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 $π_0$, 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

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

Two-flag degenerations and real circles tangent to three conics

Three general plane conics admit $184$ complex tangent circles, and it had been conjectured that at most $136$ of them could be real. We construct an explicit strongly general triple of smooth conics over $\mathbb{Q}$ with exactly $160$ real tangent circles; the same count therefore occurs on a nonempty Euclidean chamber. The construction combines a fourfold splitting theorem for two flagged double-line degenerations with exact Sturm--Tarski, elimination, and interval certificates. We also show that the Grothendieck--Witt-valued count is $92\mathbb{H}$ and express its real local signs, up to a fixed orientation convention, in terms of curvature differences, residual intersection divisors, and contact normals. The exact-arithmetic code and certificate data are archived in the accompanying repository.

math.AG↗

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 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 $η$-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 $(c-1)_εη$, hence it is zero for $c$ odd and $η$ 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 $η$, and also the homology after inverting $η$, 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

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

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

A Fan Algorithm for Chow-Witt Rings of Smooth Projective Toric Varieties

Let $R$ be a real closed field and let $X_Σ$ be a smooth projective split toric variety. For an explicitly chosen basis rigidification $\mathfrak r$ of its Picard grading, we prove that the pair $(Σ,\mathfrak r)$ determines the resulting total Chow--Witt ring and give a terminating finite algorithm for all groups, products, twists, and forgetful maps. The ring is identified with an explicit fibre product of the Picard-graded diagonal $\mathbf{I}$-cohomology ring and the integral inverse images of twisted Bockstein kernels over the mod-$2$ Chow ring. Using real cycle classes, we identify the first factor with the cohomology of the real toric variety with all sign local systems. We construct the mod-$2$ cycle map on invariant divisors as explicit deck-transition cocycles and obtain finite signed boundary and product matrices directly from the fan.

math.AG↗

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

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

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 $G/P_Θ$ 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

Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation

Machine learning has been successfully applied to improve the efficiency of Mixed-Integer Linear Programming (MILP) solvers. However, the learning-based solvers often suffer from severe performance degradation on unseen MILP instances -- especially on large-scale instances from a perturbed environment -- due to the limited diversity of training distributions. To tackle this problem, we propose a novel approach, which is called Adversarial Instance Augmentation and does not require to know the problem type for new instance generation, to promote data diversity for learning-based branching modules in the branch-and-bound (B&B) Solvers (AdaSolver). We use the bipartite graph representations for MILP instances and obtain various perturbed instances to regularize the solver by augmenting the graph structures with a learned augmentation policy. The major technical contribution of AdaSolver is that we formulate the non-differentiable instance augmentation as a contextual bandit problem and adversarially train the learning-based solver and augmentation policy, enabling efficient gradient-based training of the augmentation policy. To the best of our knowledge, AdaSolver is the first general and effective framework for understanding and improving the generalization of both imitation-learning-based (IL-based) and reinforcement-learning-based (RL-based) B&B solvers. Extensive experiments demonstrate that by producing various augmented instances, AdaSolver leads to a remarkable efficiency improvement across various distributions.

cs.LG↗

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

GenoMAS: A Multi-Agent Framework for Scientific Discovery via Code-Driven Gene Expression Analysis

Gene expression analysis holds the key to many biomedical discoveries, yet extracting insights from raw transcriptomic data remains formidable due to the complexity of multiple large, semi-structured files and the need for extensive domain expertise. Current automation approaches are often limited by either inflexible workflows that break down in edge cases or by fully autonomous agents that lack the necessary precision for rigorous scientific inquiry. GenoMAS charts a different course by presenting a team of LLM-based scientists that integrates the reliability of structured workflows with the adaptability of autonomous agents. GenoMAS orchestrates six specialized LLM agents through typed message-passing protocols, each contributing complementary strengths to a shared analytic canvas. At the heart of GenoMAS lies a guided-planning framework: programming agents unfold high-level task guidelines into Action Units and, at each juncture, elect to advance, revise, bypass, or backtrack, thereby maintaining logical coherence while bending gracefully to the idiosyncrasies of genomic data. On the GenoTEX benchmark, GenoMAS reaches a Composite Similarity Correlation of 89.13% for data preprocessing and an F$_1$ of 60.48% for gene identification, surpassing the best prior art by 10.61% and 16.85% respectively. Beyond metrics, GenoMAS surfaces biologically plausible gene-phenotype associations corroborated by the literature, all while adjusting for latent confounders. Code is available at https://github.com/Liu-Hy/GenoMAS.

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

Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective

Reinforcement Learning with Verifiable Rewards (RLVR) serves as a cornerstone technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, its training is often plagued by \emph{entropy collapse}, a rapid decline in policy entropy that limits exploration and undermines training effectiveness. While recent works attempt to mitigate this issue via several heuristic entropy interventions, the underlying mechanisms remain poorly understood. In this work, we conduct comprehensive theoretical and empirical analyses of entropy dynamics in RLVR, offering two main insights: (1) We derive a tight analytical approximation for token-level entropy change at each update step, revealing four governing factors and providing a unified theoretical framework to explain how existing methods influence entropy; (2) We reveal a fundamental limitation of recent approaches: they rely on heuristic adjustments to one or two of these factors, leaving other relevant factors unconsidered, thus inherently limiting their effectiveness. Motivated by these findings, we propose STEER, a principled entropy-modulation method that adaptively reweights tokens based on theoretically-estimated entropy variations. Extensive experiments across six mathematical reasoning and three coding benchmarks demonstrate that STEER effectively mitigates entropy collapse and consistently outperforms state-of-the-art baselines.

cs.LG↗

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

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↗