arXiv subjects

Yizhou Liu

Publications and source records attributed to Yizhou Liu.

At least 73 records · Page 4Linked to original sources

arXiv2025

Prospects for detecting cosmic filaments in Lyman-alpha emission across redshifts $z=2-5$

The standard $\rm Λ$CDM cosmological model predicts that a large amount of diffuse neutral hydrogen distributes in cosmic filaments, which could be mapped through Lyman-alpha (Ly$α$) emission observations. We use the hydrodynamical simulation Illustris-TNG50 to investigate the evolution of surface brightness and detectability of neutral hydrogen in cosmic filaments across redshifts $z=2-5$. While the HI column density of cosmic filaments decreases with redshift, due to the rising temperature with cosmic time in filaments, the surface brightness of Ly$α$ emission in filaments is brighter at lower redshifts, suggesting that the detection of cosmic filaments is more feasible at lower redshifts. However, most of the Ly$α$ emission from cosmic filaments is around $10^{-21}$ $\rm erg\ s^{-1}cm^{-2}arsec^{-2}$, making it extremely challenging to detect with current observational instruments. We further generate mock images using the Multi-Unit Spectroscopic Explorer (MUSE) spectrograph installed on the Very Large Telescope (VLT) and a MUSE-like spectrograph on the upcoming Extremely Large Telescope (ELT). Our finding indicates that while the VLT can only detect filamentary structures made of dense gas in galactic centers, the ELT is expected to reveal much finer filamentary structures from diffuse neutral hydrogen outside of galaxies. Compared to the VLT, both the number density and the longest length of filaments are greatly boosted with the ELT. Hence the forthcoming ELT is highly promising to provide a clearer view of cosmic filaments in Ly$α$ emission.

astro-ph.GA↗

arXiv2025

Quantum Langevin Dynamics for Optimization

We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms. Specifically, we examine the dynamics of a system coupled with an infinite heat bath. This interaction induces both random quantum noise and a deterministic damping effect to the system, which nudge the system towards a steady state that hovers near the global minimum of objective functions. We theoretically prove the convergence of QLD in convex landscapes, demonstrating that the average energy of the system can approach zero in the low temperature limit with an exponential decay rate correlated with the evolution time. Numerically, we first show the energy dissipation capability of QLD by retracing its origins to spontaneous emission. Furthermore, we conduct detailed discussion of the impact of each parameter. Finally, based on the observations when comparing QLD with classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by making temperature and $\hbar$ time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many non-convex landscapes.

quant-ph↗

arXiv2025

FOCUS: First Order Concentrated Updating Scheme

Large language models (LLMs) demonstrate remarkable performance, and improving their pre-training process appears to be key to enhancing their capabilities further. Based on the documented success of Adam, learning rate decay, and weight decay, we hypothesize that the pre-training loss landscape features a narrowing valley structure. Through experiments with synthetic loss functions, we discover that when gradient query noise is high relative to the valley's sharpness, Adam's performance falls behind that of Signum because Adam reduces the effective step size too drastically. This observation led us to develop FOCUS, an optimizer that enhances Signum by incorporating attraction toward moving averaged parameters, allowing it to handle noise better while maintaining larger step sizes. In training GPT-2, FOCUS proves to be more stable than Signum and faster than Adam. These results suggest that gradient noise may be an underappreciated limiting factor in LLM training, and FOCUS offers promising solutions.

cs.LG↗

arXiv2025

Physics of Skill Learning

We aim to understand physics of skill learning, i.e., how skills are learned in neural networks during training. We start by observing the Domino effect, i.e., skills are learned sequentially, and notably, some skills kick off learning right after others complete learning, similar to the sequential fall of domino cards. To understand the Domino effect and relevant behaviors of skill learning, we take physicists' approach of abstraction and simplification. We propose three models with varying complexities -- the Geometry model, the Resource model, and the Domino model, trading between reality and simplicity. The Domino effect can be reproduced in the Geometry model, whose resource interpretation inspires the Resource model, which can be further simplified to the Domino model. These models present different levels of abstraction and simplification; each is useful to study some aspects of skill learning. The Geometry model provides interesting insights into neural scaling laws and optimizers; the Resource model sheds light on the learning dynamics of compositional tasks; the Domino model reveals the benefits of modularity. These models are not only conceptually interesting -- e.g., we show how Chinchilla scaling laws can emerge from the Geometry model, but also are useful in practice by inspiring algorithmic development -- e.g., we show how simple algorithmic changes, motivated by these toy models, can speed up the training of deep learning models.

