Searcharxiv⌕ Search

arXiv subjects

Haoyang Liu

Publications and source records attributed to Haoyang Liu.

At least 19 recordsLinked to original sources
arXiv2026

Intrinsic Restriction Traces and Toric Dynamics

We prove Morita invariance of the Campbell--Lind--Malkiewich--Ponto--Zakharevich restriction-system trace after passage to perfect modules. It therefore defines an intrinsic integral restriction trace for an exact endofunctor of a small idempotent-complete stable $\infty$-category. On $\pi_0$, the $m$-th ghost is the laced trace of the $m$-fold iterate, compatibly with Frobenius. For lattice-graded algebras, the ghost targets have twisted cocenters in degree zero; over the open parameter torus, this applies to the cyclic bimodule of Dinkins--Karpov--Krylov. For finite monomial endomorphisms of toric varieties, we construct motivic restriction classes whose ghosts are sums over cones fixed by the iterates. In one example, two classes have the same first ghost, while their second ghosts differ after rational Betti realization.

math.AG↗
arXiv2026

Adjacent non-stable layers in the $\mathbb{A}^1$-homotopy of the special linear tower

We determine the two cross-stage morphisms arising from adjacent Stiefel fiber sequences in the special linear tower. Over characteristic-zero fields, the first is the Wood morphism at even stages and vanishes at odd stages; the second is induced stably by the motivic Hopf element at even stages and is zero at odd stages. Complex realization consequently classifies oriented rank-$(n-2)$ vector bundles on the split quadric $Q_{2n-1}$ for $n\geq5$. We then apply these calculations to give exact corank-two splitting and efficient generation criteria for projective modules.

math.AG↗
arXiv2026

Where Reasoning Diverges: Localized Multi-Agent Debate for Multi-Hop Question Answering

Multi-agent debate commonly exchanges complete rationales even when disagreements concern only a few intermediate claims. We introduce Localized Multi-Agent Debate (LMAD), an inference-time protocol that represents agent rationales as nodes, locates their earliest conflict, and restricts debate to the corresponding local segments. Guarded resolution extends a shared committed state so that later conflicts can be addressed without reopening accepted steps. We evaluate LMAD on four multi-hop question-answering benchmarks using ten backbones from four model families. Our method achieves the highest macro-averaged judge accuracy across all ten backbones, outperforming the strongest conventional baseline by up to 7.20 percentage points.

cs.AI↗
arXiv2026

Torus-enriched Motivic Bruhat Complexes and Maximal Compact Groups

Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation data lost in the flag quotient. Over a perfect field of characteristic zero, let the group be connected, split, semisimple, and simply connected. Fixing a Borel subgroup with split maximal torus and unipotent radical, we construct a torus-enriched motivic cellular complex for the basic affine space and compute its boundary in every degree. Each cover in Bruhat order contributes a two-face operator determined by a transported coroot, a tail determinant weight, and an explicit Milnor--Witt frame degree. Bott--Samelson purity proves the formula, while the unipotent torsor identifies the complex with that of the group. Over the real numbers, realization identifies it at chain level with the extended-Weyl complex of a maximal compact subgroup, while torus augmentation gives the flag complex. A single motivic complex therefore interpolates between the two incidence theories. A finite torus-support filtration makes this explicit; after inversion of two it splits by the characters of the component group of the real split torus, and the support spectral sequence degenerates. Calculations in the rank-three special linear and exceptional rank-two cases exhibit the first higher differentials beyond the previously known range.

