Hongpeng Zhou

Hongpeng Zhou, Wei Pan

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by designing the Mathematical Operation Network (MathONet) with a deep neural network-like hierarchical structure. Specifically, the MathONet is stacked by several layers of unary operations (e.g., sin, cos, log) and binary operations (e.g., +,-), respectively. An initialized MathONet is typically regarded as a super-graph with a redundant structure, a sub-graph of which can yield the governing equation. We develop a sparse group Bayesian learning algorithm to extract the sub-graph by employing structurally constructed priors over the redundant mathematical operations. By demonstrating the chaotic Lorenz system, Lotka-Volterra system, and Kolmogorov-Petrovsky-Piskunov system, the proposed method can discover the ordinary differential equations (ODEs) and partial differential equations (PDEs) from the observations given limited mathematical operations, without any prior knowledge on possible expressions of the ODEs and PDEs.

Hongpeng Zhou, Chahine Ibrahim, Wei Xing Zheng et al.

This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by marginal likelihood/model evidence approximation and structured group sparsity-inducing priors construction. The identification algorithm is derived as an iterative regularised optimisation procedure that can be solved as efficiently as training typical DNNs. Remarkably, an efficient and recursive Hessian calculation method for each layer of DNNs is developed, turning the intractable training/optimisation process into a tractable one. Furthermore, a practical calculation approach based on the Monte-Carlo integration method is derived to quantify the uncertainty of the parameters and predictions. The effectiveness of the proposed Bayesian approach is demonstrated on several linear and nonlinear system identification benchmarks by achieving good and competitive simulation accuracy. The code to reproduce the experimental results is open-sourced and available online.

Yizheng Sun, Hao Li, Chang Xu et al.

Vision-Language Models (VLMs) are powerful yet computationally intensive for widespread practical deployments. To address such challenge without costly re-training, post-training acceleration techniques like quantization and token reduction are extensively explored. However, current acceleration evaluations primarily target minimal overall performance degradation, overlooking a crucial question: does the accelerated model still give the same answers to the same questions as it did before acceleration? This is vital for stability-centered industrial applications where consistently correct answers for specific, known situations are paramount, such as in AI-based disease diagnosis. We systematically investigate this for accelerated VLMs, testing four leading models (LLaVA-1.5, LLaVA-Next, Qwen2-VL, Qwen2.5-VL) with eight acceleration methods on ten multi-modal benchmarks. Our findings are stark: despite minimal aggregate performance drops, accelerated models changed original answers up to 20% of the time. Critically, up to 6.5% of these changes converted correct answers to incorrect. Input perturbations magnified these inconsistencies, and the trend is confirmed by case studies with the medical VLM LLaVA-Med. This research reveals a significant oversight in VLM acceleration, stressing an urgent need for instance-level stability checks to ensure trustworthy real-world deployment.