arXiv subjects

Bin Liu

Publications and source records attributed to Bin Liu.

At least 19 recordsLinked to original sources

arXiv2026

Pervasive Vulnerability Analysis and Defense for QKD-based Quantum Private Query

Quantum Private Query (QPQ) based on Quantum Key Distribution (QKD) is among the most practically viable quantum communication protocols, with application value second only to QKD itself. However, prevalent security vulnerabilities in the post-processing stages of most existing QKD-based QPQ protocols have been severely overlooked. This study focuses on hidden information extraction under undetermined signal bits, revealing that most such QPQ protocols face severe security threats even without complex quantum resources. Specifically, direct observation attack causes incremental information leakage, while the minimum error discrimination attack efficiently steals additional database inforamtion. To address these critical flaws, the proposed multi-encryption defense scheme is compatible with existing QPQ protocols. The study demonstrates the necessity of the multi-encryption strategy for the security of databases in QPQ, providing key theoretical and technical support for constructing practical QPQ protocols resistant to real-world attacks.

quant-ph↗

arXiv2026

Utility-Aware Generative Recommendation: Utility-Enriched Semantic Codes and Utility-Guided Decoding

Generative recommendation has been widely adopted in large-scale industrial recommendation systems, where multimodal item embeddings are quantized into offline semantic identifiers (SIDs) and items are retrieved by autoregressively generating their SIDs. However, conventional SID construction often underrepresents item utility reflected in post-exposure behaviors such as shares, long views, and video completion, making semantically similar items with different utility insufficiently distinguishable while struggling to accommodate rapidly changing utility signals. Moreover, generation likelihood may be misaligned with downstream utility, causing high-utility candidates to be prematurely pruned during beam search before post-generation reranking or training-time reward alignment can effectively compensate. To address these limitations, we propose UAGR, which aligns both SID construction and decoding with downstream multi-objective utility. Our Utility-Enriched Semantic Codes preserve the original semantic information while incorporating item-level utility without increasing SID length or vocabulary size, supporting incremental utility updates with no additional tokenization or sequence-decoding cost. Meanwhile, our Utility-Guided Decoding estimates candidate utility by combining predictions of multiple post-exposure outcomes and incorporates these estimates into beam scoring, reducing the risk of prematurely pruning high-utility paths while enabling flexible utility control without interfering with generative backbone training. Extensive offline experiments and online A/B tests under real-world traffic demonstrate the effectiveness and deployability of UAGR, which has been fully deployed on Kuaishou and increases video watch time by 0.206\% online.

cs.LG↗

arXiv2026

Scaling Mathematical Proof Supervision from Structured Textbooks

Mathematical supervision for language models is typically flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original sources. We introduce TOME-Math (Textbook-Oriented Mathematical Evidence), a large-scale corpus that converts 2,118 textbooks spanning the core areas of university-level mathematics subjects into approximately 380K structured proof-supervision records while preserving chapter order, proposition-proof links, dependency references, and source provenance. Leveraging these structural signals, we explore curriculum learning across multiple mathematical subjects and characterize scaling patterns with supervision volume and source breadth. At full scale, fine-tuning on TOME-Math raises the unweighted mean score across our held-out evaluations and established public benchmarks by 16.7 percentage points over the base model, while exceeding all three public instruction-data baselines evaluated in aggregate. Our findings highlight structured textbooks as both a scalable source of mathematical supervision and an empirical framework for studying the impact of data organization on mathematical reasoning. We will release the corpus to facilitate further research on structured mathematical supervision.

cs.CL↗

arXiv2026

No evidence for a supermassive black hole binary in GSN 069

Quasi-periodic eruptions (QPEs) are recurrent soft X-ray flares from galactic nuclei and provide a new time-domain probe of stellar-mass objects (SMOs) orbiting supermassive black holes (SMBHs). In an extreme-mass-ratio inspiral (EMRI) system interacting with an accretion disk, QPEs are produced when the SMO repeatedly crosses an accretion disk, so that the eruption times trace the orbital motion of the EMRI. We investigate whether such timing information can be used to probe a more distant SMBH companion. We develop two complementary diagnostics: (1) the motion of the EMRI host SMBH around the SMBH-binary (SMBHB) center of mass induces a light-travel-time modulation in the observed QPE arrival times, specifically an \emph{in-phase} modulation in arrival times of even and odd eruptions; (2) if the QPE source contains a surviving stellar orbiter, the external SMBH must not drive the SMO into tidal disruption through eccentricity excitation by the von Zeipel--Lidov--Kozai (ZLK) mechanism. Using GSN 069 as an example, we find \emph{no} in-phase modulation in the QPE timing (i.e., no evidence for a SMBHB) and constrain the excluded parameter space of the companion SMBH. These results demonstrate that QPE timing and stellar survival offer complementary routes for constraining otherwise hidden SMBH companions in nearby galactic nuclei.