math.AG↗
arXiv2026

Cellular $\mathbb{A}^1$-homology of wonderful models of subspace arrangements

We compute the cellular $\mathbb{A}^1$-homology of De Concini--Procesi wonderful models of subspace arrangements. For a building set $\mathcal{G}$ over a field $k$, we identify the cellular $\mathbb{A}^1$-chain complex of $\mathbb{P}(\mathcal{G})$ with an $\eta$-twisted nested-set complex carrying Milnor--Witt coefficients and derived orientation data. The key geometric input is a motivic blow-up calculation: for a blow-up along a smooth center of codimension $c$, the relevant connecting class is $(c-1)_\epsilon\eta$, hence it is zero for $c$ odd and $\eta$ for $c$ even. This replaces the parity condition in the computation of Rains by a Milnor--Witt attaching class. As a consequence, the part of cellular $\mathbb{A}^1$-homology surviving after multiplication by $\eta$, and also the homology after inverting $\eta$, are expressed by the interval cohomology of the $2$-divisible subposet of the lattice generated by $\mathcal{G}$. For the braid arrangement, the condition becomes the odd-block condition on partitions, yielding explicit decompositions for the cellular $\mathbb{A}^1$-homology of $\overline{\mathcal M}_{0,N}$ and examples in low rank.

math.AG↗
arXiv2026

Multi-Knob Switchable Chiral Superconductivity Quartet in Rhombohedral Graphene

Chiral superconductors break orbital time-reversal symmetry and may host topological quasiparticles with non-Abelian statistics. In rhombohedral graphene, superconductivity develops from a spin-valley-polarized quarter-metal (QM) parent state and features unique magnetic hysteresis of resistance that indicates orbital time-reversal-symmetry-breaking. Exploring and controlling the full spin-valley flavors of such superconductivity could enable novel superconducting and topological devices, but have remained unexplored. Here we report transport measurements on rhombohedral hexalayer graphene (R6G), which reveal a new superconducting state (SCH) that is induced by an out-of-plane magnetic field, in addition to chiral superconductivity (CSC) similar to those observed in thinner layers. This SCH state emerges above 0.8 T, persists up to 1.6 T and can be switched on/off by magnetic field $H_\perp$, carrier density $n$, and gate displacement field $D$. Quantum oscillations and anomalous Hall measurements show that SCH stems from a field-induced quarter-metal (QM$'$) parent phase, which carries orbital magnetization opposite to that of the zero-field QM. Across the full $(n, D, H_\perp)$ parameter space, superconductivity can be realized from all four spin-valley isospin flavors, establishing a switchable chiral-superconductor quartet in R6G. We interpret the parent-state switching as arising from competition between a Kane-Mele-like spin-valley splitting and magnetic-field coupling to spin-valley-dependent magnetic moments. Our work establishes rhombohedral graphene as a multi-knob platform for different isospin-polarized superconductivities, which enables programmable superconducting networks with possible Majorana modes along domain walls.

cond-mat.supr-con↗
arXiv2026

Vector Bundles on Rational Topologically Contractible Affine Threefolds

The generalized Serre question asks whether every algebraic vector bundle on a topologically contractible smooth affine complex variety is trivial. We give an affirmative answer for rational threefolds. More generally, for a topologically contractible smooth affine complex threefold $X$, we prove that $\text{CH}^2(X)=0$ whenever $X$ admits a smooth projective compactification whose Chow group of $0$-cycles is supported on a curve. This uncovers the link between the generalized van de Ven question, Bloch's conjecture and the generalized Serre question for threefolds. We also prove that every Koras-Russell threefold is rational and therefore has only trivial algebraic vector bundles, hence answer a question of Koras and Russell.

math.AG↗
arXiv2026

Cellular $\mathbb{A}^1$-Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties

Let $k$ be a perfect field of characteristic different from 2, we compute the cellular $\mathbb{A}^1$-homology of the flag varieties $G/P_\Theta$ attached to split semisimple simply connected groups over $k$ and describe the differentials in the cellular $\mathbb{A}^1$-chain complex concretely. The construction applies uniformly to the type $A$ coefficient formula, to the type $B_n,C_n,D_n$ for $n\leq 7$, and to the exceptional types for $F_4,E_6,E_7$. Under real realization over $k=\mathbb{R}$, this computation recovers the corresponding results of real flag manifolds. We also provide a detailed computation for $SL_3/B$ and an application to the full split flag variety of type $F_4$.