cs.LG↗

arXiv2024

Optimal Control Operator Perspective and a Neural Adaptive Spectral Method

Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. It is central to physical systems in both academia and industry. In this paper, we propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner without direct dependence on the explicit expression of dynamics or iterative optimization processes. The control operator is implemented by a new neural operator architecture named Neural Adaptive Spectral Method (NASM), a generalization of classical spectral methods. We theoretically validate the perspective and architecture by presenting the approximation error bounds of NASM for the control operator. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach, including substantial speedup in running time, and high-quality in- and out-of-distribution generalization.

eess.SY↗

arXiv2024

Style Transfer: From Stitching to Neural Networks

This article compares two style transfer methods in image processing: the traditional method, which synthesizes new images by stitching together small patches from existing images, and a modern machine learning-based approach that uses a segmentation network to isolate foreground objects and apply style transfer solely to the background. The traditional method excels in creating artistic abstractions but can struggle with seamlessness, whereas the machine learning method preserves the integrity of foreground elements while enhancing the background, offering improved aesthetic quality and computational efficiency. Our study indicates that machine learning-based methods are more suited for real-world applications where detail preservation in foreground elements is essential.

cs.CV↗

arXiv2024

On the Computational Complexity of Schrödinger Operators

We study computational problems related to the Schrödinger operator $H = -Δ+ V$ in the real space under the condition that (i) the potential function $V$ is smooth and has its value and derivative bounded within some polynomial of $n$ and (ii) $V$ only consists of $O(1)$-body interactions. We prove that (i) simulating the dynamics generated by the Schrödinger operator implements universal quantum computation, i.e., it is BQP-hard, and (ii) estimating the ground energy of the Schrödinger operator is as hard as estimating that of local Hamiltonians with no sign problem (a.k.a. stoquastic Hamiltonians), i.e., it is StoqMA-complete. This result is particularly intriguing because the ground energy problem for general bosonic Hamiltonians is known to be QMA-hard and it is widely believed that $\texttt{StoqMA}\varsubsetneq \texttt{QMA}$.

quant-ph↗

arXiv2024

Orbital torque switching of perpendicular magnetization in light metal/ferrimagnet bilayers

Orbital torque, associated with orbital current, enables light metals to efficiently manipulate magnetization with rich tunability. A clear demonstration of perpendicular magnetization switching using light metals alone is essential for understanding orbital physics and developing high-density orbitronic devices. Here, we report orbital torque switching of perpendicular magnetization in light metal (Ti, V, Cr)/ferrimagnet (Fe1-xGdx) bilayers. Taking the Ti/ Fe1-xGdx sample as a model system, the torque efficiency increases four-fold by enhancing the spin-orbit coupling in Fe1-xGdx through modulating Gd composition, which is a characteristic feature of orbital torque. Our findings demonstrate that light metals in combination with rare earth-transition metal ferrimagnets can be employed for efficient orbitronic devices and serve as a model system for studying orbitronics.

cond-mat.mtrl-sci↗

arXiv2024

Geometrical Nonlinear Hall Effect Induced by Lorentz Force

The recently discovered nonlinear Hall (NLH) effect arises either without external magnetic field (type-I) or with an in-plane magnetic field (type-II). In this work we propose a new type of geometrical nonlinear Hall effect with an out-of-plane magnetic field (type-III) induced by the combination of Lorentz force and anomalous electronic velocity. The type-III NLH effect is proportional to the more refined structures of Bloch wave functions, i.e., the dipole moment of square of Berry curvature, thus becoming prominent near the band crossings or anticrossings. Our effective model analysis and first-principles calculations show that gate-tuned MnBi$_2$Te$_4$ thin film under uniaxial strain is an ideal platform to observe this effect. Especially, giant unidirectional magnetoresistance can occur in this material, based on which an efficient electrical transistor device prototype can be built. Finally a symmetry analysis indicates that type-III NLH effect has unique symmetry properties stemming from Berry curvature square dipole, which is different from other previously reported NLH effects and can exist in a wider class of magnetic crystals. Our study offers new paradigms for nonlinear electronics.

cond-mat.mtrl-sci↗

arXiv2024

MarsCode Agent: AI-native Automated Bug Fixing

Recent advances in large language models (LLMs) have shown significant potential to automate various software development tasks, including code completion, test generation, and bug fixing. However, the application of LLMs for automated bug fixing remains challenging due to the complexity and diversity of real-world software systems. In this paper, we introduce MarsCode Agent, a novel framework that leverages LLMs to automatically identify and repair bugs in software code. MarsCode Agent combines the power of LLMs with advanced code analysis techniques to accurately localize faults and generate patches. Our approach follows a systematic process of planning, bug reproduction, fault localization, candidate patch generation, and validation to ensure high-quality bug fixes. We evaluated MarsCode Agent on SWE-bench, a comprehensive benchmark of real-world software projects, and our results show that MarsCode Agent achieves a high success rate in bug fixing compared to most of the existing automated approaches.

