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arXiv · 2510.17622

Just-In-Time Piecewise-Linear Semantics for ReLU-type Networks

Hongyi Duan·Haoyang Liu·Jian'an Zhang·Fengrui Liu·Yiyi Wang
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Abstract

We present a JIT PL semantics for ReLU-type networks that compiles models into a guarded CPWL transducer with shared guards. The system adds hyperplanes only when operands are affine on the current cell, maintains global lower/upper envelopes, and uses a budgeted branch-and-bound. We obtain anytime soundness, exactness on fully refined cells, monotone progress, guard-linear complexity (avoiding global $\binom{k}{2}$), dominance pruning, and decidability under finite refinement. The shared carrier supports region extraction, decision complexes, Jacobians, exact/certified Lipschitz, LP/SOCP robustness, and maximal causal influence. A minimal prototype returns certificates or counterexamples with cost proportional to visited subdomains.

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Hongyi Duan, Haoyang Liu, Jian'an Zhang, Fengrui Liu, Yiyi Wang. 2025-10-20. Just-In-Time Piecewise-Linear Semantics for ReLU-type Networks. https://arxiv.org/abs/2510.17622

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