astro-ph.HE↗

arXiv2026

Discovery of an isolated RELHIC Candidate: J1351+0039

We report the discovery of J1351+0039, a new isolated dark galaxy candidate identified through a blind HI survey with the Five-hundred-meter Aperture Spherical radio Telescope (FAST), combined with deep optical imaging from the DESI Legacy Survey. The object displays a compact HI structure with a systemic velocity of V_{LSR} = 429.0 \kms and an inferred HI mass of 4.5*10^5 Msun at a distance of 3.6 Mpc. No optical counterpart is detected in the DESI images, with a g-band surface brightness limit of 28.1 mag arcsec^{-2}, corresponding to a stellar mass limit of M_{star} of 1.2*10^{5} Msun. The dynamical mass is estimated to be M_{dyn} of 1.3*10^{8} Msun, yielding a dark-to-baryonic mass ratio of 200, implying that J1351+0039 is overwhelmingly dominated by dark matter. While weak rotation is detected in J1351+0039, the kinematics are dominated by internal velocity dispersion, confirming pressure support and reminiscent of Reionization-Limited HI Clouds (RELHICs). J1351+0039 stands out as one of the most promising isolated RELHIC candidates, offering a unique laboratory for studying baryonic physics and dark matter in the absence of star formation.

astro-ph.GA↗

arXiv2026

Yuvion VL: A Multimodal Foundation Model for Adversarial Content and AI Safety

General-purpose models often struggle to reliably identify and understand real-world multimodal risks, largely due to the inherent multimodal adversarial nature of content and AI safety. We present Yuvion VL, a family of multimodal large language models purpose-built for content and AI safety, with both instruction-tuned and reasoning-oriented variants. Yuvion VL addresses this gap by treating safety as an inherently adversarial and multimodal problem and designing the entire pipeline around adversarial robustness. For data construction, we develop an automated pipeline integrating adversarial-aware data synthesis with multi-stage quality control, producing large-scale, high-quality multimodal samples augmented with domain knowledge and reasoning annotations. For training, we adopt a three-stage pipeline that includes continued pretraining for risk-concept cross-modal alignment, instruct post-training for production-grade safety tasks, and reasoning post-training for enhanced interpretability and performance in complex tasks. We further introduce Confuse-then-Contrast Fine-Tuning, a contrastive framework that mines model-specific confusions and constructs multi-image contrastive groups to enforce explicit discrimination of fine-grained visual-semantic elements, enabling the model to distinguish between visually similar cases with different safety implications in adversarial safety tasks. To support rigorous evaluation, we further introduce Yuvion VL RiskEval (YVRE), a collection of benchmarks covering diverse open and internal evaluations, with a focus on content and AI safety, adversarial robustness, and real-world capability requirements. Experiments show that Yuvion VL-32B achieves industry-leading safety performance, surpassing comparably sized open-source models and best closed-source commercial models, while maintaining comparable general capabilities.

cs.CV↗

arXiv2026

NEP-kappa 2.0: A unified framework for phonon transport and nonequilibrium thermalization with machine-learning interatomic potentials

We present NEP-kappa 2.0, a unified framework that integrates density-functional theory, material-specific machine-learning interatomic potentials, and pretrained force models for advanced phonon calculations. A common workflow enables harmonic lattice dynamics, quasi-harmonic and stochastic self-consistent phonon treatments, three- and four-phonon transport, Wigner population--coherence transport, and time-dependent phonon dynamics. Applications to 3C-SiC, BAs, and Cs$_2$AgInCl$_6$ demonstrate consistent force-model comparisons, finite-temperature renormalization, higher-order scattering, and intermode coherence. Beyond steady-state transport, mode-resolved simulations of selectively excited 3C-SiC reveal that half of the injected optical-phonon energy reaches acoustic modes within approximately 3.75 ps, primarily through one-optical--two-acoustic scattering. Acoustic branches exhibit response times differing by a factor of five, with competing scattering channels producing a transient energy overshoot. Channel-resolved entropy production and persistent nonthermal occupations distinguish interbranch energy redistribution from intrabranch thermalization. The framework connects equilibrium phonon transport with microscopic nonequilibrium energy dynamics.

