arXiv subjects

Haoyang Liu

Publications and source records attributed to Haoyang Liu.

At least 19 recordsLinked to original sources

arXiv2026

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

We determine the cellular $\mathbb{A}^1$-chain complex of full and partial flag varieties of split semisimple simply connected groups over a perfect field of characteristic different from 2. With compatible integral normal orientations and reindexing by opposite Bruhat cells, the differential in each degree at least two is represented by the motivic Hopf map $η$ times one half of the signed cellular boundary matrix of the corresponding real flag manifold. Consequently, the Smith data of the resulting integer complex give all positive-degree cellular homology sheaves in terms of Milnor--Witt $K$-theory and the kernels and cokernels of integer multiples of $η$. We obtain a uniform computation of the second cellular $\mathbb{A}^1$-homology of $SL_n/B$ for $n\geq3$, together with complete calculations for $SL_3/B$ and the full flags of types $F_4$ and $G_2$.

math.AG↗

arXiv2026

GenoMAS: Guided Multi-Agent Programming for Scientific Discovery from Genomic Data

Gene expression analysis holds the key to many biomedical discoveries, yet extracting insights from raw transcriptomic data remains challenging due to the complexity of multiple large, semi-structured files and the need for extensive domain expertise. Current approaches either rely on inflexible workflows that fail in edge cases or fully autonomous agents that lack the precision required for rigorous scientific inquiry. GenoMAS addresses this by presenting a team of LLM-based agents that integrates structured workflows with autonomous adaptability, orchestrating diverse specialized agents through typed message-passing protocols. At its core lies a guided-planning framework where programming agents decompose task guidelines into Action Units and dynamically choose to advance, revise, bypass, or backtrack, maintaining logical coherence while adapting to the idiosyncrasies of genomic data. On the GenoTEX benchmark, GenoMAS achieves 89.13% CSC for data preprocessing and 60.48% $F_1$ for identifying trait-associated genes, surpassing prior art by 10.61% and 16.85%. Beyond transcriptomics, it outperforms strong agent baselines on ScienceAgentBench and DiscoveryBench, two independent bioinformatics benchmarks. Qualitative analysis shows that GenoMAS identifies gene-phenotype associations that are biologically plausible and corroborated by the literature.

cs.AI↗

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

Algebraic Vector Bundles on Cluster Varieties

We study algebraic vector bundles on cluster varieties. Over a perfect field of characteristic different from two, every algebraic vector bundle is trivial on a cluster variety with principal coefficients at an acyclic seed of irreducible finite Dynkin type. The proof is based on integral contractions of cellular $\mathbb A^1$-chain complexes and successive freezing. We also construct smooth cluster varieties admitting indecomposable rank-two vector bundles, whose nontriviality is detected by quadratic Euler classes. The cellular calculation also gives a criterion for stable freeness and computes integral real cohomology and the images of cycle class maps.

math.AG↗

arXiv2026

ABDA-NL: A Natural-Language Scenario Explorer for Argument-Based Reasoning

ABDA-NL adds a natural-language interface to ABDA, a system for argument-based discussion using ASPIC- knowledge bases under grounded semantics. Users see which conclusions are accepted, rejected, or undecided, open an interactive rendering of the grounded discussion game to learn why, explore what-if alternatives by suspending assumptions and rules or changing preferences, ask questions that are answered from a scenario's reference documents, and author new facts, assumptions, and rules in plain English. A large language model provides the bridge between language and formalism: it answers questions from the documents and the current state of the scenario, and it translates plain-English edits into candidate formal statements. The deterministic ABDA engine remains the sole source of arguments, attacks, and acceptance labels, and every proposal of the model is validated and confirmed by the user before it takes effect.

cs.AI↗

arXiv2026

AnthroDial: Benchmarking LLM Anthropomorphism in Autonomous Social Interaction

Large language models (LLMs) are increasingly deployed as social agents, yet credible human-like interaction requires more than fluent responses or persona consistency. Agents must autonomously decide whether, when, and how to communicate while adapting to evolving contexts, goals, and relationships. Existing research, however, lacks a unified approach to enabling, evaluating, and improving such capabilities in continuous, open-ended interaction. We introduce AnthroDial, a unified framework for developing anthropomorphic social agents from three complementary aspects: MindFlow, a lightweight interaction harness that enables autonomous, asynchronous, and adaptive communication through a dynamic Mind Buffer; CAPS-Eval, a theory-grounded framework for evaluating cognitive, affective, and behavioral dimensions of anthropomorphic interaction; and a scalable training paradigm that combines SEEDS for environment expansion with DiAPO for adaptive capability optimization. We further construct evaluation datasets covering everyday communication, game interaction, and long-horizon character interaction. Extensive experiments across diverse models and scenarios demonstrate improved interaction autonomy and naturalness, validate the reliability, discriminativeness, and agreement with human rankings of CAPS-Eval, and confirm the effectiveness of our training paradigm. Together, these components provide a unified framework for developing credible human-like social agents in open-ended interaction.

cs.CL↗

arXiv2026

PhysAlign: A Benchmark for Evidence-Grounded Role Alignment in Multimodal Physics Reasoning

A key challenge in physics diagram understanding is correctly associating visual information with the physical entities, relations, and conditions it describes. Even when a value, symbol, or other local element is accurately recognized, assigning it to the wrong entity or scope can distort the underlying physical premise and lead to incorrect reasoning. To systematically study this challenge, we introduce \textbf{PhysAlign}, a benchmark designed to assess whether multimodal models correctly associate information recognized from physics diagrams with its intended physical role. By disentangling visual recognition from physical-role assignment through localized probes and controlled variants, PhysAlign isolates correspondence errors from recognition failures. It contains 3,341 human-validated probes spanning 986 physics problems, enabling systematic evaluation of visual recognition and physical-role correspondence at scale. We further introduce five complementary evaluation metrics, including CAcc, GAcc, and JAcc, which provide a comprehensive assessment of models' ability to recognize diagram content, establish correct physical correspondences, and solve the underlying physics problem. Across our evaluated multimodal models, PhysAlign reveals a consistent gap between local visual recognition and physical-role grounding. Even when the queried content is correctly recognized, the conditional correspondence error rate remains 13.8\% for GPT-6-Astra and rises to about 50.6\% for InternVL3.5-8B. These findings indicate that strong perception alone does not ensure reliable physical interpretation, exposing a distinct grounding bottleneck that is largely hidden by answer-level accuracy and highlighting the need for future models to better align recognized visual evidence with its physical meaning.

cs.AI↗

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

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

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↗