Despite the popularity of Adam optimizer in practice, most theoretical analyses study SGD as a proxy and little is known about how the solutions found by Adam differ. In this paper, we show that Adam reduces a specific form of sharpness measure shaped by its adaptive updates, leading to qualitatively different solutions from SGD. When the training loss is small, Adam wanders around the manifold of minimizers and takes semi-gradients to minimize this sharpness measure in an adaptive manner, a behavior we rigorously characterize via a continuous-time approximation using stochastic differential equations. We further illustrate how this behavior differs from that of SGD in a well-studied setting: when training overparameterized models with label noise, SGD has been shown to minimize the trace of the Hessian matrix, $\text{tr}(\textbf{H})$, whereas we prove that Adam minimizes $\text{tr}(\text{diag}(\textbf{H})^{1/2})$ instead. In solving sparse linear regression with diagonal linear networks, Adam provably achieves better sparsity and generalization than SGD due to this difference. Finally, we note that our proof framework applies not only to Adam but also to a broad class of adaptive gradient methods, including but not limited to RMSProp, Adam-mini, and Adalayer. This provides a unified perspective for analyzing how adaptive optimizers reduce sharpness and may offer insights for future optimizer design.

Given 2D point correspondences between an image pair, inferring the camera motion is a fundamental issue in the computer vision community. The existing works generally set out from the epipolar constraint and estimate the essential matrix, which is not optimal in the maximum likelihood (ML) sense. In this paper, we dive into the original measurement model with respect to the rotation matrix and normalized translation vector and formulate the ML problem. We then propose an optimal two-step algorithm to solve it: In the first step, we estimate the variance of measurement noises and devise a consistent estimator based on bias elimination; In the second step, we execute a one-step Gauss-Newton iteration on manifold to refine the consistent estimator. We prove that the proposed estimator achieves the same asymptotic statistical properties as the ML estimator: The first is consistency, i.e., the estimator converges to the ground truth as the point number increases; The second is asymptotic efficiency, i.e., the mean squared error of the estimator converges to the theoretical lower bound - Cramer-Rao bound. In addition, we show that our algorithm has linear time complexity. These appealing characteristics endow our estimator with a great advantage in the case of dense point correspondences. Experiments on both synthetic data and real images demonstrate that when the point number reaches the order of hundreds, our estimator outperforms the state-of-the-art ones in terms of estimation accuracy and CPU time.

Wireless short-hop communication is a crucial solution for information transmission between logging while drilling and measurement while drilling. It is important for closed-loop control in geosteering drilling. Compared with wired transmission, wireless short-hop communication offers a cost-effective and stable alternative. It furthermore reduces drilling risks and improves efficiency. Current research primarily concentrates on magnetic dipole antennas, where resistivity stands as the only continuous variable under investigation, and consideration of other parameters may be limited. It lacks complex models and fails to account for factors such as borehole mud and antenna slots. This paper utilizes the Finite Element Method to examine the transmitting and receiving characteristics of electric dipole and magnetic dipole antennas and investigate the effects of transmission conditions and instrument structure on the signal. Experimental validation in a water tank confirmed the reliability and practicality of the numerical simulation results. It suggests that using a coil number between 150 and 200 turns with a frequency of 5 to 8 kHz for both antenna structures in oil-based mud can achieve transmission distances of over 15 m. The antenna slot has minimal impact on the signal. Design considerations should prioritize overall structural stability and mechanical strength. These findings contribute valuable insights to the design and optimization of the instrument.

State estimation is an essential part of autonomous systems. Integrating the Ultra-Wideband (UWB) technique has been shown to correct the long-term estimation drift and bypass the complexity of loop closure detection. However, few works on robotics treat UWB as a stand-alone state estimation solution. The primary purpose of this work is to investigate planar pose estimation using only UWB range measurements. We prove the excellent property of a two-step scheme, which says we can refine a consistent estimator to be asymptotically efficient by one step of Gauss-Newton iteration. Grounded on this result, we design the GN-ULS estimator, which reduces the computation time significantly compared to previous methods and presents the possibility of using only UWB for real-time state estimation.

High-speed railway (HSR) has been widely introduced to meet the increasing demand for passenger rail travel. While it provides more and more conveniences to the people, the huge cost of the HSR has laid big burden on the government finance. Reducing the cost of HSR has been necessary and urgent. Optimizing the arrangement of the base stations (BS) by improving the prediction of the communication link is one of the most effective methods, which could reduce the number of the BSs to a reasonable number. However, it requires a carefully developed propagation model, which has been largely neglected before in the research on the HSR. In this paper, we propose a standardized path loss model for HSR channels based on an extensive measurement campaign in 4594 HSR cells of the "Zhengzhou-Xian" HSR line. The measurements are conducted using a practically deployed and operative GSM-Railway (GSM-R) system to reflect the real conditions of the HSR channels. The proposed model is validated by the measurements conducted in another operative railway - "Beijing-Shanghai" HSR line. The results are helpful for the HSR communications system designers to gain a better tool in the system planning, and propagation researchers to assess where the most pressing needs in the modeling of HSR channels lie.