cond-mat.mtrl-sci↗

arXiv2026

Atomistic prediction of magnetic behaviour across chemistry, structure and temperature

Controlling magnetic phases and properties through composition and external conditions is central to the development of magnetic materials. Atomistic foundation models offer a route to predicting such behaviour across diverse materials, but magnetic materials remain challenging because their atomic structure and local moments are strongly coupled, while temperature and disorder drive magnetic moments into non-collinear states with evolving orientations and magnitudes. Broadly pretrained atomistic models still sample only limited magnetic diversity, while finite-temperature descriptions of coupled lattice and magnetic fluctuations remain largely material-specific. Here we introduce MagPT, pretrained across 48 elements on 912,492 spin-lattice configurations spanning structural, orientational and longitudinal magnetic fluctuations over 0 $\sim$ 1,000 K and 0 $\sim$ 10 GPa. By treating species, atomic positions and vector moments together, MagPT distinguishes magnetic states that share the same atomic structure but differ in spin configuration and energy. It captures magnetic behaviour across composition, temperature and length scales, from Slater-Pauling-type composition-magnetism relations in transition-metal alloys and finite-temperature phase evolution in elemental ferromagnets and magnetic shape-memory Heusler alloys, to emergent long-wavelength non-collinear spin textures in chiral magnets and local chemistry-magnetism coupling in high-entropy alloys. MagPT moves atomistic studies of magnetic materials beyond material-specific approaches, establishing a general framework for exploring and designing magnetic matter across diverse chemistries and conditions.

cond-mat.mtrl-sci↗

arXiv2026

Post-perihelion dust activity and a candidate icy-grain halo in long-period comet C/2023 A3 (Tsuchinshan--ATLAS)

We analyze the post-perihelion coma of the Great Comet of 2024, C/2023 A3 (Tsuchinshan--ATLAS) to characterize dust activity and assess the contribution of sublimating icy grains to a candidate near-nucleus halo. Using archival Zwicky Transient Facility images from 15 February to 26 May 2025, we performed aperture photometry within a fixed projected radius of 40,000 km and derived azimuthally averaged surface-brightness profiles. The comet faded from 12.86 to 14.77 mag as heliocentric distance increased from 2.64 to 3.90 au, with two short-lived brightenings. The effective dust cross section decreased by a factor of 2.4, following $C_{\rm e}\propto r_{\rm h}^{-3.1}$, while the dust mass production rate scaled as $\dot{M}_{\rm d}\propto r_{\rm h}^{-3.41}$, consistent with a contribution from water-ice-driven activity. Extrapolating the fitted relation to perihelion implies a model-dependent cumulative dust mass loss of $3.0\times10^{11}$ kg, equivalent to a globally averaged erosion depth of $\sim1.4$ m for an assumed nucleus radius of 5.9 km. Coma profiles were shallower than the canonical steady-state expectation, suggesting radial changes in dust distribution or scattering properties, possibly due to delayed aggregate fragmentation. A persistent central brightness excess, coincident with less-red inner-coma colors, is consistent with an icy-grain halo. Among the models explored, icy grains of radius $\sim10~μ$m with carbon fraction $\sim0.1\%$ yield halo radii comparable to those observed during enhanced activity on 21--25 February 2025, with grain lifetimes of $2.8\times10^5$--$3.2\times10^5$ s. No single fixed grain size and composition reproduces the full halo evolution; an increasing carbon fraction could explain the broad halo-radius trend, possibly reflecting progressive refractory enrichment of near-surface material.

astro-ph.EP↗

arXiv2026

Dust Activity Evolution and Constraints on Icy Grains in the Interstellar Comet 3I/ATLAS

