Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this study, we incorporate a chaotic component to GD in a controlled manner, and introduce \emph{multiscale perturbed GD} (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed L\'{e}vy-stable process.

Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice.

Diffusion models have shown remarkable flexibility for solving inverse problems without task-specific retraining. However, existing approaches such as Manifold Preserving Guided Diffusion (MPGD) apply only a single gradient update per denoising step, limiting restoration fidelity and robustness, especially in embedded or out-of-distribution settings. In this work, we introduce a multistep optimization strategy within each denoising timestep, significantly enhancing image quality, perceptual accuracy, and generalization. Our experiments on super-resolution and Gaussian deblurring demonstrate that increasing the number of gradient updates per step improves LPIPS and PSNR with minimal latency overhead. Notably, we validate this approach on a Jetson Orin Nano using degraded ImageNet and a UAV dataset, showing that MPGD, originally trained on face datasets, generalizes effectively to natural and aerial scenes. Our findings highlight MPGD's potential as a lightweight, plug-and-play restoration module for real-time visual perception in embodied AI agents such as drones and mobile robots.

Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this study, we incorporate a chaotic component to GD in a controlled manner, and introduce \emph{multiscale perturbed GD} (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed L\'{e}vy-stable process. Empirical results are provided to demonstrate the advantages of MPGD.

Exploding predictive AI has enabled fast yet effective evaluation and decision-making in modern chip physical design flows. State-of-the-art frameworks typically include the objective of minimizing the mean square error (MSE) between the prediction and the ground truth. We argue the averaging effect of MSE induces limitations in both model training and deployment, and good MSE behavior does not guarantee the capability of these models to assist physical design flows which are likely sabotaged due to a small portion of prediction error. To address this, we propose mini-pixel batch gradient descent (MPGD), a plug-and-play optimization algorithm that takes the most informative entries into consideration, offering probably faster and better convergence. Experiments on representative benchmark suits show the significant benefits of MPGD on various physical design prediction tasks using CNN or Graph-based models.

Cross-silo federated learning (FL) is a typical FL that enables organizations(e.g., financial or medical entities) to train global models on isolated data. Reasonable incentive is key to encouraging organizations to contribute data. However, existing works on incentivizing cross-silo FL lack consideration of the environmental dynamics (e.g., precision of the trained global model and data owned by uncertain clients during the training processes). Moreover, most of them assume that organizations share private information, which is unrealistic. To overcome these limitations, we propose a novel adaptive mechanism for cross-silo FL, towards incentivizing organizations to contribute data to maximize their long-term payoffs in a real dynamic training environment. The mechanism is based on multi-agent reinforcement learning, which learns near-optimal data contribution strategy from the history of potential games without organizations' private information. Experiments demonstrate that our mechanism achieves adaptive incentive and effectively improves the long-term payoffs for organizations.

Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this study, we incorporate a chaotic component to GD in a controlled manner, and introduce multiscale perturbed GD (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed L\'evy-stable process. (ii) By making connections to recently developed generalization bounds for heavy-tailed processes, we derive a generalization bound for the limiting SDE and relate the worst-case generalization error over the trajectories of the process to the parameters of MPGD. (iii) We analyze the implicit regularization effect brought by the dynamical regularization and show that, in the weak perturbation regime, MPGD introduces terms that penalize the Hessian of the loss function. Empirical results are provided to demonstrate the advantages of MPGD.