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Traditional training algorithms for Gumbel Softmax Variational Autoencoders (GS-VAEs) typically rely on an annealing scheme that gradually reduces the Softmax temperature τ according to a given function. This approach can lead to suboptimal results. To improve the performance, we propose a parallel framework for GS-VAEs, which embraces dual latent layers and multiple sub-models with diverse temperature strategies. Instead of relying on a fixed function for adjusting τ, our training algorithm uses loss difference as performance feedback to dynamically update each sub-model’s temperature τ, which is inspired by the need to balance exploration and exploitation in learning. By combining diversity in temperature strategies with the performance-based tuning method, our design helps prevent sub-models from becoming trapped in local optima and finds the GS-VAE model that best fits the given dataset. In experiments using four classic image datasets, our model significantly surpasses a standard GS-VAE that employs a temperature annealing scheme across multiple tasks, including data reconstruction, generalization capabilities, anomaly detection, and adversarial robustness. Our implementation is publicly available at https://github.com/wxzg7045/Gumbel-Softmax-VAE-2024/tree/main. 

Deep Neural Networks (DNNs) have become a popular instrument for solving various real-world problems. DNNs’ sophisticated structure allows them to learn complex representations and features. For this reason, Binary Neural Networks (BNNs) are widely used on edge devices, such as microcomputers. However, architecture specifics and floating-point number usage result in an increased computational operations complexity. Like other DNNs, BNNs are vulnerable to adversarial attacks; even a small perturbation to the input set may lead to an errant output. Unfortunately, only a few approaches have been proposed for verifying BNNs.This paper proposes an approach to verify BNNs on continuous input space using star reachability analysis. Our approach can compute both exact and overapproximate reachable sets of BNNs with Sign activation functions and use them for verification. The proposed approach is also efficient in constructing a complete set of counterexamples in case a network is unsafe. We implemented our approach in NNV, a neural network verification tool for DNNs and learning-enabled Cyber-Physical Systems. The experimental results show that our star-based approach is less conservative, more efficient, and scalable than the recent SMT-based method implemented in Marabou. We also provide a comparison with a quantization-based tool EEVBNN.