We present Zwicky Transient Facility observations of the interstellar comet 3I/ATLAS to characterize its dust-activity evolution before and after perihelion. Before perihelion, the effective scattering cross section $C_{\rm e}$ brightened across the inner $2\times10^4$ km as $C_{\rm e}\propto r_{\rm H}^{-γ}$, with $γ$ increasing from $1.63\pm0.14$ to $1.88\pm0.34$ with aperture size. After perihelion, the heliocentric index decreased from $2.44\pm0.09$ in the $5\times10^3$ km aperture to $1.54\pm0.09$ in the $8\times10^4$ km aperture, indicating faster fading of the inner coma. Under adopted grain-size and residence-time assumptions, the implied dust mass-loss rates are $\sim123$--$203~{\rm kg~s^{-1}}$ before perihelion and $\sim596$--$1412~{\rm kg~s^{-1}}$ after perihelion. The morphology yields a sunward ejection-speed scale of $v_{\rm ej}\sim(190\pm3)a_{μ{\rm m}}^{-1/2}~{\rm m~s^{-1}}$ and an effective perpendicular velocity of $v_\perp=(79\pm6)a_{μ{\rm m}}^{-1/2}~{\rm m~s^{-1}}$. Post-perihelion surface-brightness profiles transiently steepened to $k\sim-2.7$ in late November and early December, then became shallower and approached $k=-1.5$ by January. Matched $g-r$ profiles show that this phase coincided with an anomalously blue outer coma that disappeared by January. We characterize the fading component with a projected destruction length of $\ell_{\rm DE}\sim(6.4$--$7.2)\times10^4$ km. Thermophysical sublimation calculations indicate that this scale, together with the order of magnitude of the water production near the main imaging epoch, is consistent with $a_0\sim5$--$10~μ{\rm m}$ icy grains containing a small absorbing carbonaceous fraction of $f_{\rm C}\sim0.1\%$. These results suggest that the early post-perihelion coma likely contained a short-lived, volatile-bearing icy-grain component whose fading contributed to the outer-coma brightness and color evolution

astro-ph.EP↗

arXiv2026

Global well-posedness of the energy-critical nonlinear Schrödinger equation on the three-dimensional torus with additive Lévy noise

This paper establishes global well-posedness for the defocusing energy-critical nonlinear Schrödinger equation on the three-dimensional torus with a class of additive Lévy noises. For arbitrary deterministic initial data in the energy space, we construct probabilistically strong solutions that are pathwise unique in the critical solution class. Continuous dependence on initial data, convergence of finite-activity approximations, and a vanishing-noise limit hold on finite time intervals. When the effective noise is nonzero, quantitative bounds for mass exit times imply almost-sure unboundedness of the mass and exclude free scattering. The expected energy then admits a cubic lower bound in time. The analysis couples pathwise critical perturbation theory with energy estimates adapted to Poisson compensation and stopping-time arguments based on the exact mass balance.

math.AP↗

arXiv2026

Black Hole Binary Mergers in Galactic Nuclei: Combined Effects of Secular Dynamics and Stellar Flybys

Galactic nuclei, with the central supermassive black holes (SMBHs) and surrounding dense star clusters, serve as natural laboratories for studying gravitational dynamics in extreme gravitational environments. In this work, we model the long term evolution of black hole binaries (BHBs) in these environments by incorporating the tidal influence of the central SMBH, the potential of the nuclear star cluster, SMBH induced relativistic precession, and stochastic perturbations from stellar flybys. Our numerical simulations show that the long term evolution of BHBs is predominantly governed by the SMBH-driven ZLK mechanism. However, once stellar flybys are included, they can modify both the binary angular momentum and energy. The cumulative effect of repeated flyby encounters substantially reshapes the long term dynamical evolution, eventually leading systems toward either merger or disruption. Based on a population synthesis study, we find that this combined secular and non-secular channel produces a merger rate of approximately $\mathcal{R}\simeq16\mathrm{Gpc^{-3}yr^{-1}}$, which is significantly higher than the rates predicted by dynamical channels that neglect stellar flybys. Furthermore, we predict that a non-negligible fraction of merging systems would retain detectable eccentricities at low frequencies around 5 Hz, thus providing a distinctive observational signature for next generation ground based GW detectors. Our results demonstrate that the stochastic perturbations from the surrounding environment are essential for modeling BHB evolution in galactic nuclei, and that this channel may contribute a major fraction of observed mergers.

