arXiv subjects

Yudong Wei

Publications and source records attributed to Yudong Wei.

6 recordsLinked to original sources

arXiv2026

Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics

Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization. We propose a unified framework, termed direction-magnitude decomposition (DMD), that decomposes the optimization variable to improve optimization efficiency even when the target rank is unknown. We develop two DMD-based approaches and establish their theoretical advantages on the canonical problem of matrix factorization. The first, overparameterized DMD, uses a rank $r$ larger than necessary and enjoys faster convergence as $r$ increases. The second, recursive DMD, is motivated by the incremental eigenpair learning, or saddle-to-saddle, behavior of overparameterized DMD. It achieves lower memory and computational costs, complementing overparameterized DMD. Both approaches are exponentially faster than gradient descent applied to the BM formulation. Numerical experiments on matrix factorization, sensing, and completion corroborate our theoretical findings and demonstrate the practical effectiveness of DMD.

math.OC↗

arXiv2026

Generalized Composed Alternating Relaxed Projection Algorithm for Two-Set Feasibility Problem

We study the two-set feasibility problem of finding a point in the intersection $X\cap Y$ of closed convex sets in a Hilbert space. We propose a generalized composed alternating relaxed projection algorithm (gCARPA) that blends Douglas-Rachford-type and projection-reflection-type dynamics via an outer averaging step $\mu$ and an internal relaxation $(\gamma,\theta,\eta)$. The algorithm contains several classical projection methods as special cases. We also introduce its non-stationary variant, in which $(\gamma_k,\theta_k,\eta_k)$ vary over iterations, and establish its convergence. For the subspace feasibility model, we derive an explicit spectral characterization via principal-angle block decompositions, yielding computable subdominant-eigenvalue factors and a minimax parameter-selection recipe in a symmetric regime that targets critical damping on principal-angle planes. Numerical experiments illustrate that the generalized relaxation and its non-stationary tuning can improve or match baseline methods in problem-dependent regimes.

math.OC↗

arXiv2026

Experimental engineering of Floquet topological phases in a one-dimensional optical lattice

Periodic driving enables realization of topological phases without static counterparts. We experimentally realize and detect a one-dimensional anomalous Floquet topological phase in an optical lattice, using multi-frequency control to manipulate the relative sign structure of the gap windings $(W_0,W_\pi)$ associated with the $0$ and $\pi$ quasienergy gaps. We develop a lattice-depth modulation scheme that induces staggered nearest-neighbor $s$-$p$ orbital couplings and realize a minimal nontrivial Floquet topology under single-tone driving. Introducing a second tone, its relative phase controls the effective coupling signs in the $0$ and $\pi$ gaps, thereby tuning the corresponding windings to add and produce a high-winding phase or to cancel while retaining nontrivial gap indices. We read out $(W_0,W_\pi)$ with a band-inversion-surface (BIS)-resolved Ramsey protocol assisted by lattice-position shaking, which measures relative Floquet phases on the BISs. Controlled quenches further confirm phase-dependent band modifications even at quasimomenta far from resonance. These results establish multi-frequency control with a tunable relative phase as a quantitative route to engineering anomalous Floquet topology, and demonstrate phase-coherent coexistence of distinct drive modalities.

cond-mat.quant-gas↗

arXiv2025

A Radio-Frequency Emitter Design for the Low-Frequency Regime in Atomic Experiments

Radio-frequency (RF) control is a key technique in cold atom experiments. We present a compact and efficient RF circuit based on a capacitive transformer network, where a low-frequency coil operating up to 30MHz serves as both an intrinsic inductor and a power-sharing element. The design enables high current delivery and flexible impedance matching across a wide frequency range. We integrate both broadband and narrowband RF networks into a unified configuration that overcomes the geometric constraints imposed by the metallic chamber. In evaporative cooling, the broadband network allows a reduction of the applied RF input power from 14.7dBW to -3.5dBW, owing to its non-zero coil current even at ultra-low frequencies. This feature enables the Bose-Fermi mixture to be cooled below 10μK. In a Landau-Zener protocol, the coil driven by the narrowband network transfers 80% of rubidium atoms from |F = 2,mF = 2> to |2,-2> in 1 millisecond, achieving a Rabi frequency of approximately 9 kHz at an input power of 0.1dBW.

physics.atom-ph↗

arXiv2025

On the Benefits of Weight Normalization for Overparameterized Matrix Sensing

While normalization techniques are widely used in deep learning, their theoretical understanding remains relatively limited. In this work, we establish the benefits of (generalized) weight normalization (WN) applied to the overparameterized matrix sensing problem. We prove that WN with Riemannian optimization achieves linear convergence, yielding an exponential speedup over standard methods that do not use WN. Our analysis further demonstrates that both iteration and sample complexity improve polynomially as the level of overparameterization increases. To the best of our knowledge, this work provides the first characterization of how WN leverages overparameterization for faster convergence in matrix sensing.

cs.LG↗

arXiv2025

The fundamental localization phases in quasiperiodic systems: A unified framework and exact results

The disordered quantum systems host three classes of quantum states, the extended, localized, and critical, which bring up seven distinct fundamental phases in nature: three pure phases and four coexisting ones with mobility edges, yet a unified theory built on universal mechanism and full realization of all these phases has not been developed. Here we propose a unified framework based on a spinful quasiperiodic (QP) system which realizes all the fundamental localization phases, with the exact and universal results being obtained for their characterization. First, we show that the pure phases are obtained when the chiral(-like) symmetry preserves in the proposed spinful QP model, giving a criterion for emergence of the pure phases and otherwise the coexisting ones. Further, we uncover a novel mechanism for the critical states that their emergence is protected by the generalized incommensurate matrix element zeros in the spinful QP model, which considerably broadens rigorous realizations of the exotic critical states. We then show criteria of exact solvability for the present spinful QP system, with which we construct various exactly solvable models for all distinct localization phases. In particular, we propose two novel models, dubbed spin-selective QP lattice model and QP optical Raman lattice model, to achieve all basic types of mobility edges and all the seven fundamental phases of Anderson localization physics, respectively. The experimental scheme is proposed and studied in detail to realize these models with high feasibility. This study establishes a complete and profound theoretical framework which enables an in-depth exploration of the broad classes of all fundamental localization phenomena in QP systems, and offers key insights for constructing their exactly solvable models with experimental feasibility.

cond-mat.dis-nn↗