arXiv subjects

Wei Bu

Publications and source records attributed to Wei Bu.

At least 19 recordsLinked to original sources

arXiv2026

Perturbative methods for non-parametric instrumental variable

We introduce a perturbative approach for nonparametric instrumental variable (NPIV) estimation. By drawing inspiration from perturbation theory in physics, we extend standard kernel ridge methods with systematic higher perturbation order corrections that significantly improve estimation accuracy. Spectrally, the perturbation introduces mixing between different eigenmodes of the expectation integral operator, which becomes especially useful when the integral equation is ill-defined. One source for such ill-definedness can be the curse of dimensionality. Our method performs across various dimensionality regimes, particularly when the dimensionality parameter $\beta$ which is defined through the number of samples $n$ and dimension $d$ as $n^\beta = d$, becomes large. Experimental results show that our first-order perturbative corrections can reduce prediction error by up to 99\% in high-dimensional ill-defined cases ($\beta > 0.7$) compared to standard ridge regression approaches. The performance improvement is maintained across a wide range of dimensions, with the advantage becoming more pronounced as dimensionality increases.

cs.LG↗

arXiv2025

Globally aware optimization with resurgence

Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(\theta)/g} d\theta$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

cs.LG↗

arXiv2025

Fokker-Planck to Callan-Symanzik: evolution of weight matrices under training

The dynamical evolution of a neural network during training has been an incredibly fascinating subject of study. First principal derivation of generic evolution of variables in statistical physics systems has proved useful when used to describe training dynamics conceptually, which in practice means numerically solving equations such as Fokker-Planck equation. Simulating entire networks inevitably runs into the curse of dimensionality. In this paper, we utilize Fokker-Planck to simulate the probability density evolution of individual weight matrices in the bottleneck layers of a simple 2-bottleneck-layered auto-encoder and compare the theoretical evolutions against the empirical ones by examining the output data distributions. We also derive physically relevant partial differential equations such as Callan-Symanzik and Kardar-Parisi-Zhang equations from the dynamical equation we have.

cs.LG↗

arXiv2024

2d theory for asymptotic dynamics of 4d (self-dual) Einstein gravity

In this paper, we present a simple chiral 2d theory living on a momentum space celestial sphere whose behaviour exactly produces various IR dynamics of recent resurged interests for 4d (selfdual) Einstein gravity in asymptotically flat spacetimes. We demonstrate how to use simple 2d CFT computations to reproduce 4d BMS algebra and $w_{1+\infty}$ algebra, deduce the form of both chiral and anti-chiral stress tensors and recover the necessity for dressing hard particles asymptotically with soft modes. We further discuss how possible extensions of this 2d theory incorporates further dynamical information of 4d Einstein gravity.

hep-th↗

arXiv2024

Effect of Grafting Density on the Two-dimensional Assembly of Nanoparticles

Employing grazing-incidence small-angle X-ray scattering (GISAXS) and X-ray reflectivity (XRR), we demonstrate that films composed of polyethylene glycol (PEG)-grafted silver nanoparticles (AgNP) and gold nanoparticles (AuNP), as well as their binary mixtures, form highly stable hexagonal structures at the vapor-liquid interface. These nanoparticles exhibit remarkable stability under varying environmental conditions, including changes in pH, mixing concentration, and PEG chain length. Short-chain PEG grafting produces dense, well-ordered films, while longer chains produce more complex, less dense quasi-bilayer structures. AuNPs exhibit higher grafting densities than AgNPs, leading to more ordered in-plane arrangements. In binary mixtures, AuNPs dominate the population at the surface, while AgNPs integrate into the system, expanding the lattice without forming a distinct binary superstructure. These results offer valuable insights into the structural behavior of PEG-grafted nanoparticles and provide a foundation for optimizing binary nanoparticle assemblies for advanced nanotechnology applications.

cond-mat.soft↗

arXiv2024

Infrared structures of scattering on self-dual radiative backgrounds

The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional celestial sphere. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level collinear splitting functions -- or celestial OPEs -- and infinite-dimensional chiral soft algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the MHV sectors of gauge theory and gravity.

hep-th↗

arXiv2024

Eikonal amplitudes on the celestial sphere

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: $2\to2$ scattering of scalars in flat spacetime and $1\to1$ scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.

