arXiv subjects

Guang Lin

Publications and source records attributed to Guang Lin.

At least 37 records · Page 2Linked to original sources

arXiv2026

A Hyperbolic Neural Closure for M1 Radiation Transfer

In radiation transfer simulations, an M1 method achieves substantial computational savings by replacing the full angular transport equation with a low-order moment system. Because this reduced system is not closed, a closure model is required to represent the unknown higher-order moments using lower-order moments. While machine learning (ML)-based closures can improve accuracy beyond classical analytic closures, unconstrained learned closures may produce non-real characteristic speeds and consequently cause numerical solver breakdown. To guarantee real eigenvalues of the Jacobian associated with ML closures, we propose a hyperbolic neural closure for the M1 radiative transfer system. Rather than directly predicting closure terms, we parameterize the Jacobian through two neural networks: (i) a symmetric matrix network and (ii) a strictly convex entropy network whose Hessian defines a positive definite symmetrizer. These components are combined to yield a Jacobian that is similar to a symmetric matrix, thereby ensuring real eigenvalues. The closure is then reconstructed by numerical integration of the learned Jacobian field along a prescribed integration path. Numerical experiments show that the proposed closure not only achieves higher closure accuracy than classical analytic closures, but also improves solution accuracy and remains stable in discontinuous Galerkin simulations for radiative transfer problems.

cs.LG↗

arXiv2026

A Fast-Convergence Resolution of the Stochastic Eigenproblem Using Halley's Method and the Spectral-Chaos Approach

Solving stochastic eigenvalue problems has long been essential for informed decision-making, advancing scientific knowledge, and ensuring the reliability of engineering designs and applications. This paper underscores the need to continue enhancing existing numerical methods for solving the stochastic eigenproblem in order to improve convergence rates, computational efficiency, and robustness. Specifically, we propose a novel spectral-chaos method for solving the stochastic (linear) eigenvalue problem, employing Halley's method as the root-finding algorithm to leverage its cubic convergence properties. Our method achieves maximal convergence in solving stochastic eigenvalue problems since its rate cannot be further improved using a higher-order Householder method due to the quadratic nature of the resulting system of equations. Additionally, due to the complexity of the resulting system of equations, a tensorial approach was developed to tackle the challenges associated with the dimensional multiplicity of the stochastic eigenvalue problem, without which the solution would have been intractable. The method is derived rigorously, with a detailed error analysis that highlights the benefit of using our approach when the eigenvector components are nearly known, the computational cost of the method is also rigorously presented, and an illustrative example is provided to demonstrate the implementation of the method. Subsequently, a case study is demoed to analyze the results and validate the advantages of using Halley's method over Newton's method and Monte Carlo simulations.

math.NA↗

arXiv2026

Generalized Discrete Diffusion with Self-Correction

Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such approaches often suffer from limited generalization and may impair reasoning performance. GIDD pioneers pretraining-based self-correction via a multi-step BERT-style uniform-absorbing objective. However, GIDD relies on a continuous interpolation-based pipeline with opaque interactions between uniform transitions and absorbing masks, which complicates hyperparameter tuning and hinders practical performance. In this work, we propose a Self-Correcting Discrete Diffusion (SCDD) model to reformulate pretrained self-correction with explicit state transitions and learn directly in discrete time. Our framework also simplifies the training noise schedule, eliminates a redundant remasking step, and relies exclusively on uniform transitions to learn self-correction. Experiments at the GPT-2 scale demonstrate that our method enables more efficient parallel decoding while preserving generation quality.

