Just-In-Time Piecewise-Linear Semantics for ReLU-type Networks
Hongyi Duan, Haoyang Liu, Jian'an Zhang, Fengrui Liu, Yiyi Wang
TL;DR
This paper introduces a Just-In-Time piecewise-linear semantics for ReLU networks, enabling efficient, exact, and certified analysis through a guarded CPWL transducer with shared guards and advanced pruning techniques.
Contribution
It proposes a novel JIT PL semantics framework that improves efficiency and accuracy in analyzing ReLU networks, supporting various certification and robustness tasks.
Findings
Achieves anytime soundness and exactness on refined cells.
Maintains guard-linear complexity, avoiding quadratic guard growth.
Provides a prototype that returns certificates or counterexamples efficiently.
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 ), 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.
Peer Reviews
Decision·Submitted to ICLR 2026
- The problem formulation is clear. Unrolling ReLU layer-by-layer results in exponentially growing computational complexity. This paper proposed a principled approach with formal guarantees. - Guard-sharing and unified representation are neat contributions. Inserting comparator faces only when needed yields better computational complexity. Having a single object support multiple verification tasks (Lipschitz, robustness) through a common LP/SOCP interface could meaningfully simplify verificatio
- The paper is hard to read. The main text still feels like navigating a theorem catalog rather than a coherent story. The paper is dense with theorem families and heavy notations. It lacks descriptions of theoretical results and their role in the proposed method. Table 1 helps a bit, but a major streamlining pass is needed. - Results AF-1 through AF-5 appear to be standard CPWL preliminaries (closure, continuity, differentiability). The paper should explicitly delineate which theoretical resul
1. Unified Theoretical Framework: The primary strength is the unification of disparate geometric and formal tasks into a single symbolic carrier. Instead of specialized algorithms for Lipschitz estimation vs. robustness verification, the JIT-SWT provides a common substrate where these become differing objectives on the same refinement engine. 2. Anytime Guarantees & Monotonicity: The proofs for sound anytime envelopes (DYN-1) and monotonic progress without regression (DYN-3) are theoretically sa
1. Scalability Concerns: While "JIT" mitigates immediate exponential explosion, the reliance on solving LPs/SOCPs in the inner loop of the Branch-and-Bound driver 8 represents a significant computational bottleneck. The experimental validation is limited to very small-scale problems (MNIST FFNs, subsets of CIFAR-10 with tiny CNNs, Karate Club GNNs). There is little evidence this approach can scale to standard Deep RL policy networks (e.g., ResNet-50 size or Transformer-based policies), where the
Originality: The formalization seem novel and the idea of bridging algebraic formalisms and neural verification seems new. Quality: Comprehensive theoretical framework with proofs of soundness, decidability, and budgeted complexity bounds.
Accessibility: The main text is quite dense and does not provide enough background, motivation, or illustrations for several of the definitions and proofs in the paper. A brief paragraph before each definition or at the beginning of each subsection providing an intuition on why the concepts are needed, or how they work at an intuitive level would be appreciated. Scalability: Experiments are on small networks and restricted settings. A clearer discussion on when this can be applied and when it c
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Taxonomy
TopicsFormal Methods in Verification · Interconnection Networks and Systems · Embedded Systems Design Techniques