hep-th↗

arXiv2024

A systematic approach to celestial holography: a case study in Einstein gravity

We propose a systematic approach to celestial holography in massless theories beginning by studying the implications of properly incorporating field configurations built using the eigenstates of central interest: massless conformal primary wavefunctions that diagonalize the dilatation generator. Due to their singular behaviour on the locus $k\cdot x=0$, they do not belong to the space of Fourier decomposable functions, and incorporating them in the path integral domain requires careful manipulations. In this paper, we include these singular field configurations by a splitting procedure using large pure gauge/diffeomorphism transformations on the action functional. We demonstrate that doing so splits the action into an integrand supported on the singular locus $k\cdot x=0$ and an integrand on the rest of the space. Mellin transforms single out the scalings/conformal dimension in $x$, geometrically, we treat this as a proper non-compact scaling reduction, where we are able to further isolate the dynamics of the large pure diffeomorphism transformations. This takes the form of 2d chiral CFT on a 2d sphere on the singular locus $k\cdot x=0$ - the celestial sphere where the null cone of the origin cuts $\mathscr{I}$. Using this framework, we study Einstein gravity perturbatively around its self-dual sector, where the resulting microscopic 2d CFT couples to bulk scattering states. We are able to obtain an explicit representation of the $\mathcal{L} w_{1+\infty}$ algebra and leading soft splitting functions. With further marginal deformations, we also write down effective interaction vertices which provide form factors of tree-level graviton scattering in Minkowski space.

hep-th↗

arXiv2023

Assembling PNIPAM-Capped Gold Nanoparticles in Aqueous Solutions

Employing small angle X-ray scattering (SAXS), we explore the conditions under which the assembly of gold nanoparticles (AuNPs) grafted with the thermo-sensitive polymer Poly(N-isopropylacrylamide) (PNIPAM) emerges. We find that short-range order assembly emerges by combining the addition of electrolytes or poly-electrolytes with raising the temperature of the suspensions above the lower-critical solution temperature (LCST) of PNIPAM. Our results show that the longer the PNIPAM chain is, the better organization in the assembled clusters. Interestingly, without added electrolytes, there is no evidence of AuNP assembly as a function of temperature, although untethered PNIPAM is known to undergo a coil-to-globule transition above its LCST. This study demonstrates another approach to assembling potential thermo-sensitive nanostructures for devices by leveraging the unique properties of PNIPAM.

cond-mat.soft↗

arXiv2023

A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor action to a CP1 after scaling reduction of twistor space. Under a projection, it can be mapped to the celestial sphere at the light-cone cut of the origin on null infinity. Geometrically, this is the common boundary celestial sphere shared by Euclidean AdS3 or Lorentzian dS3 slices of Minkowski space. We comment on the geometric meaning of the derivation from the perspective of minitwistor spaces of the 3d slices embedded in 4d Minkowski space. Using the action functional of this 2d CFT, we compute its stress-energy tensor and central charge. By a further marginal deformation, we calculate correlation functions of current algebra generators purely from the 2d side which reproduce 4d MHV form factors.

hep-th↗

arXiv2023

Celestial holography and AdS3/CFT2 from a scaling reduction of twistor space

Celestial amplitudes obtained from Mellin transforming 4d momentum space scattering amplitudes contain distributional delta functions, hindering the application of conventional CFT techniques. In this paper, we propose to bypass this problem by recognizing Mellin transforms as integral transforms projectivizing certain components of the angular momentum. It turns out that the Mellin transformed wavefunctions in the conformal primary basis can be regarded as representatives of certain cohomology classes on the minitwistor space of the hyperbolic slices of 4d Minkowski space. Geometrically, this amounts to treating 4d Minkowski space as the embedding space of AdS3. By considering scattering of such on-shell wavefunctions on the projective spinor bundle PS of Euclidean AdS3, we bypass the difficulty of the distributional properties of celestial correlators using the traditional AdS3/CFT2 dictionary and find conventional 2d CFT correlators for the scaling reduced Yang-Mills theory living on the hyperbolic slices. In the meantime, however, one is required to consider action functionals on the auxiliary space PS, which introduces additional difficulties. Here we provide a framework to work on the projective spinor bundle of hyperbolic slices, obtained from a careful scaling reduction of the twistor space of 4d Minkowski spacetime.