cs.LG↗

arXiv2026

On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

This paper develops an Operator Learning framework for approximating the dynamic response of synchronous generators. The framework can be used to (i) build a neural network-based generator model that interacts with a power grid simulator or (ii) shadow the true generator's transient response. First, we develop a data-driven Deep Operator Network (DeepONet) to approximate the infinite-dimensional solution operator of the generators. Then, we design a numerical scheme based on DeepONet that simulates the generator's response over a given time horizon. The proposed scheme recursively employs the trained DeepONet to simulate the response for a given multi-dimensional input that describes the interaction between the generator and the power grid. In addition, we design a residual DeepONet numerical scheme that can incorporate information from existing mathematical models. We accompany this residual DeepONet scheme with an estimate for the prediction's cumulative error. Finally, we build a data aggregation (DAgger) strategy that allows fine-tuning of DeepONets using aggregated training data that the DeepONets will likely encounter during interactive simulations with other grid components. As a proof of concept, we demonstrate that the proposed frameworks can effectively approximate the transient model of a synchronous generator.

cs.LG↗

arXiv2026

Spectral Anatomy of Quantum Gaussian Process Kernels

Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy $S(K)/\log n$ of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom $d_σ(K)$, and a characterization of the \emph{target-dependent} optimal entropy via the intrinsic dimension of the target in the kernel eigenbasis. Empirically, the diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP \emph{and} RBF/Matérn/RFF/deep-kernel families all collapse onto identical $S/\log n$ curves on dequantization, ECE, and variance-contraction panels. The NLL sweet spot lives at high entropy for smooth targets and at low entropy for band-limited quantum-data targets. The diagnostic transfers from simulator to IBM Heron hardware with median absolute error $3.2\%$ and mean $5.2\%$ in $S/\log n$ across $24$ configurations at $n_q = 4$, with matchgate and IQP within $5\%$ mean and a single HE configuration returning a $30\%$ outlier that drops to $0.5\%$ on rerun (attributed to calibration drift); the same diagnostic transfers to a second Heron backend (mean error $2.7\%$) and to a $n_q = 6$ scale-up on the original backend (mean error $1.7\%$). No error mitigation is applied throughout.

cs.LG↗

arXiv2026

Fine-Tuning Diffusion Models for Molecular Generation via Reinforcement Learning and Fast Sampling

Generating molecules that simultaneously satisfy drug-like properties and conform to the 3D structure of a target protein is a core challenge in structure-based drug design (SBDD). Existing generative approaches, however, often rely on costly post-hoc processing during Sampling or require carefully curated datasets during training, yet still achieve modest gains. These limitations are especially pronounced in multi-objective settings, where balancing conflicting criteria remains a core challenge. To address these challenges, We propose FTDiff, a reinforcement learning fine-tuning framework tailored for diffusion-based molecular generation under structural constraints. To ensure stable and sample-efficient optimization, FTDiff adopts a group relative policy optimization (GRPO) style strategy. Furthermore, FTDiff builds upon a time-free pretrained diffusion model and incorporates a fast sampling mechanism that reduces the number of denoising steps, significantly accelerating both training and inference while maintaining generation quality. By optimizing a fixed threshold-aware reward, FTDiff effectively guides the model to produce valid, diverse, and high- quality molecules that balance multiple drug design objectives. Extensive experiments on benchmark datasets demonstrate that FTDiff consistently outperforms prior methods, without requiring expensive post-hoc optimization or intricate data engineering.

cs.LG↗

arXiv2026

Spurious Correlation Learning in Preference Optimization: Mechanisms, Consequences, and Mitigation via Tie Training

Preference learning methods like Direct Preference Optimization (DPO) are known to induce reliance on spurious correlations, leading to sycophancy and length bias in today's language models and potentially severe goal misgeneralization in future systems. In this work, we provide a unified theoretical analysis of this phenomenon, characterizing the mechanisms of spurious learning, its consequences on deployment, and a provable mitigation strategy. Focusing on log-linear policies, we show that standard preference-learning objectives induce reliance on spurious features at the population level through two channels: mean spurious bias and causal-spurious correlation leakage. We then show that this reliance creates an irreducible vulnerability to distribution shift: more data from the same training distribution fails to reduce the model's dependence on spurious features. To address this, we propose tie training, a data augmentation strategy using ties (equal-utility preference pairs) to introduce data-driven regularization. We demonstrate that this approach selectively reduces spurious learning without degrading causal learning. Finally, we validate our theory on log-linear models and provide empirical evidence that both the spurious learning mechanisms and the benefits of tie training persist for neural networks and large language models.

