalence and imposes a hard requirement [13]. Definition 2.2, in turn, is a flexible form of equivalence [12]. As noted by Eleftheriadis et al [13], Top-Equivalence is a true equivalence relation, that is, it is reflexive…”

“…2) Geometric Path Enumeration (GPE) Encoding: Tran et al, 2019 [27] proposed GPE, a methodology for verifying NNs' safety properties and the verification approach used by the tool proposed by Teuber et al [12], namely NNEQUIV. We briefly describe NNEQUIV and how it encodes NNs and equivalence property (EP) into a verification problem.…”

“…The neural networks f and g are equivalent if c f = c g and G f = G g for each tile P ′ . The NNEQUIV's algorithm [12] computes the tiling T via repeated reachability analysis as follows. First, the input domain I is propagated through NN f , outputting a union of star sets.…”

“…Unfortunately, quantization-aware training may break the assumptions of the existing NNE verification tools [11][12][13]39]. Thus, in this paper, we focus on post-training quantization.…”

“…Indeed, specific inputs may exist for which a network's performance degrades significantly [5,10]. Consequently, the only way to guarantee accuracy for a QNN is reformulating the problem under the notion of equivalence checking (EC) [11][12][13]. This property states that two NN are equivalent when they produce similar outputs for inputs in a given domain [12,13].…”