arXiv subjects

Liang Zhang

Publications and source records attributed to Liang Zhang.

At least 19 recordsLinked to original sources

arXiv2026

General Form Factors from String Amplitudes

We extend the string-amplitude construction of single-insertion form factors to multiple operator insertions carrying independent off-shell momenta. By deforming the bulk closed-string punctures onto the open-string boundary, we establish a relation between stringy general form factors and scattering amplitudes. Using this relation, we evaluate the field-theory limit and find that the resulting form factors receive contributions from both separate operator insertions and local contact terms. Furthermore, we uncover several hidden structures of stringy general form factors at finite $α'$: $2$-splits and hidden zeros analogous to those of scattering amplitudes, bulk zeros specific to form factors, and a decoupling split unique to multiple insertions.

hep-th↗

arXiv2026

Turán number of three disjoint cliques of arbitrary sizes

The Turán number $\rm ex(n,H)$ of a given graph $H$ is the maximum number of edges in an $n$-vertex $H$-free graph. In this paper, for all $p\ge q\ge r\ge 2$ and $n\geq p+q+r$, we determine the exact value of $\rm ex(n,K_p\cup K_q\cup K_r)$ and describe all extremal graphs.

math.CO↗

arXiv2026

Square-root logarithmic bounds for the arithmetic complexity of factorial multiples

Assume that the Riemann zeta function has no zeros in $\Re(s)>1-δ$, $s\neq1$, for some fixed $0<δ\leq1/2$. We prove that, for every sufficiently large integer $k$, a positive multiple $m_k k!$ has arithmetic complexity $τ(m_k k!)\leq\exp(C\sqrt{\log k\log\log k})$, where $C$ depends only on $δ$. We first establish a smooth-number asymptotic at every sufficiently large center $x$ in intervals of length at least $x^{3/4}$. Combining this estimate with an established genus-two construction yields the arithmetic bound without Cheng's conjecture on smooth numbers in elliptic Hasse intervals. The bound includes the cost of constructing all integer parameters. This work was carried out with assistance from the UniMath model, developed by UniDT (Shanghai) Co., Ltd., and OpenAI's GPT-6.1 Sol and GPT-6 Astra.

math.NT↗

arXiv2026

Before Blaming the LLM, Diagnose the Workflow: A Role-Level Difficulty Profile for Translating Natural Language into Ontology-Grounded Statements

Natural-language-to-domain-specific-language (NL-to-DSL) semantic parsing systems increasingly translate informal user descriptions into structured artifacts such as Structured Query Language (SQL) queries, Application Programming Interface (API) calls, workflows, formal specifications, and ontology-grounded domain-specific language (DSL) statements. This paper focuses on ontology-grounded Assertion Box (ABox) DSL generation: the translation of natural language domain descriptions into assertion-level DSL statements grounded in a pre-existing ontology vocabulary. In this setting, syntactic validity is often easier to achieve than semantic adequacy. Failures are frequently attributed to weak generator models, but recurring sources of difficulty are also structural: insufficient input, weak domain grounding, output template and vocabulary gaps, weak validation, and non-local repair. We propose a role-level difficulty profile for diagnosing difficulty in ontology-grounded NL-to-DSL semantic parsing at the workflow level. The profile organizes diagnostic variables across five recurring workflow roles: Input, Generator, Output, Validator, and Repairer. The seven variables are input sufficiency, context availability, grounding complexity, template fit, vocabulary coverage, validation strength, and error observability. Practitioners construct the difficulty profile through qualitative judgment over available evidence. This experience-informed, non-exhaustive difficulty profile is intended to support workflow diagnosis and guide redesign or human-in-the-loop intervention.

cs.AI↗

arXiv2026

What Transfers from Training-Only Priors? Separating Knowledge, Ordinal Targets, and Optimization