cs.LG↗

arXiv2026

Diff-Instruct with Diffused Reward: Towards Principled One-step Generator RL

Recent advances in one-step text-to-image generation have enabled real-time synthesis with remarkable efficiency and quality. Previous reinforcement learning methods for one-step generators combine image-space reward optimization with diffusion noisy-space distribution matching. This paradigm brings challenges due to a mismatch between terminal reward optimization and the underlying generative dynamics. As a result, optimization tends to exploit stochastic degrees of freedom, often improving reward at the expense of image fidelity. To address this issue, we propose Diff-Instruct with Diffused Reward (DIDR), a data-free trajectory-level alignment framework derived from Integral KL minimization. DIDR propagates the RLHF-optimal reward-tilted clean-image distribution across all noise levels along the diffusion trajectory. We show that this objective admits the same minimizer as clean-image RLHF, while naturally inducing the Diffused Reward Score (DRS), which acts as a reward-driven correction to the reference score function. To make this practical, we further introduce the Diffused Reward Proxy (DRP), an efficient estimator of DRS based on differentiable short-step denoising. Extensive experiments demonstrate that DIDR consistently Pareto-dominates existing one-step SDXL baselines. Moreover, when transferred to a 6B DiT backbone (Z-Image), DIDR surpasses its 50-step teacher in preference alignment while requiring only a single generation step.

cs.CV↗

arXiv2026

ATLAS: A Multi-LLM Training Framework for EvoDPO with Adaptive Reference Evolution

Recent multi-LLM agent systems have shown promising capabilities for automated problem-solving, yet they predominantly rely on frozen agents or static fine-tuning pipelines. To address this limitation, our primary contribution is ATLAS (Adaptive Task-distributed Learning for Agentic Self-evolution), a multi-agent framework where specialized meta-agents collaboratively train and refine an active agent toward a domain-specific policy. A core challenge in iterative preference learning within these pipelines is the reliance on fixed reference models, which typically leads to overly conservative updates or training stagnation. To overcome this, the framework's algorithmic engine utilizes Evolving Direct Preference Optimization (EvoDPO). EvoDPO employs an inspection agent to perform adaptive, proxy-KL gated reference policy updates based on continuous training telemetry. We evaluate this full framework across a diverse set of challenging environments-including non-stationary contextual bandits, partial differential equations (PINNs), and combinatorial optimization tasks (TSP, Bin Packing). Through comparison against fixed-reference, adaptive-reference, and external automated-discovery baselines, our results suggest that ATLAS combines supporter-driven exploration with EvoDPO-driven stability to improve long-horizon evaluator-driven self-improvement.

cs.AI↗

arXiv2026

fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations

In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy for the Caputo fractional derivative of order $β\in (1,2)$. Building upon this foundation, we propose the fPINN-DeepONet framework, a novel approach that integrates operator learning with the $L_2$ approximation to efficiently solve fractional partial differential equations (FPDEs). Our framework is successfully applied to both fixed and variable fractional-order PDEs, demonstrating the framework's versatility and broad applicability. To evaluate the performance of the proposed model, we conduct a series of numerical experiments that involve dynamically varying fractional orders in both space and time, as well as scenarios with noisy data. These results highlight the accuracy, robustness, and efficiency of the fPINN-DeepONet framework.

