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Song Sun

Publications and source records attributed to Song Sun.

At least 19 recordsLinked to original sources

DMRL: Document-Mediated Reinforcement Learning for Skill Optimization in Advertising Recommendation

Advertising recommendation requires continuously tuning complex system parameters while balancing commercial returns and user experience. Recent work has introduced large language models (LLMs) with skill documents to assist this labor-intensive process, but skill optimization remains largely prompt-driven, lacking a principled mechanism to attribute rewards to specific document edits. To address this limitation, we propose Document-Mediated Reinforcement Learning (DMRL), a skill self-evolution framework that models skill document optimization as a sequence of structured editing actions. In DMRL, an upper-level agent performs controlled document edits, while a frozen lower-level task agent evaluates their effects through A/B testing. To address credit assignment and long-term outcomes, we introduce two key components: (1) Dual-Relative Policy Optimization (DRPO), a post-training policy optimization method for robust and risk-aware advantage estimation; and (2) Long-term Reward Predictor (LRP), which estimates long-term outcomes by modeling population heterogeneity with disentangled representation learning and cross-attention transfer. DMRL was deployed on a large-scale short-video ads platform and extensive empirical evaluation shows that DMRL outperforms state-of-the-art baselines across key advertising metrics

cs.LG

Geometry of gravitational instantons

We survey recent progress in the classification of hyperk\"ahler and Hermitian gravitational instantons (i.e., complete noncompact 4 dimensional Ricci-flat manifolds with quadratic curvature decay), as well as the construction of non-Hermitian gravitational instantons via harmonic maps. We also present a list of open questions related to gravitational instantons.

math.DG

Gravitational instantons and harmonic maps

We study the interaction between toric Ricci-flat metrics in dimension 4 and axisymmetric harmonic maps from the 3-dimensional Euclidean space into the hyperbolic plane. Applications include (1). The construction of complete Ricci-flat 4-manifolds that are non-spin, simply-connected, and with arbitrary second Betti number. Our method is non-perturbative and is based on ruling out conical singularities arising from axisymmetric harmonic maps. These metrics also give systematic counterexamples to various versions of the Riemannian black hole uniqueness conjecture. (2). A PDE classification result for axisymmetric harmonic maps of degree at most 1, via the Gibbons-Hawking ansatz and the LeBrun-Tod ansatz, in terms of axisymmetric harmonic functions. This is motivated by the study of hyperkahler and conformally Kahler gravitational instantons.

math.DG

From almost smooth spaces to RCD spaces

We provide various characterizations for a given almost smooth space to be an RCD space, in terms of a local volume doubling and a local Poincar\'e inequality. Applications include a characterization of Einstein $4$-orbifolds.

math.DG

On conical asymptotically flat manifolds

We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question.

math.DG

K\"ahler-Ricci shrinkers and Fano fibrations

In this paper, we build connections between K\"ahler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient K\"ahler-Ricci solitons, and algebraic geometry. In particular, we (1). prove that a K\"ahler-Ricci shrinker is naturally a quasi-projective variety, using birational algebraic geometry; (2). formulate a conjecture relating the existence of K\"ahler-Ricci shrinkers and K-stability of polarized Fano fibrations, which unifies and extends the YTD type conjectures for K\"ahler-Einstein metrics, Ricci-flat K\"ahler cone metrics and compact K\"ahler-Ricci shrinkers; (3). formulate conjectures connecting tangent flows at singularities of K\"ahler-Ricci flows and algebraic geometry, via a 2-step degeneration for the weighted volume of a Fano fibration.

math.DG

VASP2KP: kp models and Lande g-factors from ab initio calculations

The $k\cdot p$ method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zeeman's coupling Hamiltonian with Land\'e $ g $-factors. Here, we develop an open-source package VASP2KP (including two parts: vasp2mat and mat2kp) to compute $k\cdot p$ parameters and Land\'e $g$-factors directly from the wavefunctions provided by the density functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP). First, we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operator $ \mathbf{\hat{\pi}}=\mathbf{\hat{p}}+\frac{1}{2mc^2}\left(\mathbf{\hat{s}}\times\nabla V(\mathbf{r})\right) $, spin operator $\mathbf{\hat{s}}$, time reversal operator $\hat{T}$ and crystalline symmetry operators $\hat{R}$ on the DFT wavefunctions. Second, we develop a python code mat2kp to obtain the unitary transformation $U$ that rotates the degenerate DFT basis towards the standard basis, and then automatically compute the $k\cdot p$ parameters and $g$-factors. The theory and the methodology behind VASP2KP are described in detail. The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method. We apply this package to some materials, e.g., Bi$_2$Se$_3$, Na$_3$Bi, Te, InAs and 1H-TMD monolayers. The obtained effective model's dispersions are in good agreement with the DFT data around the specific wave vector, and the $g$-factors are consistent with experimental data. The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.