hep-th↗

arXiv2022

All-order celestial OPE in the MHV sector

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

hep-th↗

arXiv2022

The 4d/2d correspondence in twistor space and holomorphic Wilson lines

We give an explicit realization of the 4d local operator / 2d conformal block correspondence of Costello and Paquette in the case of gauge theories. This is accomplished by lifting the 4d local operators to non-local operators in twistor space using a holomorphic generalization of the Wilson line. This procedure automatically constructs the 2d conformal blocks corresponding to the local operator. We interpret this lifting as effectively integrating out the 2d degrees of freedom living on the defect. We present some 2d chiral CFT representations of the defect algebra whose correlators reproduce the conformal blocks obtained by the lifting procedure.

hep-th↗

arXiv2022

Moyal deformations, $W_{1+\infty}$ and celestial holography

We consider the Moyal deformation of self-dual gravity. In the conformal primary basis, holomorphic collinear limits of the amplitudes of this theory show that it enjoys a perturbatively exact symmetry algebra $LW_\wedge$ that generalises $Lw_\wedge$, the loop algebra of the wedge algebra of $w_{1+\infty}$, which appears in self-dual gravity.

hep-th↗

arXiv2022

Celestial operator products from the worldsheet

We compute the operator product expansions of gluons and gravitons in celestial CFT from the worldsheet OPE of vertex operators of four-dimensional ambitwistor string theories. Remarkably, the worldsheet OPE localizes on the short-distance singularity between vertex operator insertions which in turn coincides with the OPE limit of operator insertions on the celestial sphere. The worldsheet CFT dynamically produces known celestial OPE coefficients -- as well as infinite towers of SL$(2,\mathbb{R})$ descendant contributions to the celestial OPE -- without any truncations or approximations. We obtain these results for all helicities and incoming/outgoing configurations. Furthermore, the worldsheet OPE encodes the infinite-dimensional symmetry algebras associated with the conformally soft sectors of gauge theory and gravity. We provide explicit operator realizations of the currents generating these symmetries on ambitwistor space in terms of vertex operators for soft gluons and gravitons, also computing their actions on hard particles of all helicities. Lastly, we show that the worldsheet OPE for momentum eigenstates produces the collinear splitting functions of gluons and gravitons.

hep-th↗

arXiv2022

Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet

Using the ambitwistor string, we complete the list of celestial OPE coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet CFT to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to the purely bosonic cases.

hep-th↗

arXiv2020

The Role of Specific Ion Effects in Ion Transport: The Case of Nitrate and Thiocyanate

The selective transport of trivalent rare earth metals from aqueous to organic environments with the help of amphiphilic "extractants" is an industrially important process. When the amphiphilic extractant is positively charged or neutral, the coextracted background anions are not only necessary for charge balance but also have a large impact on extraction efficiency and selectivity. In particular, the opposite selectivity trends observed throughout the lanthanide series in the presence of nitrate and thiocyanate ions have not been explained. To understand the role of background anions in the phase transfer of lanthanide cations, we use a positively charged long-chain aliphatic molecule, modeling a common extractant, and gain molecular level insight into interfacial headgroup-anion interactions. By combining surface sensitive sum frequency generation spectroscopy with X-ray reflectivity and grazing incidence X-ray diffraction, we observed qualitative differences in the orientational and overall interfacial structure of nitrate and thiocyanate solutions at a positively charged Langmuir monolayer. Though nitrate adsorbs without dramatic changes to the solvation structure at the interface or the monolayer ordering, thiocyanate significantly alters the water structure and reduces monolayer ordering. We suggest that these qualitatively different adsorption trends help explain a reversal in system selectivity toward lighter or heavier lanthanides in solvent extraction systems in the presence of nitrate or thiocyanate anions.

cond-mat.soft↗

arXiv2019

Higher Order Quantum Ghost Imaging with Ultra-Cold Atoms

Ghost imaging is a quantum optics technique that uses correlations between two beams to reconstruct an image in one beam from photons that do not interact with the object being imaged. While pairwise (second order) correlations are usually used to create the image, higher order correlations can be utilized to improve the performance of ghost imaging. In this paper, we demonstrate higher order atomic ghost imaging, using entangled ultracold metastable helium atoms from an s-wave collision halo. We construct higher order ghost images up to 5th order and show that using higher order correlations can improve the visibility of the images without impacting the resolution. This is the first demonstration of higher order ghost imaging with massive particles and the first higher order ghost imaging protocol of any type using a quantum source.

cond-mat.quant-gas↗