math.AG↗
arXiv2026

Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the solutions' validity, confirming that the optimization models are logically and mathematically sound. Experiments on popular benchmarks demonstrate that our approach achieves over 20\% improvement in accuracy.

cs.AI↗
arXiv2026

MBABench: Evaluating LLM Agents on End-to-End Spreadsheet Tasks in Finance

LLM agents are increasingly expected to carry out end-to-end workflows, producing complete artifacts from high-level user instructions. To meet enterprise needs, frontier AI labs have developed agents that can construct entire spreadsheets from scratch. This is especially relevant in finance, where core workflows such as financial modeling, forecasting, and scenario analysis are commonly conducted through spreadsheets. Yet, existing spreadsheet benchmarks do not measure this new capability, focusing instead on question-answering or single-formula edits. To address this gap, we provide one of the first evaluations of agents on end-to-end spreadsheet tasks, focusing on economically critical financial workflows such as modeling and scenario analysis. Since deliverables therein are routinely reviewed and revised by multiple stakeholders, judging their quality necessarily involves high-level criteria such as readability or ease of modification. To reflect the multidimensional nature of solution quality, we develop an evaluation taxonomy comprising three dimensions: Accuracy, Formula, and Format, each comprising fine-grained criteria that reflect professional standards. Evaluating over 18 agents, the benchmark reveals that even the strongest agents fall short of basic professional finance standards, and their performance degrade sharply as the difficulty increases beyond a few chained calculations. This suggests that current agents are not yet able to reliably produce professional-quality spreadsheets at the level of complexity real-world workflows demand.

cs.AI↗
arXiv2026

Reconstructing the Stripping History of the Sagittarius Stream with Neural Networks

The Sagittarius (Sgr) Stream is produced by the ongoing disruption of the Sgr dwarf spheroidal (dSph) galaxy and is thought to contain multiple wraps that were stripped during different pericentric passages. In this study, we introduce a neural-network--based method trained on $N$-body simulations to infer the stripping time of Sgr Stream stars directly from their phase-space coordinates. We combine spectroscopic data from SEGUE, APOGEE DR17, and LAMOST DR7 LRS with \textit{Gaia} EDR3 astrometry and distance estimates from the latest \texttt{StarHorse} catalog to identify high-quality Sgr Stream members. Applying our method to these stars, we measure a clear metallicity gradient with stripping time, well described by a linear relation with slope $\sim 0.3~\mathrm{dex~Gyr^{-1}}$. We further predict the stripping times of globular clusters previously suggested to originate from the Sgr dSph. M 54, Terzan 7, Terzan 8, and Arp 2 exhibit stripping times consistent with being currently bound to the Sgr remnant. Pal 12, Whiting 1, and NGC 2419 are inferred to have been stripped $0.9 \pm 0.1$, $1.1 \pm 0.2$, and $2.1 \pm 0.2$ Gyr ago, respectively. For NGC 4147 and NGC 5634, whose membership in the Sgr system remains uncertain, our analysis suggests stripping times of $1.1 \pm 0.4$ and $1.1 \pm 0.1$ Gyr, respectively, if they are ultimately confirmed as genuine Sgr members. These results demonstrate that data-driven models of dynamical stripping histories offer a promising approach for reconstructing the formation and chemical evolution of the Sgr Stream.

astro-ph.GA↗
arXiv2026

NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling

Automating the translation of Operations Research (OR) problems from natural language to executable models is a critical challenge. While Large Language Models (LLMs) have shown promise in linear tasks, they suffer from severe performance degradation in real-world nonlinear scenarios due to semantic misalignment between mathematical formulations and solver codes, as well as unstable information extraction. In this study, we introduce NED-Tree, a systematic framework designed to bridge the semantic gap. NED-Tree employs (a) a sentence-by-sentence extraction strategy to ensure robust parameter mapping and traceability; and (b) a recursive tree-based structure that adaptively decomposes complex nonlinear terms into solver-compatible sub-elements. Additionally, we present NEXTOR, a novel benchmark specifically designed for complex nonlinear, extensive-constraint OR problems. Experiments across 10 benchmarks demonstrate that NED-Tree establishes a new state-of-the-art with 72.51% average accuracy, NED-Tree is the first framework that drives LLMs to resolve nonlinear modeling difficulties through element decomposition, achieving alignment between modeling semantics and code semantics. The NED-Tree framework and benchmark are accessible in the anonymous repository https://anonymous.4open.science/r/NORA-NEXTOR.

