Mingfei Sun

Yingxiao Huo, Satya Prakash Dash, Radu Stoican et al.

Natural gradients have long been studied in deep reinforcement learning due to their fast convergence properties and covariant weight updates. However, computing natural gradients requires inversion of the Fisher Information Matrix (FIM) at each iteration, which is computationally prohibitive in nature. In this paper, we present an efficient and scalable natural policy optimization technique that leverages a rank-1 approximation to full inverse-FIM. We theoretically show that under certain conditions, a rank-1 approximation to inverse-FIM converges faster than policy gradients and, under some conditions, enjoys the same sample complexity as stochastic policy gradient methods. We benchmark our method on a diverse set of environments and show that it achieves superior performance to standard actor-critic and trust-region baselines.

Satya Prakash Dash, Hossein Abdi, Wei Pan et al.

Gradient regularization (GR) has been shown to improve the generalizability of trained models. While Natural Gradient Descent has been shown to accelerate optimization in the initial phase of training, little attention has been paid to how the training dynamics of second-order optimizers can benefit from GR. In this work, we propose Gradient-Regularized Natural Gradients (GRNG), a family of scalable second-order optimizers that integrate explicit gradient regularization with natural gradient updates. Our framework provides two complementary algorithms: a frequentist variant that avoids explicit inversion of the Fisher Information Matrix (FIM) via structured approximations, and a Bayesian variant based on a Regularized-Kalman formulation that eliminates the need for FIM inversion entirely. We establish convergence guarantees for GRNG, showing that gradient regularization improves stability and enables convergence to global minima. Empirically, we demonstrate that GRNG consistently enhances both optimization speed and generalization compared to first-order methods (SGD, AdamW) and second-order baselines (K-FAC, Sophia), with strong results on vision and language benchmarks. Our findings highlight gradient regularization as a principled and practical tool to unlock the robustness of natural gradient methods for large-scale deep learning.

Fei Jiang, Jiyang Xia, Junjie Yu et al.

Quantifying the impacts of air pollution on health and climate relies on key atmospheric particle properties such as toxicity and hygroscopicity. However, these properties typically require complex observational techniques or expensive particle-resolved numerical simulations, limiting the availability of labeled data. We therefore estimate these hard-to-measure particle properties from routinely available observations (e.g., air pollutant concentrations and meteorological conditions). Because routine observations only indirectly reflect particle composition and structure, the mapping from routine observations to particle properties is noisy and input-dependent, yielding a heteroscedastic regression setting. With a limited and costly labeling budget, the central challenge is to select which samples to measure or simulate. While active learning is a natural approach, most acquisition strategies rely on predictive uncertainty. Under heteroscedastic noise, this signal conflates reducible epistemic uncertainty with irreducible aleatoric uncertainty, causing limited budgets to be wasted in noise-dominated regions. To address this challenge, we propose a confidence-aware active learning framework (CAAL) for efficient and robust sample selection in heteroscedastic settings. CAAL consists of two components: a decoupled uncertainty-aware training objective that separately optimises the predictive mean and noise level to stabilise uncertainty estimation, and a confidence-aware acquisition function that dynamically weights epistemic uncertainty using predicted aleatoric uncertainty as a reliability signal. Experiments on particle-resolved numerical simulations and real atmospheric observations show that CAAL consistently outperforms standard AL baselines. The proposed framework provides a practical and general solution for the efficient expansion of high-cost atmospheric particle property databases.

Jinshu Huang, Mingfei Sun, Chunlin Wu

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new mathematical insights into the structure and learning behavior of DNNs. In this work, we establish generalization error bounds for both discrete- and continuous-time residual networks (ResNets) by combining Rademacher complexity, flow maps of dynamical systems, and the convergence behavior of ResNets in the deep-layer limit. The resulting bounds are of order $O(1/\sqrt{S})$ with respect to the number of training samples $S$, and include a structure-dependent negative term, yielding depth-uniform and asymptotic generalization bounds under milder assumptions. These findings provide a unified understanding of generalization across both discrete- and continuous-time ResNets, helping to close the gap in both the order of sample complexity and assumptions between the discrete- and continuous-time settings.