cond-mat.mtrl-sci

An infinite dimensional balanced embedding problem I:existence

We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient flow in a Hilbert space; both the long-time existence and convergence at infinite time are non-trivial. The long time existence is established by choosing a perturbation of the ODE; the convergence depends on a priori bounds that uses techniques in the proof of the Tauber-Hardy-Littlewood theorem.

math.CV

Bubbling of K\"ahler-Einstein metrics

We prove the finite step termination of bubble trees for singularity formation of polarized K\"ahler-Einstein metrics in the non-collapsing situation. We also raise several questions and conjectures in connection with algebraic geometry and Riemannian geometry.

math.DG

Anomalous Nernst effect induced terahertz emission in a single ferromagnetic film

By developing a bidirectional-pump terahertz (THz) emission spectroscopy, we reveal an anomalous Nernst effect (ANE) induced THz emission in a single ferromagnetic film. Based on the distinctive symmetry of the THz signals, ANE is unequivocally distinguished from the previously attributed ultrafast demagnetization and anomalous Hall effect mechanisms. A quantitative method is established to separate the different contributions, demonstrating a significant ANE contribution that even overwhelms other competing mechanisms. Our work not only clarifies the origin of the ferromagnetic-based THz emission, but also offers a fertile platform for investigating the ultrafast magnetism and THz spintronics.

cond-mat.mes-hall

Generation of nearly pure and highly directional magnetic light in fluorescence of rare earth ions

A thorough analysis of the emission via the magnetic dipole (MD) transition, called magnetic light below, of trivalent rare-earth ions in or near dielectric homogeneous spheres has been performed. In the search for enhancement of fluorescence from magnetic light, one faces the difficult task of identifying the regions where the combined fluorescence due to multiple electric dipole (ED) transitions becomes negligible compared to the fluorescence of the MD transition. We have succeeded in identifying a number of configurations with dielectric sphere parameters and a radial position of a trivalent rare-earth emitter wherein the branching ratio of the MD transition approaches its limit of one, implying that transitions from a given initial level (e.g., $^5$D$_0$-level of Eu$^{3+}$) are completely dominated by the MD transition. The dimensionless directivity of the MD emission, the radiative decay rates, and the fluorescence of the magnetic light can be increased by a factor of more than $25$, $10^3$, and $10^4$, respectively.

physics.optics

No semistability at infinity for Calabi-Yau metrics asymptotic to cones

We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of K\"ahler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein.

math.DG

Quantized and half-quantized Anomalous Hall effect induced by in-plane magnetic field

In this paper we propose that, quantized and nearly half-quantized intrinsic anomalous Hall effect can be induced by in-plane external magnetic field through the Zeeman coupling in non-magnetic 2D systems with sizeable spin-orbital coupling but without two-fold rotational symmetry. An analytical result is derived for 2D electron gas model with $C_{3v}$ symmetry. Based on the $\boldsymbol{k\cdot p}$ Hamiltonian derived from first principle calculations, we find that quantized and nearly half-quantized conductance can be observed in $\mathrm{Sb_2Te_3}$ thin film in the clean limit with strong in-plane magnetic field $B>20\ \mathrm{T}$ and low temperature $T<100\ \mathrm{mK}$.

cond-mat.mes-hall

Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals

The geometric phase (Berry phase) of an electronic wave function is the fundamental basis of the topological properties in solids. Modulating band structure provides a tuning knob for the Berry phase, and in the extreme case drives a topological phase transition. Despite the significant developments in topological materials study, it remains a challenge to tune between different topological phases while tracing the impact of the Berry phase on quantum charge transport, in the same material. Here we report both in a magnetotransport study of ZrTe5. By tuning the band structure with uniaxial strain, we directly map a weak- to strong- topological phase transition through a gapless Dirac semimetal phase via quantum oscillations. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry phase, largely neglected in solid-state systems, is critical in modeling quantum oscillations in Dirac bands in topological materials.

cond-mat.mtrl-sci

Asymptotically Calabi metrics and weak Fano manifolds

We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the compactification, and we prove a strong uniqueness theorem. We also give an application of this result to the surface case.

math.DG

Authentication of optical physical unclonable functions based on single-pixel detection

Physical unclonable function (PUF) has been proposed as a promising and trustworthy solution to a variety of cryptographic applications. Here we propose a non-imaging based authentication scheme for optical PUFs materialized by random scattering media, in which the characteristic fingerprints of optical PUFs are extracted from stochastical fluctuations of the scattered light intensity with respect to laser challenges which are detected by a single-pixel detector. The randomness, uniqueness, unpredictability, and robustness of the extracted fingerprints are validated to be qualified for real authentication applications. By increasing the key length and improving the signal to noise ratio, the false accept rate of a fake PUF can be dramatically lowered to the order of 10^-28. In comparison to the conventional laser-speckle-imaging based authentication with unique identity information obtained from textures of laser speckle patterns, this non-imaging scheme can be implemented at small speckle size bellowing the Nyquist--Shannon sampling criterion of the commonly used CCD or CMOS cameras, offering benefits in system miniaturization and immunity against reverse engineering attacks simultaneously.

cs.CR