math.NA↗

arXiv2026

Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning

A central challenge in continual learning for large language models (LLMs) is catastrophic forgetting, where adapting to new tasks can substantially degrade performance on previously learned ones. Existing projection-based methods mitigate such interference by restricting parameter updates to subspaces that are orthogonal to directions associated with past tasks. However, these methods are typically formulated under Euclidean parameter geometry, with update magnitudes and projections governed by the Frobenius norm. The recent empirical success of the Muon optimizer, which applies orthogonalized matrix updates and admits a spectral-norm interpretation, suggests that Frobenius geometry may not be the most effective choice for matrix-valued LLM parameters. Motivated by this observation, we propose Muon-OGD, a spectral-norm-aware continual learning framework that integrates Muon-style operator-norm geometry with orthogonal projection constraints. Our method formulates each update as a spectral-norm-constrained optimization problem with linear non-interference constraints, and solves it efficiently through dual iterations and Newton--Schulz matrix-sign approximations. By applying orthogonalized momentum updates that avoid protected directions associated with prior tasks, Muon-OGD aims to improve the stability--plasticity trade-off in sequential LLM adaptation. We evaluate the proposed method on standard continual learning benchmarks, TRACE, and domain-specific Coding--Math--Medical curricula using both encoder--decoder and decoder-only architectures. Empirically, Muon-OGD consistently improves over sequential fine-tuning and competitive orthogonal-gradient baselines, while remaining computationally scalable. These results suggest that spectral-norm-aware update geometry provides a practical and effective alternative to Frobenius-norm projection for continual learning in LLMs.

cs.LG↗

arXiv2026

f-GRPO and Beyond: Divergence-Based Reinforcement Learning Algorithms for General LLM Alignment

Recent work shows that preference alignment objectives can be interpreted as divergence estimators between aligned (preferred) & unaligned (less-preferred) distributions, yielding a principled recipe for designing alignment losses. However, this view has so far been limited to preference-based supervision. We extend it to general LLM alignment, including reinforcement learning with verifiable rewards (RLVR), where alignment feedback is given only as scalar rewards. We introduce $f$-Group Relative Policy Optimization ($f$-GRPO), a class of on-policy RL objectives, and $f$-Hybrid Alignment Loss ($f$-HAL), which combines on-policy reward optimization with off-policy preference supervision. We show that these objectives estimate $f$-divergences between reward-aligned & reward-unaligned distributions induced by above- & below-average reward responses, and prove expected reward improvement after alignment. Empirically, $f$-GRPO improves over GRPO on math-reasoning RLVR tasks, while hybrid $f$-HAL mitigates reward hacking in on-policy safety alignment when verifiable rewards are unavailable and learned reward models must be used.

cs.LG↗

arXiv2026

AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training

Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs), but standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights. This often leads to ill-conditioning, sensitivity to loss weights, and poor constraint satisfaction. In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP). The key idea is to view the constraint residuals as the output of a controlled dynamical system and to compute the Lagrange multiplier as a feedback input that locally drives these residuals toward stable linear contraction dynamics. AdamFLIP then applies Adam-style first- and second-moment adaptation to the resulting feedback-linearized Lagrangian gradient, combining principled constraint handling with the scalability and robustness of adaptive neural-network optimization. We test AdamFLIP on a range of benchmark forward and inverse PDE problem, and it consistently outperforms both the standard soft-constrained PINN and state-of-the-art constrained optimizers. Specifically, on the Navier--Stokes equations benchmark, AdamFLIP \textbf{reduces relative $L_2$ error by more than two thirds} for the predicted solution compared to the next best method. Our AdamFLIP framework provides an effective and computationally scalable hard constraint optimization method for PINN training.

cs.LG↗

arXiv2026

Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systems

Neural surrogates for stiff differential-algebraic equations (DAEs) face two barriers: soft-constraint methods leave algebraic residuals that stiffness amplifies into errors, and hard-constraint methods require trajectory data from stiff integrators. We introduce an extended Newton implicit layer that enforces algebraic constraints exactly and reduces fast dynamics to their quasi-steady-state values in a single differentiable solve. Embedded in a physics-informed DeepONet, the layer recovers all fast and algebraic states exactly from slow-state predictions, removes the per-window stiffness-amplification pathway, and yields a stiffness-scaled Implicit Function Theorem gradient absent from penalty methods. Cascaded implicit layers extend this to multi-component systems with provable convergence. On a grid-forming inverter (stiffness ratio of about 4712), extended Newton attains 1.42% error versus 39.3% (penalty) and 57.0% (standard Newton); augmented Lagrangian and feedback linearization diverged. Two independently trained models compose without retraining (0.72% to 1.16% error, exact constraint satisfaction). Cross-domain validation on the Robertson stiff DAE (stiffness ratio up to $10^5$) confirms generalization. Conformal prediction provides 90% coverage with automatic out-of-distribution detection.