Training-only teacher access lets a compact student deploy with local features and exported weights. This established distillation interface does not identify what transfers or when it helps. We separate label, query, capacity, and source-access budgets on three public credit archives and a previously unexamined bankruptcy archive. Shared tree parameters, shuffles, and optimizer interventions expose limitations of historical Ranking Prior Alignment; no tested single repair consistently rescues it. Heldout source queries and matched warmup and mappings retain a rank-listwise advantage over mapped staged KD in 24 credit configuration means and all six teacher--capacity means of a frozen new-archive test, with explicit query failures and stronger source-weight delivery under a different interface. A pretrained TabICLv2 follow-up at 100 labels initially improves matched supervision in only one of eight means; six of nine source-predicted policy gains reverse on target. A registered seen-archive intervention adds 500 or 2,000 unlabeled queries: all eight matched AUC means become positive under selected and fixed alpha. However, outer effects are mixed and no conditional paired-draw interval for these supervised contrasts lies wholly above zero. Increasing teacher context at 500 student labels does not beat matched supervision in any of eight ordinary-context means, despite stronger direct teacher performance. Rank KD retains substantial probability errors. Independent reloads verify zero guarded external inference accesses. Results support query/context boundary diagnostics, without universal superiority, population significance, a prospective transfer rule, or an LLM-specific advantage.

cs.LG↗

arXiv2026

Unconditional Subexponential Arithmetic Circuits for Positive Factorial Multiples

Let $τ(n)$ be the least number of binary additions, subtractions and multiplications required to construct $n$ from $1$ and $2$, with reuse of intermediate values. We show that, for every sufficiently large integer $k$, some positive integer $m$ satisfies \[ τ(mk!)\leq \exp\!\left(O\!\left((\log k)^{2/3}(\log\log k)^{1/3}\right)\right). \] The proof combines unconditional results of Lenstra, Pila and Pomerance on smooth numbers in short intervals and on orders of genus-two Jacobians with a five-parameter family carrying a rational divisor class of infinite order. We encode rational divisor arithmetic, including the tests determining its branches, by a nonzero division-free integer circuit. A common finite sampling space yields circuits whose outputs collectively contain every prime at most $k$, and repeated squaring supplies the required factorial valuations. The circuit bound includes the cost of constructing all integer parameters. This work was carried out with assistance from the UniMath model, developed by UniDT (Shanghai) Co., Ltd., and GPT-6.1 Sol.

math.NT↗

arXiv2026

Ask, Answer, and Detect: Role-Playing LLMs for Personality Detection with Question-Conditioned Mixture-of-Experts

Understanding human personality is important for personalized recommendation and mental health assessment. Existing personality detection methods typically encode social media posts into user representations and predict personality labels. Despite advances in large language models (LLMs), these methods face limited supervision from scarce labels and an unclear mapping between user language and psychological constructs. We propose ROME, a framework that incorporates psychological knowledge into personality detection. Inspired by standardized self-assessment tests, ROME uses LLM role-playing to simulate users' responses to validated psychometric questionnaires. These question-level answers provide interpretable, questionnaire-grounded evidence and intermediate supervision. A question-conditioned Mixture-of-Experts module jointly routes post and question representations to predict questionnaire answers under explicit supervision. The predicted answers are aggregated into an interpretable answer vector and fused with user representations for final personality prediction in a multi-task learning framework. Experiments on two real-world datasets show that ROME outperforms state-of-the-art baselines, with relative improvements of 13.60% on Kaggle and 19.72% on Pandora. Code is available at https://github.com/JasmineLyf/ROME.

cs.CL↗

arXiv2026

Prime-EVC: One-Step Expressive Emotional Voice Conversion via Emotion-Primed Flow Matching

Recent diffusion- and conditional flow matching (CFM)-based emotional voice conversion (EVC) systems achieve strong conversion quality. However, they typically rely on multiple sampling steps, because the conditioning specifies which emotion to impose while its acoustic realization is left to the sampler. In this paper, we propose Prime-EVC, a one-step expressive EVC architecture based on emotion-primed flow matching. Our key idea is to reallocate the emotional conversion between the conditioning and the sampler: a FiLM-fused speaker-emotion style, an emotional variance adaptor, and direct emotion and spectro-temporal supervision assemble an emotion-rich conditioning upstream, rendering the residual conversion left to the CFM decoder attainable within one Euler step. Experiments on the ESD corpus demonstrate that single-step Prime-EVC surpasses five representative EVC systems on every quality metric and exceeds 4- and 100-step DurFlex-EVC in subjective naturalness and emotion while running 3.4--50 times faster than both.

