Parameter Estimation of Ringdown Quasinormal Modes with Autoencoder
本文使用自编码器框架解决引力波信号中准正模式参数估计问题，通过训练潜在空间表示单个模式的物理参数，实现波形降噪和参数估计。
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Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks
This work addresses the challenge of improving neural network generalization by analyzing optimization dynamics through the lens of data distribution and parameter structure, with a focus on steering training toward flat minima. Leveraging the Wolkowicz–Styan inequality, the authors derive, for the first time, a closed-form expression for the gradient of the largest eigenvalue of the Hessian of the cross-entropy loss—enabling explicit optimization of its spectral upper bound without numerical approximation. By updating parameters along the steepest descent direction defined by this gradient, the method effectively compresses the Hessian eigenvalue spectrum in three-layer networks, thereby avoiding sharp minima and saddle points. This approach guides convergence toward flatter minima that exhibit superior generalization, offering a novel theoretical and algorithmic pathway for understanding and promoting flatness in deep learning optimization.
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Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression
This study addresses the lack of a priori convergence assessment for the Difference-of-Convex Algorithm (DCA) in Gaussian radial basis function kernel support vector regression (RBF-SVR). By exploiting the analytical structure of the RBF kernel, the authors construct an explicit DC decomposition and, for the first time, derive closed-form expressions for the lower bound μ of the strong convexity parameter and the upper bound L of the gradient Lipschitz constant of the DC components. They further identify the scalar Cαρ—determined by the hyperparameters C and γ—as the key quantity governing DCA’s convergence rate and dependence on initialization. Numerical experiments on six benchmark functions confirm that Cαρ alone effectively predicts DCA’s convergence behavior both before and after training, establishing the first analytical link between RBF-SVR hyperparameters and DCA convergence.
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Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks
Existing theoretical frameworks struggle to characterize the largest eigenvalue of the Hessian of the loss function in smooth nonlinear multilayer neural networks, hindering a deeper understanding of the relationship between loss sharpness and generalization. This work addresses this gap by deriving, for the first time, a closed-form upper bound on the largest Hessian eigenvalue for deep networks employing cross-entropy loss and smooth activation functions—extending beyond prior results limited to linear or ReLU networks. The bound is established through a combination of the Wolkowicz–Styan inequality, second-order Taylor expansion, and spectral analysis, and it explicitly depends on network parameters, hidden layer dimensions, and the orthogonality of training samples. Notably, it requires no numerical computation, thereby offering a new analytical tool for theoretically studying loss sharpness.
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Generating High-Level Test Cases from Requirements using LLM: An Industry Study
Existing advanced test case generation approaches heavily rely on manual effort or customized RAG systems, suffering from poor generalizability and high construction costs. Method: This paper proposes a pure prompt-engineering–driven large language model (LLM) approach that automatically generates functional-level natural language test cases directly from requirements documents—without retrieval-augmented generation (RAG). It first guides the LLM to identify appropriate test design techniques for the given requirements, then leverages this selection to generate concrete test cases, enabling end-to-end zero-shot inference. Contribution/Results: The method significantly improves cross-domain generalization and industrial deployability. On the Bluetooth and Mozilla datasets, it achieves macro-recall scores of 0.81 and 0.37, respectively, demonstrating both effectiveness and practical potential. To our knowledge, this is the first work achieving high-level test case automation solely through structured prompting—without any retrieval augmentation.
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Parameter Estimation of Ringdown Quasinormal Modes with Autoencoder
本文使用自编码器框架解决引力波信号中准正模式参数估计问题，通过训练潜在空间表示单个模式的物理参数，实现波形降噪和参数估计。
0 citationsRead paper
Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks
This work addresses the challenge of improving neural network generalization by analyzing optimization dynamics through the lens of data distribution and parameter structure, with a focus on steering training toward flat minima. Leveraging the Wolkowicz–Styan inequality, the authors derive, for the first time, a closed-form expression for the gradient of the largest eigenvalue of the Hessian of the cross-entropy loss—enabling explicit optimization of its spectral upper bound without numerical approximation. By updating parameters along the steepest descent direction defined by this gradient, the method effectively compresses the Hessian eigenvalue spectrum in three-layer networks, thereby avoiding sharp minima and saddle points. This approach guides convergence toward flatter minima that exhibit superior generalization, offering a novel theoretical and algorithmic pathway for understanding and promoting flatness in deep learning optimization.
0 citationsRead paper
Analytical Evaluation of DCA Convergence Properties for Minimizing Prediction Functions of Gaussian RBF Support Vector Regression
This study addresses the lack of a priori convergence assessment for the Difference-of-Convex Algorithm (DCA) in Gaussian radial basis function kernel support vector regression (RBF-SVR). By exploiting the analytical structure of the RBF kernel, the authors construct an explicit DC decomposition and, for the first time, derive closed-form expressions for the lower bound μ of the strong convexity parameter and the upper bound L of the gradient Lipschitz constant of the DC components. They further identify the scalar Cαρ—determined by the hyperparameters C and γ—as the key quantity governing DCA’s convergence rate and dependence on initialization. Numerical experiments on six benchmark functions confirm that Cαρ alone effectively predicts DCA’s convergence behavior both before and after training, establishing the first analytical link between RBF-SVR hyperparameters and DCA convergence.
0 citationsRead paper
Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks
Existing theoretical frameworks struggle to characterize the largest eigenvalue of the Hessian of the loss function in smooth nonlinear multilayer neural networks, hindering a deeper understanding of the relationship between loss sharpness and generalization. This work addresses this gap by deriving, for the first time, a closed-form upper bound on the largest Hessian eigenvalue for deep networks employing cross-entropy loss and smooth activation functions—extending beyond prior results limited to linear or ReLU networks. The bound is established through a combination of the Wolkowicz–Styan inequality, second-order Taylor expansion, and spectral analysis, and it explicitly depends on network parameters, hidden layer dimensions, and the orthogonality of training samples. Notably, it requires no numerical computation, thereby offering a new analytical tool for theoretically studying loss sharpness.
0 citationsRead paper
Generating High-Level Test Cases from Requirements using LLM: An Industry Study
Existing advanced test case generation approaches heavily rely on manual effort or customized RAG systems, suffering from poor generalizability and high construction costs. Method: This paper proposes a pure prompt-engineering–driven large language model (LLM) approach that automatically generates functional-level natural language test cases directly from requirements documents—without retrieval-augmented generation (RAG). It first guides the LLM to identify appropriate test design techniques for the given requirements, then leverages this selection to generate concrete test cases, enabling end-to-end zero-shot inference. Contribution/Results: The method significantly improves cross-domain generalization and industrial deployability. On the Bluetooth and Mozilla datasets, it achieves macro-recall scores of 0.81 and 0.37, respectively, demonstrating both effectiveness and practical potential. To our knowledge, this is the first work achieving high-level test case automation solely through structured prompting—without any retrieval augmentation.
0 citationsRead paper