cs.LG↗

arXiv2026

Generative Prior-Guided Neural Interface Reconstruction for 3D Electrical Impedance Tomography

Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization struggles with topological changes and regularization tuning, while emerging deep learning approaches often compromise physical fidelity or require prohibitive amounts of paired training data. We present a transformative ``solver-in-the-loop'' framework that bridges this divide by coupling a pre-trained 3D generative prior with a rigorous boundary integral equation (BIE) solver. Unlike Physics-Informed Neural Networks (PINNs) that treat physics as soft constraints, our architecture enforces the governing elliptic PDE as a hard constraint at every optimization step, ensuring strict physical consistency. Simultaneously, we navigate a compact latent manifold of plausible geometries learned by a differentiable neural shape representation, effectively regularizing the ill-posed problem through data-driven priors rather than heuristic smoothing. By propagating adjoint shape derivatives directly through the neural decoder, we achieve fast, stable convergence with dramatically reduced degrees of freedom. Extensive experiments on 3D high-contrast EIT demonstrate that this principled hybrid approach yields superior geometric accuracy and data efficiency which is difficult to achieve using traditional methods, establishing a robust new paradigm for physics-constrained geometric discovery.

math.NA↗

arXiv2026

DiLO: Decoupling Generative Priors and Neural Operators via Diffusion Latent Optimization for Inverse Problems

Diffusion models have emerged as powerful generative priors for solving PDE-constrained inverse problems. Compared to end-to-end approaches relying on massive paired datasets, explicitly decoupling the prior distribution of physical parameters from the forward physical model, a paradigm often formalized as Plug-and-Play (PnP) priors, offers enhanced flexibility and generalization. To accelerate inference within such decoupled frameworks, fast neural operators are employed as surrogate solvers. However, directly integrating them into standard diffusion sampling introduces a critical bottleneck: evaluating neural surrogates on partially denoised, non-physical intermediate states forces them into out-of-distribution (OOD) regimes. To eliminate this, the physical surrogate must be evaluated exclusively on the fully denoised parameter, a principle we formalize as the Manifold Consistency Requirement. To satisfy this requirement, we present Diffusion Latent Optimization (DiLO), which transforms the stochastic sampling process into a deterministic latent trajectory, enabling stable backpropagation of measurement gradients to the initial latent state. By keeping the trajectory on the physical manifold, it ensures physically valid updates and improves reconstruction accuracy. We provide theoretical guarantees for the convergence of this optimization trajectory. Extensive experiments across Electrical Impedance Tomography, Inverse Scattering, and Inverse Navier-Stokes problems demonstrate DiLO's accuracy, efficiency, and robustness to noise.

math.NA↗

arXiv2026

BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems

Traditional methods for system discovery frequently struggle with efficient data usage and uncertainty quantification. Identifying the governing equations of complex dynamical systems from data presents a significant challenge in scientific discovery, especially when high-quality measurements are scarce and expensive to obtain. To overcome these limitations, we propose Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems (BLADE), a novel Bayesian framework that combines replica-exchange stochastic gradient Langevin Monte Carlo with active learning. By balancing gradient-driven exploration and exploitation in coefficient space, BLADE provides probabilistic parameter estimation and principled uncertainty quantification. Faced with data scarcity, the probabilistic foundation of BLADE further facilitates the integration of active learning through a hybrid acquisition strategy that combines predictive uncertainty with space-filling design, enabling efficient selection of informative samples. Across benchmark systems, BLADE reduces measurement requirements by roughly 60% for Lotka-Volterra and 40% for Burgers' equation relative to random sampling, demonstrating substantial data-efficiency gains. These results highlight BLADE as a general uncertainty-aware framework for discovering interpretable dynamical systems, particularly valuable when high-fidelity data acquisition is prohibitively expensive.

stat.ML↗

arXiv2026

Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation

Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.

cs.LG↗