A classical consequence of Carleman’s condition is that polynomials are dense in L2(µ), but qualitative density does not quantify the degree needed for approximation over general noncompact measures. We give a basis-free Fourier-analytic framework in which orthogonality of the degree-D residual forces a zero of order D in its transformed residual, and analyticity of the moment generating function turns that zero into explicit approximation rates. In the two regimes used in this proceedings version, this yields superexponential low-frequency decay under strictly sub-exponential inputs and tanh(cΩ)D decay under sub-exponential inputs. These two formulas are concrete special cases of a broader quantitative Denjoy–Carleman principle under Carleman’s condition, whose full logarithmic-integral form is deferred to the full version. As an application, we show that Gaussian smoothing, intrinsic-dimension reduction, and low-degree polynomial regression together give low-degree approximation guarantees for smoothed low-intrinsic-dimensional targets. This lets us solve the sub-exponential case of smoothed agnostic learning left open by Chandrasekaran, Klivans, Kontonis, Meka, and Stavropoulos, while removing the Gaussian surface area assumption in the strictly sub-exponential setting.

This paper aims to enhance the performance of Vehicular Platooning (VP) systems integrated with Wireless Federated Learning (WFL). In highly dynamic environments, vehicular platoons experience frequent communication changes and resource constraints, which significantly affect information exchange and learning model synchronization. To address these challenges, we first formulate WFL in VP as a joint optimization problem that simultaneously considers Age of Information (AoI) and Federated Learning Model Drift (FLMD) to ensure timely and accurate control. Through theoretical analysis, we examine the impact of FLMD on convergence performance and develop a two-stage Resource-Aware Control framEwork (RACE). The first stage employs a Lagrangian dual decomposition method for resource configuration, while the second stage implements a multi-agent deep reinforcement learning approach for vehicle selection. The approach integrates Multi-Head Self-Attention and Long Short-Term Memory networks to capture spatiotemporal correlations in communication states. Experimental results demonstrate that, compared to baseline methods, the proposed framework improves AoI optimization by up to 45%, accelerates learning convergence, and adapts more effectively to dynamic VP environments on the AI4MARS dataset.

Brain tumor segmentation from low-quality MRI scans poses significant challenges, particularly in sub-Saharan Africa, where the scans frequently suffer from low resolution and artifacts. Such degradations introduce substantial domain shifts that hinder the effectiveness of existing test-time adaptation (TTA) methods, largely due to catastrophic forgetting and the unreliability of pseudo-labels. In response, we introduce DRTTA, a dynamic and robust framework designed for effective test-time adaptation. This method maintains essential knowledge from the source domain by freezing certain parameters and utilizing adaptive BatchNorm, allowing for successful alignment with the target domain. During inference, DR-TTA employs a learnable augmentation strategy that is optimized to simulate distortions specific to the target domain. Additionally, a hybrid loss function incorporating geometric constraints is used to filter out unreliable pseudo-labels, thus stabilizing the training process. Our extensive experiments on the BraTS-SSA and BraTS-SIM datasets demonstrate that DR-TTA significantly surpasses existing state-of-the-art methods across key performance metrics. This advancement provides a viable solution for deploying brain tumor segmentation technology in real-world scenarios, particularly within resource-limited environments. Our source code is available at https://github.com/baiyou1234/DR-TTA.

In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal statistical-computational tradeoff in learning Gaussian single-index models? Prior research has shown that any polynomial-time algorithm under the statistical query (SQ) framework requires $\Omega(d^{s^\star/2}\lor d)$ samples, where $s^\star$ is the generative exponent representing the intrinsic difficulty of learning the underlying model. However, it remains unknown whether neural networks can achieve this sample complexity. Inspired by prior techniques such as label transformation and landscape smoothing for learning single-index models, we propose a unified gradient-based algorithm for training a two-layer neural network in polynomial time. Our method is adaptable to a variety of loss and activation functions, covering a broad class of existing approaches. We show that our algorithm learns a feature representation that strongly aligns with the unknown signal $\theta^\star$, with sample complexity $\tilde O (d^{s^\star/2} \lor d)$, matching the SQ lower bound up to a polylogarithmic factor for all generative exponents $s^\star\geq 1$. Furthermore, we extend our approach to the setting where $\theta^\star$ is $k$-sparse for $k = o(\sqrt{d})$ by introducing a novel weight perturbation technique that leverages the sparsity structure. We derive a corresponding SQ lower bound of order $\tilde\Omega(k^{s^\star})$, matched by our method up to a polylogarithmic factor. Our framework, especially the weight perturbation technique, is of independent interest, and suggests potential gradient-based solutions to other problems such as sparse tensor PCA.

Reconfigurable Intelligent Surface (RIS)-assisted uncrewed Aerial Vehicle (UAV) communications have been realized as essential to space-air-group system integration in the 6 G technology landscape. Trajectory planning plays a crucial role in RIS-assisted UAV communications to face the challenges of UAV’s limited power capacities and dynamic wireless channels. Existing solutions assume complete channel state information, focus on single-rotor UAVs, and rely heavily on time-consuming training processes for machine learning; thus, they lack applicability to deal with highly dynamic real-world scenarios. To fill these research gaps, we aim to characterize RIS-assisted UAV communications and design responsive and accurate UAV trajectory planning algorithms in this paper. We first develop a communication model with incomplete information and an energy consumption model for quadrotor UAVs. We then formulate UAV trajectory planning as an optimization problem to minimize UAV’s energy consumption while maintaining communication throughput. To solve this problem, we design an acceleration framework,FedX, for reinforcement learning (RL) solvers and present two fast trajectory planning algorithms, FedSAC and FedPPO, as instantiations of theFedXframework. Our evaluation results indicate that the proposed framework is effective and efficient–more than 3 times faster with 5 agents and 7 times faster with 10 agents than standard RL algorithms, making it suitable for using RL solvers within wireless networks and mobile computing environments. We also discuss and identify the pros and cons of our proposed framework.

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by SGD with large learning rates turns out to be beneficial to the generalization of the NN, potentially improving over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon “benign oscillation”. Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small $\ell_2$-norm and appear in each data point; (ii) strong features which have a large $\ell_2$-norm but appear only in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but make little progress in learning the weak features. Consequently, when it comes to the new testing data points that consist of only weak features, the NN trained by oscillating SGD with a large learning rate can still make correct predictions, while the NN trained by SGD with a small learning rate could not. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our findings on the phenomenon of “benign oscillation”.