cs.SE↗

arXiv2024

Sliding Dynamics of Current-Driven Skyrmion Crystal and Helix in Chiral Magnets

The skyrmion crystal (SkX) and helix (HL) phases, present in typical chiral magnets, can each be considered as forms of density waves but with distinct topologies. The SkX exhibits gyrodynamics analogous to electrons under a magnetic field, while the HL state resembles topological trivial spin density waves. However, unlike the charge density waves, the theoretical analysis of the sliding motion of SkX and HL remains unclear, especially regarding the similarities and differences in sliding dynamics between these two spin density waves. In this work, we systematically explore the sliding dynamics of SkX and HL in chiral magnets in the limit of large current density. We demonstrate that the sliding dynamics of both SkX and HL can be unified within the same theoretical framework as density waves, despite their distinct microscopic orders. Furthermore, we highlight the significant role of gyrotropic sliding induced by impurity effects in the SkX state, underscoring the impact of nontrivial topology on the sliding motion of density waves. Our theoretical analysis shows that the effect of impurity pinning is much stronger in HL compared with SkX, i.e., $χ^{SkX}/χ^{HL}\sim α^2$ ($χ^{SkX}$, $χ^{HL}$: susceptibility to the impurity potential, $α$ ($\ll 1$) is the Gilbert damping). Moreover, the velocity correction is mostly in the transverse direction to the current in SkX. These results are further substantiated by realistic Landau-Lifshitz-Gilbert simulations.

cond-mat.mes-hall↗

arXiv2024

Deep Band Crossings Enhanced Nonlinear Optical Effects

Nonlinear optical (NLO) effects in materials with band crossings have attracted significant research interests due to the divergent band geometric quantities around these crossings. Most current research has focused on band crossings between the valence and conduction bands. However, such crossings are absent in insulators, which are more relevant for NLO applications. In this work, we demonstrate that NLO effects can be significantly enhanced by band crossings within the valence or conduction bands, which we designate as "deep band crossings" (DBCs). As an example, in two dimensions, we show that shift conductivity can be substantially enhanced or even divergent due to a mirror-protected "deep Dirac nodal point". In three dimensions, we propose GeTe as an ideal material where shift conductivity is enhanced by "deep Dirac nodal lines". The ubiquity of this enhancement is further confirmed by high-throughput calculations. Other types of DBCs and NLO effects are also discussed. By manipulating band crossings between arbitrary bands, our work offers a simple, practical, and universal way to greatly enhance NLO effects.

cond-mat.mes-hall↗

arXiv2024

Complex fractal trainability boundary can arise from trivial non-convexity

Training neural networks involves optimizing parameters to minimize a loss function, where the nature of the loss function and the optimization strategy are crucial for effective training. Hyperparameter choices, such as the learning rate in gradient descent (GD), significantly affect the success and speed of convergence. Recent studies indicate that the boundary between bounded and divergent hyperparameters can be fractal, complicating reliable hyperparameter selection. However, the nature of this fractal boundary and methods to avoid it remain unclear. In this study, we focus on GD to investigate the loss landscape properties that might lead to fractal trainability boundaries. We discovered that fractal boundaries can emerge from simple non-convex perturbations, i.e., adding or multiplying cosine type perturbations to quadratic functions. The observed fractal dimensions are influenced by factors like parameter dimension, type of non-convexity, perturbation wavelength, and perturbation amplitude. Our analysis identifies "roughness of perturbation", which measures the gradient's sensitivity to parameter changes, as the factor controlling fractal dimensions of trainability boundaries. We observed a clear transition from non-fractal to fractal trainability boundaries as roughness increases, with the critical roughness causing the perturbed loss function non-convex. Thus, we conclude that fractal trainability boundaries can arise from very simple non-convexity. We anticipate that our findings will enhance the understanding of complex behaviors during neural network training, leading to more consistent and predictable training strategies.