astro-ph.HE↗

arXiv2026

The PSR J0435+3233 Triple System

The detailed evolution of triple star systems is complicated and poorly known. Using archived optical/infrared and $γ$-ray data, we identified the pulsar PSR~J0435+3233 as a $γ$-ray pulsar in a hierarchical triple system, with a helium white dwarf (WD) as a close inner binary companion and a Sun-like star as the distant tertiary. PSR~J0435+3233 and the WD companion are in a circular orbit with a period of $P_{\rm orb1} = 8.0$~days and an eccentricity of $e=0.00016$. The tertiary is a G-type subgiant with a mass of $0.98(12) M_\odot$ at a distance of $2.1(4)$ kpc from the Earth. By simultaneously fitting the observed spin-period variations of the $γ$-ray emission (over 16.7 years) and radio emission (over 4.9 years) from PSR~J0435+3233, the changes in the inner orbital parameters, the Shapiro delay, Gaia astrometry, and the outer companion mass, we determined the outer elliptical orbit for the tertiary, with a period $P_{\rm orb2} = 73.5$~yrs and an eccentricity $e_2 = 0.598$. The outer orbit is either nearly perpendicular to the inner orbit with a mutual inclination of $\sim 85^\circ$, or moderately inclined by $\sim 54^\circ$. For the former geometry, the pulsar, the WD, and the tertiary star have masses of $1.16(5) M_\odot$, $0.273(8) M_\odot$, and $0.91(5) M_\odot$, respectively; for the latter geometry, the corresponding masses are $1.34(15) M_\odot$, $0.305(23) M_\odot$, and $1.13(7) M_\odot$. This is a unique triple system for detailed multi-band observations and for studying the evolutionary path and dynamic processes of a primordial triple star system. It will ultimately evolve into a system consisting of a neutron star and two white dwarfs.

astro-ph.HE↗

arXiv2026

ProxyEraseAgent: Blind Watermark Removal in the Wild

Invisible image watermark removal has received growing attention. Despite substantial progress, existing attacks face a tension between practicality and specificity. Attacks exploiting detector outputs, decoder responses, or paired images can be tailored to the watermark decision boundary, but require information rarely available in realistic scenarios. Conversely, attacks based on compression, geometric distortion, or reconstruction are easily deployed from a single watermarked image, but remain largely open-loop: they apply generic transformations without knowing if the image is moving toward watermark failure. Thus, the key challenge in single-image blind watermark removal is not merely how to transform the image, but how to obtain a useful removal direction without accessing the hidden decoder. To bridge this gap, we propose ProxyEraseAgent, an agent-driven framework recovering attack specificity through proxy decoder responses. Publicly available watermarking schemes provide a natural knowledge base of candidate decoders, where some are informative for a given unknown image. Our insight is that a decoder producing a strong calibrated response to the query image likely shares a nearby decoding boundary with the hidden target mechanism. ProxyEraseAgent ranks these decoders by calibrated response strength and uses the top ones as proxy boundary estimators. Their responses then guide a progressive search over heterogeneous removal operations (e.g., geometric distortion, JPEG compression, image reconstruction, and gradient perturbation) under perceptual-quality constraints. Experiments across 11 watermarking systems show ProxyEraseAgent achieves a 94.8% attack success rate, demonstrating the effectiveness of response-guided proxy retrieval and feedback-driven sequential planning for blind watermark removal.

cs.CR↗

arXiv2026

Conditional Accuracy Profiles: Diagnosing LLM Judges across Deployment Conditions

LLM-as-judge is now a standard tool for scalable evaluation, but judge performance is still often summarized by a single accuracy number. This aggregate view hides the deployment conditions under which a judge succeeds or fails. We introduce \textbf{Conditional Accuracy Profiling} (CAP), a post-hoc diagnostic framework that decomposes pairwise LLM-judge accuracy into eight conditions organized into content sensitivity, robustness, and rationale quality. CAP is benchmark-agnostic: it can be applied directly when a benchmark provides the required annotations, approximately through task-subset proxies, or through controlled augmentation when perturbation pairs can be generated. We instantiate CAP on seven LLM judges across six pairwise judging benchmarks, including \textsc{judgerEva-Standard}, a controlled testbed we created to support all eight conditions. CAP exposes profile differences hidden by aggregate accuracy: on \textsc{judgerEva}'s judge-independent Hard-Constructed subset, the two judges most sensitive to omitted qualifications rank in the bottom three of seven by overall accuracy, so omission sensitivity is not predicted by aggregate accuracy. Across benchmarks, Position Robustness shows the strongest rank stability (mean Spearman $\barρ{=}0.87$) but is itself fragile under JudgeBench-Pro adversarial stress, showing the largest mean accuracy drop among the shared conditions, though the dominant degradation channel varies by judge. Condition-level profiles provide a more actionable basis than aggregate accuracy for selecting LLM judges.

cs.LG↗

arXiv2026

When Is Enough Enough in Self-Evolving LLM Systems?