cs.SD↗

arXiv2026

Conditioned in Training, Dispensable at Inference: Typological Conditioning for Multilingual Speech Translation

Multilingual speech translation frontends built on speech large language models typically condition on language identity, as a learned embedding or a prompted language name. Such a signal, however, is learned separately for each language and transfers nothing between typologically related languages. In this paper, we present TypoCast, a frontend that conditions on the typological profile of the source language rather than on its label alone. A typology-informed hierarchical language encoding represents each language by its morphological type, constituent order and family, so that supervision is shared among related languages. A dual-route mixture-of-experts adapter routes inputs through a shared typological route together with a per-language residual, and a typology-aware prompt conveys the same profile to the decoder. Extensive experiments on CVSS-C demonstrate that TypoCast surpasses state-of-the-art speech-to-speech translation systems on French, German and Spanish to English, averaged over the three directions, and outperforms the identity-conditioned S2ST-Omni on every language of a seven-language inventory, with only 228M trainable parameters. Ablation studies further reveal that the conditioning signal acts during training and is dispensable at inference: a model trained without it is consistently worse, whereas removing it from a trained model changes BLEU by less than 0.2, and expert usage is consistent with the signal shaping how adapter capacity is divided among languages.

cs.CL↗

arXiv2026

Turán number of four vertex-disjoint cliques

Given a graph $H$, the Turán number ${\rm ex}(n,H)$ of $H$ is the maximum number of edges of an $n$-vertex simple graph containing no $H$ as a subgraph. Let $kK_p$ denote the disjoint union of $k$ copies of the complete graph $K_p$. In this paper, utilizing the idea of the proof of the Hajnal-Szemerédi Theorem and discharging, we determine the value ${\rm ex}(n,4K_p)$ for all $n$ and $p\ge 3$.

math.CO↗

arXiv2026

AgentWebRec: Compact Evidence Fusion over the Agent Web for Personalized Recommendation

LLM-based personal agents are emerging as persistent carriers of user semantics and intermediaries between users and recommendation platforms, maintaining richer user knowledge locally. As agents interact with one another, the conventional \textit{User--Platform} relation evolves into a \textit{User--Agent Web--Platform} information pathway, enabling distributed user-side information to complement item-side information. This new pathway, however, defies conventional recommendation: evidence is scattered across mutually opaque agents and reachable only through bounded queries, only a small portion of it is relevant to the current recommendation decision, and the responses returned by different agents are semantically heterogeneous. We therefore recast recommendation over the agent web as a \emph{task-time evidence acquisition and fusion} problem under a finite evidence budget by deciding what to ask and what to keep, rather than learning from aggregated data. We propose AgentWebRec, a user-agent-oriented framework that progressively acquires and fuses distributed evidence for each user-item decision while keeping underlying agent memories local. It grounds each decision in platform-provided item semantics and task-relevant evidence from the target user agent's private memory, and conditionally queries neighboring user agents for complementary preference patterns when local evidence is insufficient. Experiments on four InstructRec datasets show that AgentWebRec consistently outperforms baseline recommenders, and ablations verify that the evidence layers contribute complementary gains.

cs.IR↗

arXiv2026

Sage: Formalization with Semantic Correction

While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 formal statements are already provided. Translating informal natural language into a formal language is a critical data bottleneck plagued by an "illusion of rigor": standard type-checkers accept statements that compile but drop hypotheses, introduce vacuous truths, or subtly alter mathematical bounds. To resolve this, we introduce Sage (Semantic Agent-Guided Formalization Engine), an agentic framework that replaces monolithic translation with a four-stage decomposed generation pipeline coupled with a dual-signal semantic correction loop. By pairing Lean 4 compiler diagnostics with multi-dimensional semantic feedback, our correction loop enforces mathematical fidelity alongside syntactic validity. By explicitly accounting for the gap between open-ended queries and declarative formal targets, our pipeline prevents models from achieving high formalization rates by guessing unverified answers (exhibiting a 70.9% answer leakage rate in monolithic baselines). Consequently, Sage suppresses leakage to 2.7% while achieving 73.3% pass@4 joint compilation and semantic fidelity on the Omni-MATH without proofs (compared to 42.0% for a fine-tuned Goedel-Formalizer-V2 baseline). Finally, on IMO-Unformalized, a novel frontier of 175 unformalized International Mathematical Olympiad problems, Sage demonstrates effective zero-shot generalization with 87.4% pass@4 verified fidelity compared to just 19.4% for the baseline, winning over 79% of blind pairwise evaluations.

