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Out of the Shadows: Exploring a Latent Space for Neural Network Verification

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Neural Network VerificationZonotopeSet-Based ComputingLatent SpaceFormal Methods
Abstract:

Neural networks are ubiquitous. However, they are often sensitive to small input changes. Hence, to prevent unexpected behavior in safety-critical applications, their formal verification -- a notoriously hard problem -- is necessary. Many state-of-the-art verification algorithms use reachability analysis or abstract interpretation to enclose the set of possible outputs of a neural network. Often, the verification is inconclusive due to the conservatism of the enclosure. To address this problem, we propose a novel specification-driven input refinement procedure, i.e., we iteratively enclose the preimage of a neural network for all unsafe outputs to reduce the set of possible inputs to only enclose the unsafe ones. For that, we transfer output specifications to the input space by exploiting a latent space, which is an artifact of the propagation of a projection-based set representation through a neural network. A projection-based set representation, e.g., a zonotope, is a "shadow" of a higher-dimensional set -- a latent space -- that does not change during a set propagation through a neural network. Hence, the input set and the output enclosure are "shadows" of the same latent space that we can use to transfer constraints. We present an efficient verification tool for neural networks that uses our iterative refinement to significantly reduce the number of subproblems in a branch-and-bound procedure. Using zonotopes as a set representation, unlike many other state-of-the-art approaches, our approach can be realized by only using matrix operations, which enables a significant speed-up through efficient GPU acceleration. We demonstrate that our tool achieves competitive performance compared to the top-ranking tools of the last neural network verification competition (VNN-COMP'24).

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Overview

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
0
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: formal verification of neural networks. The field has organized itself around several major branches that reflect both algorithmic and application-oriented concerns. Verification Algorithms and Techniques encompasses a wide range of methods—from reachability analysis and abstract interpretation to branch-and-bound approaches and set-based propagation—each trading off precision and scalability in different ways. Network Architectures and Representations addresses how different model structures (convolutional, recurrent, quantized, or spiking networks) demand specialized verification strategies, while Verification Properties and Specifications focuses on the kinds of guarantees one seeks (robustness, fairness, safety). Application Domains highlights deployment contexts such as autonomous systems and cyber-physical systems, and Tools and Frameworks catalogs the software ecosystems that make verification practical. Additional branches cover hardware verification, theoretical complexity and limits, mathematical foundations of deep learning, and surveys that synthesize these diverse threads. Within the algorithmic landscape, a particularly active line of work centers on set-based propagation and abstract interpretation methods, which aim to efficiently over-approximate network behavior while maintaining useful precision. Shadows Latent Space[0] sits squarely in this cluster, exploring how latent-space representations can be leveraged for tighter reachability bounds. Nearby efforts such as Quantized Network Verification[13] and QVIP ILP Verification[10] tackle similar propagation challenges but focus on discrete or integer-linear formulations to handle quantized architectures. In contrast, works like Branch Bound Nonlinearities[15] emphasize search-based refinement to manage complex activation functions. A recurring theme across these studies is the tension between completeness and computational cost: some approaches prioritize sound over-approximations that scale to larger networks, while others pursue exact or near-exact bounds at the expense of runtime. Shadows Latent Space[0] contributes to this dialogue by proposing novel abstractions in the latent domain, offering a middle ground that balances expressiveness with tractability in set-based verification.

Claimed Contributions

Novel specification-driven input refinement procedure using latent space

The authors introduce an iterative refinement method that exploits a latent space arising from projection-based set representations (e.g., zonotopes) to transfer output specifications back to the input space. This allows them to iteratively constrain the input set to enclose only unsafe inputs, thereby reducing the number of subproblems in branch-and-bound verification.

0 retrieved papers
Efficient GPU-accelerated verification algorithm using matrix operations

The authors develop a verification tool that relies exclusively on matrix operations, enabling efficient GPU acceleration and batch-wise computations. This design choice significantly speeds up the verification process compared to approaches that cannot leverage GPU parallelism.

0 retrieved papers
Extensive evaluation and ablation studies on VNN-COMP'24 benchmarks

The authors provide a comprehensive empirical evaluation comparing their tool against top-ranking tools from VNN-COMP'24 and perform ablation studies to validate their design decisions, including the impact of input refinement, GPU acceleration, and falsification methods.

0 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Novel specification-driven input refinement procedure using latent space

The authors introduce an iterative refinement method that exploits a latent space arising from projection-based set representations (e.g., zonotopes) to transfer output specifications back to the input space. This allows them to iteratively constrain the input set to enclose only unsafe inputs, thereby reducing the number of subproblems in branch-and-bound verification.

Contribution

Efficient GPU-accelerated verification algorithm using matrix operations

The authors develop a verification tool that relies exclusively on matrix operations, enabling efficient GPU acceleration and batch-wise computations. This design choice significantly speeds up the verification process compared to approaches that cannot leverage GPU parallelism.

Contribution

Extensive evaluation and ablation studies on VNN-COMP'24 benchmarks

The authors provide a comprehensive empirical evaluation comparing their tool against top-ranking tools from VNN-COMP'24 and perform ablation studies to validate their design decisions, including the impact of input refinement, GPU acceleration, and falsification methods.

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