cs.LG↗

arXiv2024

The abundance of dark matter haloes down to Earth mass

We use the Voids-within-Voids-within-Voids (VVV) simulations, a suite of successive nested N-body simulations with extremely high resolution (denoted, from low to high resolution, by L0 to L7), to test the Press-Schechter (PS), Sheth-Tormen (ST), and extended Press-Schechter (EPS) formulae for the halo abundance over the entire mass range, from mini-haloes of $10^{-6}\ \mathrm{M_\odot}$, to cluster haloes of $10^{15}\ \mathrm{M_\odot}$, at different redshifts, from $z=30$ to the present. We find that at $z=0$ and $z=2$, ST best reproduces the results of L0, which has the mean cosmic density (overdensity $δ=0$), at $10^{11-15} ~\mathrm{M_\odot}$. The higher resolution levels (L1-L7) are biased underdense regions ($δ<-0.6$). The EPS formalism takes this into account since it gives the mass function of a region conditioned, in this case, on having a given underdensity. EPS provides good matches to these higher levels, with deviations $\lesssim 20\%$, at $10^{-6-12.5} ~\mathrm{M_\odot}$. At $z \sim 7-15$, the ST predictions for L0 and the EPS for L1-L7 show somewhat larger deviations from the simulation results. However, at even higher redshifts, $z \sim 30$, EPS fits the simulations well again. We confirm our results by picking more subvolumes from the L0 simulation, finding that our conclusions depend only weakly on the size and overdensity of the region. The good agreement of EPS with the higher-level simulations implies that PS (or ST) gives an accurate description of the total halo mass function in representative regions of the universe.

astro-ph.GA↗

arXiv2024

Valley-dependent Multiple Quantum States and Topological Transitions in Germanene-based Ferromagnetic van der Waals Heterostructures

Topological and valleytronic materials are promising for spintronic and quantum applications due to their unique properties. Using first principles calculations, we demonstrate that germanene (Ge)-based ferromagnetic heterostructures can exhibit multiple quantum states such as quantum anomalous Hall effect (QAHE) with Chern numbers of C=-1 or C=-2, quantum valley Hall effect (QVHE) with a valley Chern number of C$v$=2, valley-polarized quantum anomalous Hall effect (VP-QAHE) with two Chern numbers of C=-1 and C$v$=-1 as well as time-reversal symmetry broken quantum spin Hall effect (T-broken QSHE) with a spin Chern number of C$s$~1. Furthermore, we find that the transitions between different quantum states can occur by changing the magnetic orientation of ferromagnetic layers through applying a magnetic field. Our discovery provides new routes and novel material platforms with a unique combination of diverse properties that make it well suitable for applications in electronics, spintronics and valley electronics.

physics.comp-ph↗

arXiv2023

Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors

The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly-discovered kagome metals AV$_3$Sb$_5$ (where A can refer to K, Rb, or Cs) exhibit phenomena including topological band structure, symmetry-breaking charge-density waves and superconductivity. Nevertheless, the nature of the symmetry breaking in the charge-density wave phase is not yet clear, despite the fact that it is crucial in order to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy on all three members of this family and find that six-fold rotation symmetry is broken at the onset of the charge-density wave transition in all these compounds. We show that the three nematic domains are oriented at 120$^\circ$ to each other and propose that staggered charge-density wave orders with a relative $π$ phase shift between layers is a possibility that can explain these observations. We also perform magneto-optical Kerr effect and circular dichroism measurements. The onset of both signals is at the transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in that phase.

cond-mat.str-el↗

arXiv2023

Anomalous Circularly Polarized Light Emission induced by the Optical Berry Curvature Dipole

The ability to selectively excite light with fixed handedness is crucial for circularly polarized light emission. It is commonly believed that the luminescent material chirality determines the emitted light handedness, regardless of the light emitting direction. In this work, we propose an anomalous circular polarized light emission (ACPLE) whose handedness actually relies on the emission direction and current direction in electroluminescence. In a solid semiconductor, the ACPLE originates in the band structure topology characterized by the optical Berry curvature dipole. ACPLE exists in inversion-symmetry breaking materials including chiral materials. We exemplify the ACPLE by estimating the high circular polarization ratio in monolayer WS$_2$. In addition, the ACPLE can be further generalized to magnetic semiconductors in which the optical Berry curvature plays a leading role instead. Our finding reveals intriguing consequences of band topology in light emission and promises optoelectric applications.

physics.optics↗

arXiv2023

On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks

Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima. We show that QTW achieves quantum speedup over classical stochastic gradient descents (SGD) when the barriers between different local minima are high but thin and the minima are flat. Based on this observation, we construct a specific double-well landscape, where classical algorithms cannot efficiently hit one target well knowing the other well but QTW can when given proper initial states near the known well. Finally, we corroborate our findings with numerical experiments.

quant-ph↗