cs.LG↗

arXiv2026

Error-Aware Reverse Auction Mechanism for Large Language Model Routing

Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We formulate LLM routing as a market-based allocation problem among strategic providers and propose a routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers submit self-predicted acceptance probabilities and execution costs. To account for noisy provider predictions and center evaluations, we introduce the \textit{\textbf{E}rror-\textbf{A}ware \textbf{R}everse \textbf{A}uction \textbf{M}echanism} (EA-RAM), which explicitly models this Dual Error. We prove that, under a private-evaluation-belief structure, truthful effective-surplus reporting is incentive compatible in the reduced-form score space and individually rational under sellers' subjective beliefs, establish sufficient conditions for center rationality, and derive an explicit social-welfare loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps and reduces their maximal local sensitivity. Simulations and real-world benchmarks show that EA-RAM is robust to Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains from provider-side local information, validating its practical effectiveness.

cs.GT↗

arXiv2026

ERSkill: Evolving for Skill-Guided Adaptive Memory Retrieval

While Large Language Model (LLM) agents increasingly rely on long-term memory for persistent interactions, the retrieval mechanisms governing this memory are rarely treated as evolvable components. This static approach limits performance on heterogeneous memory queries, which often demand diverse evidence construction strategies. To address this, we introduce \textbf{ERSkill}, a retrieval-centric framework for evolving, skill-guided memory access. ERSkill compiles interaction histories into a structured memory store and represents retrieval behaviors as executable skills composed of fundamental primitives. At inference time, a trained router dynamically matches each query to a suitable retrieval skill to construct tailored evidence for answer generation. ERSkill co-evolves the skill set and the router during training. It employs an experience trie to efficiently record explored retrieval paths, alongside a double-frontier mechanism that separates oracle-side capability expansion from router-validated deployment. Experiments across multiple agent memory benchmarks demonstrate that ERSkill substantially outperforms strong non-evolving and evolving baselines. Notably, it improves the overall average across F1, BLEU-1, and LLM-judge scores by 31.3\% with Qwen3-Next-80B-A3B-Instruct and by 21.4\% with GPT-5.4-nano.

cs.CL↗

arXiv2026

EmoPose: Vision-Language Model Guided Emotion-Aware Gesture Generation for Humanoid Robots

Socially competent humanoid robots must communicate affect and intent through gesture as well as speech, yet open-ended interaction must become motion that is both expressive and executable on a specific body. This demands semantic flexibility for contextual social intent while preserving deterministic, embodiment-aware robot control. We present EmoPose, a vision-language model (VLM)-guided framework that bridges this gap through an executable semantic interface. Given language, dialogue history, and optional visual context, the VLM selects an ordered gesture plan containing a communicative class, library variant, intensity, and speech anchor. A scalable robot-owned motion library defines the available expressive vocabulary and the source of 14-DoF joint targets. Pose Studio supports automatic trajectory generation, MuJoCo preview, and automatic synchronization of new library entries with the VLM guide; deterministic robot-side modules validate plans, construct trajectories, schedule gestures, and manage queueing and interruption. This division lets the interaction repertoire grow for new social contexts without changing the control interface or delegating raw joint commands to the foundation model. On the EmoPose-Bench, structured GPT-5.5 planning reaches $98.25\pm0.52\%$ on the Easy tier and $76.50\pm0.54\%$ overall, exceeding same-model direct-label prompting. Further tests validate dialogue-context use and ordered multi-action composition. The system completes the nominal MuJoCo suite and realizes all 29 authored variants on the physical Unitree G1. A four-stop laboratory tour demonstrates expressive narration with interruption, camera-grounded dialogue, and navigation.