cs.AI↗
arXiv2026

Revisiting candidate high-velocity stars associated with the Sagittarius dwarf spheroidal galaxy

Hypervelocity stars (HVSs) are valuable tracers of extreme dynamical processes. The Sagittarius dwarf spheroidal galaxy (Sgr dSph), currently undergoing tidal disruption, offers a unique environment to search for such stars. We aim to identify candidate HVSs dynamically linked to the Sgr dSph and to assess their possible origins. Using Gaia DR3, DESI DR1, and LAMOST DR12, we selected stars with galactocentric velocities above 400 km\,s$^{-1}$ and traced their orbits in a realistic Galactic potential including the Sgr dSph and the Large Magellanic Cloud. We then tested three scenarios for their origin: the Hills mechanism, tidal disruption, and random halo star encounters. We identified 95 candidates passing within 2.5 half-mass radii of the Sgr dSph. Their kinematics are inconsistent with production by the Hills mechanism or tidal disruption but are well reproduced by halo stars that naturally cross the Sgr orbit. Furthermore, their metallicity distribution is consistent with that of the Milky Way halo rather than the Sgr stream or Sgr dSph. Our results suggest that our candidates and those in previous studies are most likely halo stars rather than genuine Sgr-origin HVSs. This highlights the need to account for the halo population when inferring stellar origins from orbital analysis and that chemical abundances will be a valuable constraint in the future. While we detect no unbound Sgr HVSs, such a discovery would directly imply extreme dynamical processes. Our results serve as a basis for future studies with upcoming surveys.

astro-ph.GA↗
arXiv2026

Joint Optimization of Multi-agent Memory System

Memory systems are critical for LLMs, mitigating context window limitations and supporting long-horizon user-LLM interactions. Such systems typically comprise multiple agents responsible for memory construction and retrieval. Existing approaches often optimize each agent independently under a shared global objective (e.g., downstream QA accuracy), treating other agents as a static environment. However, this design has two key limitations: (1) independent optimization ignores inter-agent dependencies and lacks agents' co-adaptation, and (2) relying solely on sparse global rewards provides limited guidance for optimizing specialized agents and causes ambiguous credit assignment. These may ultimately limit agents' effective collaboration in the memory system. To address these limitations, we propose CoMAM, a joint optimization framework that promotes collaboration among agents via end-to-end reinforcement learning and an adaptive credit assignment mechanism. Specifically, we model the multi-agent pipeline as a Markov decision process (MDP) to expose inter-agent dependencies during end-to-end training. Agents are then jointly optimized using a combination of their local task reward and an adaptively weighted global reward, enabling agents to co-adapt while receiving targeted feedback for their respective roles. Experiments show that CoMAM consistently outperforms leading memory systems, validating the effectiveness of the joint optimization framework.

cs.MA↗
arXiv2026

Chemical Properties and Sagittarius-induced Dynamical Perturbations of the GD-1 Stream

In this study, we investigate the chemical properties of the GD-1 stream using cross-matched, data-driven elemental abundances. The results reveal no clear $\alpha$-knee in the [Mg/Fe]-[Fe/H] plane, and strong abundance consistency between the thin stream and cocoon, supporting a common origin. The absence of multiple-population signatures (e.g., C-N anti-correlation) suggests a low-mass progenitor. Using a test-particle simulation with the particle spray method and including perturbations from the Sagittarius (Sgr) dwarf galaxy, it shows that Sgr does not significantly heat the stream to form the cocoon, but modifies the intrinsic $\phi_2$ distribution, in agreement with observations. The trailing arm narrowly distributed across the width of the stream, while the leading arm is more diffuse, indicating that major fraction of cocoon stars are present towards the leading arm. Sgr also drags more stream particles moving toward the Galactic center, producing an excess at $V_{\text{GSR}}<0$, consistent with data. Our study confirms the Sgr has a non-negligible dynamical influence on the GD-1 stream. Other heating mechanisms (e.g., dark matter sub-halo encounters and pre-stripping process inside the parent halo) remain to be considered, and higher-resolution spectroscopy is needed to further constrain chemical abundances.

