Abstract Formal verification of Semantic Segmentation Networks is challenging due to high-dimensional output spaces and cumulative over-approximation errors in deep architectures. Existing verification methods based on specific Star-set reachability suffer from either exponential state explosion (exact splitting) or excessive conservativeness (interval-based relaxation). In this work, we present ATKVerifier , a verification framework for SSNs operating on an abstract domain named constrained-star (C-star), which captures spatial dependencies within MaxPool receptive fields through explicit predicate constraints. Our framework features: (1) an adaptive top-K lower bound mechanism that dynamically encodes K potential maximizers based on layer depth and interval overlap, balancing precision and computational cost through parameter-free adaptation; (2) an adaptive affine upper bound exploiting linear relationships between top candidates to replace conservative constant bounds; and (3) region-level completeness (RLC), a spatial robustness metric quantifying the integrity of verified contiguous object regions. Experiments on M2NIST with three SSN architectures (16 $$\sim $$ ∼ 24 layers) demonstrate 8 $$\sim $$ ∼ 25% improvement in robust Intersection-over-Union (IoU) over the ImageStar-based NNV baseline, with the improvement scaling with the network’s depth. For the 24-layer architecture, ATKVerifier achieves 59.2% RLC versus 43.8% of NNV, certifying 35.2% more complete semantic objects.

Deep neural networks (DNNs) have become integral to numerous safety-critical applications, necessitating rigorous verification of their trustworthiness. However, the problem of verifying DNNs has high computational complexity, and existing techniques have limited efficiency, insufficient to deal with large-scale network models. To address this challenge, we propose a novel abstraction-refinement verification method that reduces network size while maintaining verification accuracy. Specifically, the method quantifies the similarity between neurons based on various factors such as their interval outputs, and then merges similar neurons to generate a smaller abstract network. In addition, a counterexample-guided refinement process is developed to mitigate the impact of potential spurious counterexamples, so that verification results from the abstract network are applicable to the original network. We have implemented this method as a tool named ARVerifier and integrated it with three state-of-the-art verification tools for evaluation on ACAS Xu and MNIST benchmarks. Experimental results demonstrate that ARVerifier significantly reduces network size and yields verification time reductions by 11.61%, 18.70%, and 12.20% compared to α,β-CROWN, Verinet, and Marabou, respectively. Moreover, ARVerifier exhibits efficiency improvements by 26.64% and 46.87% compared to existing abstraction-refinement methods NARv and CEGAR-NN, respectively.

Abstract With the goal of solving the problem of feature extractors lacking strong supervision training and insufficient time information concerning single‐sequence model learning, a hierarchical sequence memory network with a multi‐level iterative optimisation strategy is proposed for continuous sign language recognition. This method uses the spatial‐temporal fusion convolution network (STFC‐Net) to extract the spatial‐temporal information of RGB and Optical flow video frames to obtain the multi‐modal visual features of a sign language video. Then, in order to enhance the temporal relationships of visual feature maps, the hierarchical memory sequence network is used to capture local utterance features and global context dependencies across time dimensions to obtain sequence features. Finally, the decoder decodes the final sentence sequence. In order to enhance the feature extractor, the authors adopted a multi‐level iterative optimisation strategy to fine‐tune STFC‐Net and the utterance feature extractor. The experimental results on the RWTH‐Phoenix‐Weather multi‐signer 2014 dataset and the Chinese sign language dataset show the effectiveness and superiority of this method.

The finite-iteration tracking for singular coupled systems with packet-dropping learning controllers is discussed in this paper. The singular coupled systems are constructed to describe systems with some algebraic constraints, and iterative learning controllers are then designed to achieve the finite-iteration tracking of singular systems. The definition of the finite-iteration tracking is first proposed and the settling iteration is explicitly calculated. Moreover, the iterative learning controllers are designed to consider the case of packet losses. Simulation results are given to elaborate the correctness of the given theorems.