cs.RO↗

arXiv2026

Dynamics of Weighted Backward Shifts on Cesàro Spaces of Rooted Trees

We study the dynamics of weighted backward shifts on Ces`aro spaces associated with leafless locally finite rooted trees. We first characterize their boundedness in terms of adjacent level cardinalities and edge weights. We then characterize their $\mathcal{F}$-transitivity by a growth condition involving level cardinalities, products of weights along paths, and a level-dependent Ces`aro factor. As consequences, we obtain criteria for hypercyclicity, weak mixing, topological ergodicity, and topological mixing. We also characterize the existence of nonzero orbit limit points and chaotic weighted shifts, the latter in terms of normalized fixed points and unit flows satisfying an explicit summability condition. Examples show that $\mathcal{F}_{\underline{d}>0}$-transitivity need not imply frequent hypercyclicity, that a nonhypercyclic weighted shift may nevertheless have a nonzero orbit limit point, and that topological mixing need not imply chaos.

math.DS↗

arXiv2026

LiteViLNet: Lightweight Vision-LiDAR Fusion Network for Efficient Road Segmentation

Road segmentation is a fundamental perception task for autonomous driving and mobile robotics, where both appearance and geometric cues must be processed under edge-computing constraints. Existing multi-modal approaches often improve accuracy with large encoders or expensive global interaction, which limits their use on embedded platforms. We present \textbf{LiteViLNet}, a lightweight RGB-geometry fusion network that combines a MobileNetV3 RGB encoder with a 0.12M-parameter depth-wise-separable geometry encoder. A multi-scale feature fusion module performs modality-specific enhancement, global-query cross-modal interaction, and adaptive gating, while a depth-wise large-kernel bridge enlarges the contextual support of the deepest representation with low overhead. The resulting U-Net-style decoder uses deep supervision only during training. On the KITTI Road benchmark, the 14.04M-parameter full model obtains $97.23\pm0.15\%$ MaxF. On the held-out ORFD test set under the released OFF-Net evaluation protocol, the full model achieves $96.74\pm0.09\%$ F-score and $93.68\pm0.18\%$ IoU. On a Jetson Orin NX, model-only PyTorch FP16 inference reaches $22.18\pm0.21$ FPS; a separate TensorRT FP16 measurement reaches $68.73\pm0.06$ FPS on the Jetson. Camera-depth adaptations and perception-and-control demonstrations on three heterogeneous robot platforms further illustrate the portability of the dual-stream design.

cs.CV↗

arXiv2026

Compelling evidence of a link between the lags of the quasi-periodic oscillations and the radio jet in the black-hole X-ray binary GRS 1915+105

GRS 1915+105 is one of the most studied black-hole X-ray binaries, known for its extreme variability and rich phenomenology. Previous studies of this source with the Rossi X-ray Timing Explorer reported a transition of the phase-lags of type-C quasi-periodic oscillations (QPOs) from soft, where low-energy photons lag the high-energy ones, when the QPO frequency is higher than ${\sim} 2 ~{\rm Hz}$, to hard when the QPO frequency decreases below ${\sim} 2 ~{\rm Hz}$. The hard-lags of the QPO coincide with episodes of strong radio emission. We analyse NICER observations of GRS 1915+105 obtained between 2018 and 2020, during a period in which the source flux decreased steadily, and perform a detailed spectral-timing study of the detected type-C QPOs. We find a type-C QPO with frequencies in the range of ${\sim} 1.3$-$3.9 ~{\rm Hz}$, which displays soft lags and, contrary to the RXTE observations, shows no evidence of hard phase lags at frequencies below $2~{\rm Hz}$. Quasi-simultaneous AMI-LA radio observations show consistently low radio flux (${\lesssim} 5 ~{\rm mJy}$) during this period. These results appear to show that the hard QPO lags in GRS 1915+105 are linked to the presence of strong radio activity, suggesting that the relativistic jet is responsible for the hard phase lags, supporting a scenario in which QPO phase lags trace changes in coronal geometry and accretion-ejection coupling in GRS 1915+105.

astro-ph.HE↗