astro-ph.GA↗
arXiv2026

RobustSCI: Beyond Reconstruction to Restoration for Snapshot Compressive Imaging under Real-World Degradations

Deep learning algorithms for video Snapshot Compressive Imaging (SCI) have achieved great success, yet they predominantly focus on reconstructing from clean measurements. This overlooks a critical real-world challenge: the captured signal itself is often severely degraded by motion blur and low light. Consequently, existing models falter in practical applications. To break this limitation, we pioneer the first study on robust video SCI restoration, shifting the goal from "reconstruction" to "restoration"--recovering the underlying pristine scene from a degraded measurement. To facilitate this new task, we first construct a large-scale benchmark by simulating realistic, continuous degradations on the DAVIS 2017 dataset. Second, we propose RobustSCI, a network that enhances a strong encoder-decoder backbone with a novel RobustCFormer block. This block introduces two parallel branches--a multi-scale deblur branch and a frequency enhancement branch--to explicitly disentangle and remove degradations during the recovery process. Furthermore, we introduce RobustSCI-C (RobustSCI-Cascade), which integrates a pre-trained Lightweight Post-processing Deblurring Network to significantly boost restoration performance with minimal overhead. Extensive experiments demonstrate that our methods outperform all SOTA models on the new degraded testbeds, with additional validation on real-world degraded SCI data confirming their practical effectiveness, elevating SCI from merely reconstructing what is captured to restoring what truly happened.

cs.CV↗
arXiv2026

PPI-SVRG: Unifying Prediction-Powered Inference and Variance Reduction for Semi-Supervised Optimization

We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates -- PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the neighborhood size. When predictions are perfect, we recover SVRG exactly. When predictions degrade, convergence remains stable but reaches a larger neighborhood. Experiments confirm the theory: PPI-SVRG reduces MSE by 43--52\% under label scarcity on mean estimation benchmarks and improves test accuracy by 2.7--2.9 percentage points on MNIST with only 10\% labeled data.

cs.LG↗
arXiv2026

A Low-mass Model of The Milky Way: The Disk Warp Resulting from A Galaxy Merger

Previous studies have shown that disk warps can result from galaxy mergers. Recent research indicates a noticeable decline in the rotation curve (RC) of the Milky Way (MW), suggesting the need for a new low-mass model to describe its dynamical features. This study constructs a new Gaia-Sausage-Enceladus (GSE) merger model to characterize the RC features of our galaxy. We use the GIZMO code to simulate mergers with various orbital parameters to investigate how the disk warp evolves under different conditions. This simulation demonstrates the evolutionary mechanism of disk warp, which arises due to the asymmetric gravitational potential of the dark matter (DM) halo generated universally by galaxy mergers. The results indicate that the tilt angle of the DM halo partly reflects the gravitational strength at the $Z=0$ plane, while the gravitational strength on the disk plane reflects the amplitude of disk warp. We identify a dual-regime interaction mechanism driven by the asymmetric halo potential. On short timescales, we find a distinct anti-correlation between the halo's tilt angle and the disk's warp amplitude, indicating a `seesaw' mechanism of angular momentum exchange. On secular timescales, however, dynamical friction drives a global alignment, causing both the halo tilt and the warp amplitude to decay simultaneously. Furthermore, we demonstrate that high-inclination mergers can sustain long-lived prograde precession, where the persistent yet decaying gravitational torque maintains the prograde bending mode against differential wind-up.

astro-ph.GA↗