Self-evolving large language model (LLM) systems repeatedly propose, evaluate, and incorporate updates to prompts, skills, or other persistent artifacts. Despite their growing effectiveness, these systems typically operate under a predetermined iteration or compute budget, without a principled criterion to determine when further evolution is no longer worthwhile. This can lead to two undesirable consequences: unnecessary computation after performance has saturated and the risk of returning late updates that overfit or exploit the evaluation signal. These issues motivate us to study two fundamental questions: when should a self-evolving system stop, and what should it output once it stops? We address the first by formulating an online sequential testing problem and constructing an anytime-valid restart detector using the per-item paired evaluation outcomes already produced by self-evolving LLM systems. We address the second by formulating a change-point estimation problem and using the estimated transition to select an earlier artifact for output. The resulting procedure is plug-and-play and requires no modification of the underlying self-evolving algorithms. Across two self-evolving frameworks, three LLM model families, and five benchmarks, our method substantially reduces computation costs while maintaining comparable unseen-test performance. For example, on SearchQA with SkillOpt and DeepSeek V4 Flash, our method stops at round 4 rather than the full budget of 40, reducing token usage by 91.6% while achieving 82.43% unseen-test accuracy versus 82.00% under the full-budget run.

cs.AI↗

arXiv2026

Well-posedness of the Stochastic Landau--Lifshitz--Baryakhtar Equation in $\mathbb{R}^d$

This paper studies the Cauchy problem for the stochastic Landau--Lifshitz--Baryakhtar equation on $\mathbb{R}^d$, $d=1,2,3$, subject to Stratonovich Gaussian perturbations. We establish a low-regularity well-posedness theory for initial data in $\mathbb{L}^2$, $\mathbb{H}^1$, and $\mathbb{H}^2$. For $\mathbb{L}^2$ initial data, we prove the existence and pathwise uniqueness of global very weak solutions in dimensions one and two, while in dimension three we construct martingale very weak solutions on every finite time interval. For arbitrary $\mathbb{H}^1$ initial data, we prove the existence and uniqueness of global pathwise weak solutions in all dimensions $d\leq3$. Furthermore, for $\mathbb{H}^2$ initial data, we establish the existence and uniqueness of global pathwise strong solutions in the same range of dimensions. The analysis is based on a frequency-truncation approximation scheme combined with stochastic compactness arguments in the whole-space setting. The key step in global continuation is to justify the stochastic effective-field balance at $\mathbb{H}^1$ regularity, where the drift is available only in a negative Sobolev space. Spatial mollification and passage to the limit yield the energy identity for local weak solutions. A coercive modification then gives global energy moments and excludes finite-time blow-up.

math.AP↗

arXiv2026

SymbolicLM: Training Language Models as Symbolic Regressors

Large Language Models (LLMs) have shown promising capabilities in scientific reasoning, yet scientific discovery ultimately requires deriving precise laws directly from observational data, known as Symbolic Regression (SR). This poses a challenge for LLMs due to the gap between probabilistic text generation and the exact structural requirements of SR. Existing approaches rely on complex external scaffolds, which are computationally expensive and separate symbolic reasoning from the model itself. To address this limitation, we propose to directly equip LLMs with symbolic regression capabilities through dedicated numerical-symbolic and physical supervision. We introduce PhysSymbArena, a large-scale benchmark containing over 160,000 equations and 1.8B tokens of numerical-symbolic data with physical descriptions, enabling systematic training and evaluation. Based on PhysSymbArena, we develop SymbolicLM, which enhances the symbolic regression ability of LLMs through mathematical and physical supervision. During inference, we further introduce SymbolicSGA, a refinement framework that leverages quantitative feedback to iteratively improve generated equations. Experiments on multiple symbolic regression benchmarks show that SymbolicLM substantially improves structural recovery while maintaining competitive numerical fitting performance. These results demonstrate that symbolic regression can be explicitly learned as an intrinsic capability of LLMs.

cs.CE↗